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[Display omitted] Processing of electrode slurry, which is highly non-Newtonian fluid, is a critical step in the mass production of lithium-ion batteries (LIBs). While extensional flow plays an important role in the electrode slurry processes such as coating, most previous studies have focused only on the shear rheology, due to the lack of a reliable method to measure the extensional rheological properties of the slurry. Here, it is demonstrated that the extensional rheological properties of the anode slurries can be successfully characterized using the stop-flow-dripping-onto-substrate/capillary break-up rheometry (SF-DoS/CaBER). Using this system, it is observed that the extensional rheology of the anode slurry is significantly affected by the blend ratio of the natural and synthetic graphite, as well as the binder and conductive concentrations. Furthermore, the shear rheology-based model predicts much shorter pinch-off times than those measured experimentally, indicating that the yield-stress of the anode slurry is much larger in extensional flow than in shear flow. [ABSTRACT FROM AUTHOR]

[Display omitted] Achieving rapid capillary wetting is highly desirable in nature and industries. Previous endeavors have primarily concentrated on passive wetting strategies through surface engineering. However, these approaches are inadequate for high-viscosity fluids due to the significant viscous resistance, especially for non-Newtonian fluids. In contrast, forced wetting emerges as a promising method to address the challenges associated with achieving rapid wetting of non-Newtonian fluids in capillaries. To investigate the forced wetting behavior of viscoelastic fluids in capillaries, we employ Xanthan Gum (XG) aqueous solutions as target fluids with the storage modulus significantly exceeding the loss modulus. We utilize smooth glass capillaries connected to a syringe pump to achieve high moving speeds of up to 1 m/s. Our experiments reveal a significant distinction in the power-law exponent that governs the scaling relationship between the dynamic contact angle and velocity for viscoelastic fluids compared to Newtonian fluids. This exponent is considerably smaller and varies based on the concentration of viscoelastic fluids and the diameter of the capillaries. We suggest that the viscosity dominates the wetting dynamics of viscoelastic fluids, manifested by the contact line morphology-dependent behavior. This insight has significant implications for microfluidics and drug injectability. [ABSTRACT FROM AUTHOR]

We consider the Nernst-Planck-Navier-Stokes system describing the electrodiffusion of ions in a viscous Newtonian fluid. We prove the exponential nonlinear stability of constant steady states in the case of periodic boundary conditions in any dimension of space without constraints on the number of species, valences and diffusivities. We consider also the case of two spatial dimensions, and we prove the exponential stability from arbitrary large data. [ABSTRACT FROM AUTHOR]

We consider a non-Newtonian incompressible heat conducting fluid with a prescribed nonuniform temperature on the boundary and with the no-slip boundary condition for the velocity. We assume no external body forces. For the power-law like models with the power law index bigger than or equal to 11/5 in three dimensions, we identify a class of solutions fulfilling the entropy equality and converging to the equilibria exponentially in a proper metric. In fact, we show the existence of a Lyapunov functional for the problem. Consequently, the steady solution is nonlinearly stable and attracts all proper weak solutions. [ABSTRACT FROM AUTHOR]

In this paper, we prove that a weak solution of the Cauchy problem for 3D unsteady flows of a generalized Newtonian fluid becomes a strong solution for 5 3 < p < 11 5 provided that the velocity field belongs to the critical space L 2 p − 1 (0 , T ; B M O (R 3)). The main key is to apply variants of Gagliardo–Nirenberg's inequality including a BMO -norm. In particular, when 2 < p < 11 5 , we derive and use a nonlinear variant of Gagliardo–Nirenberg's inequality including ‖ u ‖ B M O and ‖ | D u | p − 2 2 ∇ 2 u ‖ 2. [ABSTRACT FROM AUTHOR]

[Display omitted] Hypothesis Although extensive research has been conducted on the dynamic wetting of Newtonian fluids, limited insights have been gained for viscoelastic fluids, particularly on engineered surfaces. We hypothesize that differences in dynamic wetting on microstructured surfaces exist between such fluids, which may be attributed to variations in viscosity and elasticity as well as changes in the microscopic morphology of the moving contact line. Experiments To systematically investigate the wetting differences between Newtonian and viscoelastic fluids on microstructured surfaces, we conducted forced wetting experiments of glycerol-water and carboxymethyl cellulose aqueous solutions on microstructured polytetrafluoroethylene surfaces through a modified Wilhelmy plate method. Findings Results demonstrated an apparent difference in the relationship between the dynamic contact angle and moving velocity with different microstructured surfaces for Newtonian and viscoelastic fluids. The power-law exponent between the capillary number and cubic of the dynamic contact angle increases with the strengthening of shear thinning and elastic effects. In contrast, this exponent is rarely influenced by the scale of microstructured surfaces, particularly in highly viscous regions where viscous force dominates. In addition, viscosity affects the viscous bending and distance that liquid molecules jump at the contact line. These findings have potential applications in coating complex fluids on engineered surfaces. [ABSTRACT FROM AUTHOR]

Hypothesis: The dip coating of suspensions made of monodisperse non-Brownian spherical particles dispersed in a Newtonian fluid leads to different coating regimes depending on the ratio of the particle diameter to the thickness of the film entrained on the substrate. In particular, dilute particles dispersed in the liquid are entrained only above a threshold value of film thickness. In the case of anisotropic particles, in particular fibers, the smallest characteristic dimension will control the entrainment of the particle. Furthermore, it is possible to control the orientation of the anisotropic particles depending on the substrate geometry. In the thick film regime, the Landau-Levich-Derjaguin model remains valid if one account for the change in viscosity. Experiment: To test the hypotheses, we performed dip-coating experiments with dilute suspensions of non-Brownian fibers with different length-to-diameter aspect ratios. We characterize the number of fibers entrained on the surface of the substrate as a function of the withdrawal velocity, allowing us to estimate a threshold capillary number below which all the particles remain in the liquid bath. Besides, we measure the angular distribution of the entrained fibers for two different substrate geometries: flat plates and cylindrical rods. We then measure the film thickness for more concentrated fiber suspensions. Findings: The entrainment of the fibers on a flat plate and a cylindrical rod is primarily controlled by the smaller characteristic length of the fibers: their diameter. At first order, the entrainment threshold scales similarly to that of spherical particles. The length of the fibers only appears to have a minor influence on the entrainment threshold. No preferential alignment is observed for non-Brownian fibers on a flat plate, except for very thin films, whereas the fibers tend to align themselves along the axis of a cylindrical rod for a large enough ratio of the fiber length to the radius of the cylindrical rod. The Landau-Levich-Derjaguin law is recovered for more concentrated suspension by introducing an effective capillary number accounting for the change in viscosity. [ABSTRACT FROM AUTHOR]

[Display omitted] • Spreading dynamic of a deposited drop on a solid substrate is studied. • Viscous timescale mainly governs the spreading at a certain Bond number and static contact angle. • Droplet spreading master curves to capture the dynamic shape of the droplet are developed. • A correlation to predict the equilibrium shape of droplet is developed. There exists a generalized solution for the spontaneous spreading dynamics of droplets taking into account the influence of interfacial tension and gravity. This work presents a generalized scaling theory for the problem of spontaneous dynamic spreading of Newtonian fluids on a flat substrate using experimental analysis and numerical simulations. More specifically, we first validate and modify a dynamic contact angle model to accurately describe the dependency of contact angle on the contact line velocity, which is generalized by the capillary number. The dynamic contact model is implemented into a two-phase moving mesh computational fluid dynamics (CFD) model, which is validated using experimental results. We show that the spreading process is governed by three important parameters: the Bo number, viscous timescale τ viscous , and static advancing contact angle, θ s . More specifically, there exists a master spreading curve for a specific Bo and θ s by scaling the spreading time with the τ viscous . Moreover, we developed a correlation for prediction of the equilibrium shape of the droplets as a function of both Bo and θ s . The results of this study can be used in a wide range of applications to predict both dynamic and equilibrium shape of droplets, such as in droplet-based additive manufacturing. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to deal with the issue of well-posedness for a class of non-Newtonian fluid dynamics equations. The equations describing the motion of such fluids are characterized by a non-linear constitutive law relating the state of stress to the rate of deformation. We show the local-in-time existence and uniqueness of strong solutions to two important models: the Power Law model and the Bingham model. While our result for the first model holds over a periodic domain Ω = R 3 , the result obtained on the second model is limited to the one-dimensional case. This is because Bingham's constitutive law is discontinuous due to phase transition that may appear during the time when flows change nature, particularly from liquid motion to rigid motion and vice-versa. This property reduces the probability of showing smooth solutions to such a system in higher dimension space. [ABSTRACT FROM AUTHOR]

[Display omitted] Despite their apparent simplicity, suspensions of hard spheres in a Newtonian fluid show complex non-Newtonian behaviors and remain poorly understood. Recent works have pointed out the crucial role of interparticle contact forces in these behaviors. Here, we show that the same (polystyrene) particles, when immersed in different Newtonian solvents, show different behaviors at both the microscopic and macroscopic scales. Thanks to interparticle force measurements in each solvent together with rheological measurements, we show how the fine details of the pairwise particle interactions impact the macroscopic behavior. The rheological properties (shear thinning, shear thickening, jamming solid fraction value) of the suspensions, made up of same particles, are shown to depend on the nature of the solvent. Here, we highlight several mechanisms at the particle scale: the swelling of polymeric particles in an organic solvent, the role of colloidal repulsive forces and inertia for particles in a water solution, and the variation of the friction coefficient as a function of the load for particles immersed in silicone oils. Our study provides new quantitative data to test micromechanical models and simulations. It questions the interpretation of previous experimental works. Finally, it shows the need to systematically characterize the interparticle normal and tangential forces when studying a given suspension of hard spheres in a Newtonian fluid [ABSTRACT FROM AUTHOR]

The paper is concerned with the homogenization of a nonlinear differential system describing the flow of an electrically conducting, incompressible and viscous Newtonian fluid through a periodic porous medium, in the presence of a magnetic field. We introduce a variational formulation of the differential system equipped with boundary conditions. We show the existence of a solution of the variational problem, and derive uniform estimates of the solutions depending on the characteristic parameters of the flow. Using the two-scale convergence method, we rigorously derive a two-scale equation for the two-scale current density, and a two-pressure Stokes system. We derive, in the case of constant magnetic permeability, an explicit relation expressing the macroscopic velocity as a function of the macroscopic Lorentz force, the pressure gradient, the external body force, and the macroscopic current density, via two permeability filtration tensors. When the magnetic field is absent, this relation reduces to the Darcy law. [ABSTRACT FROM AUTHOR]

We are interested in the multi-dimensional compressible viscoelastic flows of Oldroyd type, which is one of non-Newtonian fluids exhibiting the elastic behavior. In order to capture the damping effect of the additional deformation tensor, to the best of our knowledge, the "div-curl" structural condition plays a key role in previous efforts. Our aim of this paper is to remove the structural condition and prove a global existence of strong solutions to compressible viscoelastic flows in critical spaces. In absence of compatible conditions, the new effective flux is introduced, which enables us to capture the dissipation arising from combination of density and deformation tensor. The partial dissipation in non-Newtonian compressible fluids, is weaker than that of classical Navier-Stokes equations. [ABSTRACT FROM AUTHOR]

We present a new regularized Oldroyd-B model in three dimensions which satisfies an energy estimate analogous to that of the standard model, and maintains the positive semi-definiteness of the conformation tensor. This results in the unique existence and stability of global solutions in a periodic domain. To be precise, given an initial velocity u 0 and initial conformation tensor σ 0 , both with components in H 2 , we obtain a velocity u and conformation tensor σ both with components in C ([ 0 , T ] ; H 2) for all T > 0. Assuming better regularity for the initial data allows us to obtain better regularity for the solutions. We treat both the diffusive and non-diffusive cases of the model. Notably, the regularization in the equation for the conformation tensor in our new model has been applied only to the velocity, rather than to the conformation tensor, unlike other available regularization techniques [5]. This is desired since the stress, and thus the conformation tensor, is typically less regular than the velocity for the creeping flow of non-Newtonian fluids. In [9] the existence and regularity of solutions to the non-regularized two dimensional diffusive Oldroyd-B model was established. However, the proof cannot be generalized to three dimensions nor to the non-diffusive case. The proposed regularization overcomes these obstacles. Moreover, we show that the solutions in the diffusive case are stable in the H 2 norm. In the non-diffusive case, we are able to establish that the solutions are stable in the L 2 norm. Furthermore, we show that as the diffusivity parameter goes to zero, our solutions converge in the L 2 norm to the non-diffusive solution. [ABSTRACT FROM AUTHOR]

We present and analyze a series of benchmark tests regarding the application of the immersed boundary (IB) method to viscoelastic flows through and around non-trivial, stationary geometries. The IB method is widely used to simulate biological fluid dynamics and other modeling scenarios in which a structure is immersed in a fluid. Although the IB method has been most commonly used to model systems involving viscous incompressible fluids, it also can be applied to visoelastic fluids and has enabled the study of a wide variety of dynamical problems including the settling of vesicles and the swimming of elastic filaments in fluids modeled by the Oldroyd-B constitutive equation. In the viscoelastic context, however, relatively little work has explored the accuracy or convergence properties of this numerical scheme. Herein, we present benchmarking results for an IB solver applied to viscoelastic flows in and around non-trivial geometries using either the idealized Oldroyd-B constitutive model or the more physically realistic, polymer-entanglement-based Rolie-Poly constitutive equations. We use two-dimensional numerical test cases along with results from rheology experiments to benchmark the IB method and compare it to more complex finite element and finite volume viscoelastic flow solvers. Additionally, we analyze different choices of regularized delta function and relative Lagrangian grid spacings which allow us to identify and recommend the key choices of these numerical parameters depending on the present flow regime. • The Immersed Boundary method is applied to viscoelastic flows around non-trivial, stationary geometries. • Computational results are compared to previous numerical benchmarks and macrorheology experiments. • Choices of relative Lagrangian grid spacings and delta functions are analyzed, with recommendations for current flow regimes. [ABSTRACT FROM AUTHOR]

In this study, soyasaponin (Ssa), corn oil, and soybean protein isolate (SPI) were used to prepare a water-in-oil-in-water (W/O/W) double emulsion system that can protect Lactobacillus plantarum (L.P) in the upper gastrointestinal tract for delivery to the small intestine and colon. Incorporating different amounts of L.P (0.1–0.6% (w/v)) in the W/O/W double emulsion caused the viscoelastic modulus and droplet size of the L.P-embedded emulsion system to change, and the emulsion system transformed from a non-Newtonian fluid to a "solid-like" gel. These results revealed that L.P encapsulation led to significantly improved stability of the W/O/W emulsion. In addition, different concentrations of L.P had different effects on the survival rate of L.P in simulated digestive fluids, and after in vitro digestion, L.P was naturally delivered from the stomach into the intestines. The optimal concentration of L.P for obtaining a stable emulsion was found to be 0.3%, and the survival rate of the encapsulated L.P in the small intestine was as high as 78.96% after 1 h. Thus, choosing an appropriate amount of L.P was crucial. The W/O/W emulsion system effectively maintained the viability of L.P and successfully delivered it to the small intestine and colon. • Ssa-SPI W/O/W emulsion improves the survival of LP in the gastrointestinal tract. • L.P shows better resistance to gastric acid upon encapsulation in inner phase. • Addition of 0.2–0.4% of L.P resulted higher stability in Ssa-SPI W/O/W emulsions. • The adsorption and film formation of L.P at the interface helps stabilize emulsion. [ABSTRACT FROM AUTHOR]

• A novel magnetic helical swimmer is designed and fabricated. • Propulsion force and translational velocity of the novel swimmer are improved. • The motion of the novel swimmer is simulated. • The translational velocity of the novel swimmer is analyzed parametrically. Magnetic helical swimmers are one type of robots that swim at low Reynolds number environments by rotating around the helix axis. Considering the importance and dramatic increase in the use of robots and microrobots in the near future, optimizing and increasing their efficiency is very important and noteworthy. Propulsion force and translational velocity are among the most important features of the magnetic helical swimmer, which improves the function of the swimmer as each of them increases. In this paper, a new design has been proposed for the magnetic helical swimmer by changing the geometry of the tail region, which has increased the propulsion force and improved its translational velocity. A suitable experimental setup has been designed and built in accordance with the required experiments to evaluate the translational velocity of the proposed swimmer. Using the experimental results, two models have been presented to express the translational velocity and propulsion force of the swimmer in terms of its angular velocity. The results of the experiments show that the propulsion force of the built swimmer is 698.89 % higher than that of the common magnetic helical swimmer with similar dimensions and the same environmental conditions in Newtonian fluid. At the end of the experiments, the motion of the proposed swimmer is simulated in the COMSOL software, and the results of the experiments are used to validate the simulation results. Finally, the effect of parameters such as the helix pitch and the number of turns of the helix on the translational velocity of the swimmer is investigated using the computer simulations. [ABSTRACT FROM AUTHOR]

[Display omitted] Bubbles in a liquid rise under gravity and separate to the top. Bubbly liquids exist commonly in nature and play a significant role in energy-conversion, oil and chemical industries. Therefore, understanding how bubbles rise is of great importance. Rheological properties of the fluid have a strong impact on single bubble rise and have been shown to change collective bubble rise at low gas volume fractions significantly. We expect that a viscoelastic fluid can strongly modify the rise of bubbles in more concentrated suspensions. We generate bubbly liquids up to gas fractions of 30 %. We measure the bubble size and the rise velocity in micellar solutions made of cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal), a common system to create shear-thinning solutions. We show that when the NaSal concentration is small and the solutions are Newtonian, the bubble rise velocity decreases with increasing volume fraction of bubbles and the relationship between the two follows the Richardson-Zaki prediction. For the shear thinning viscoelastic solutions, the Richardson-Zaki relation no longer applies. Bubble clustering leads to faster rise velocities and a weaker dependence on the bubble volume fraction. At the largest concentration two rise regimes are observed. A fast one similar to that in the other shear thinning samples, followed by a very slow bubble rise. The slow rise velocity is attributed to the smallest bubbles rising so slowly, that at the shear rates around them, the fluid behaves as a Newtonian fluid. Therefore, bubble rise becomes again comparable to Stokes expectations. We also show that the peculiar dependence of the rise velocity with volume fraction of bubbles in the shear thinning viscoelastic solutions can have important implications in flotation as the area flux changes strongly with bubble volume fraction. [ABSTRACT FROM AUTHOR]

[Display omitted] Shear thickening fluids (STFs) have been the research focus for decades because of the prospect as a damping ingredient. However, their inherent liquid character confines their practical applications. In this work, inspired by the assembly engineering, novel gelatinous shear thickening fluids (GSTFs) are fabricated by integrating low molecular weight gelators (LMWGs) into STFs and investigated by rheological experiments. The results show that the apparent performances of GSTFs are determined by the LMWGs content. LMWGs inside GSTFs can assemble into three-dimensional network that can constraint the flowability of liquid molecular and their content dominate the density and strength of assembly network. At a moderate content, GSTFs exhibit desired properties with restricted quasi-static flowability and almost undamaged dynamic shear thickening character. While a higher content will disappear shear thickening and a lower content cannot gelate STFs. Besides, three different LMWGs are employed to gelate STFs and all they can gelate STFs in spite of the distinct minimum gelation concentration, indicating the universality for GSTFs preparation and the superiority of a reasonable molecular structure of LMWGs. Further, the temperature sweep experiments suggest that GSTFs can endure higher temperature without flowing due to its higher gel-sol transition temperature. Basing on these advanced mechanical properties, we believe that the GSTFs with more expected characters have significance for the study of non-Newtonian fluids and will broaden the special application field of STFs. [ABSTRACT FROM AUTHOR]

(a) A surfactant-covered droplet deformed by uniform electric field; (b) Steady deformation as a function of electric capillary number; (c) Unsteady deformation for various dilatational viscosity values. [Display omitted] • Surfactants affect the deformation of a conducting droplet in an electric field. • Steady drop deformation is enhanced by surfactants but reduced by surface elasticity. • Surface dilatational viscosity controls unsteady deformation and delays equilibration. A conducting droplet suspended in an insulating continuous phase, e.g. an aqueous electrolyte in an oil, is deformed by an applied electric field to nonspherical equilibrium shapes, and can even break-up under strong fields. Many technologies use electro-deformation to manipulate fluid dispersions, with surfactants present on the droplet interfaces forming stabilizing monolayers. While surfactants lower the interface tension which facilitates electro-deformation, the monolayer elasticity resists deformation. High molecular weight surfactants, with large dilatational viscosities, can potentially retard the deformation dynamics. A boundary integral method simulates the dynamic interfacial deformation of a perfectly conducting droplet in a dielectric in a uniform field. The interface contains an insoluble monolayer which is a Newtonian fluid with constant dilatational viscosity obeying a Langmuir state equation. A range of initial surfactant surface concentrations are studied, with elasticity proportional to concentration. Equilibrium drop deformations, unaffected by surface viscosity, are strongly resisted by elasticity at high surface concentrations, and field strengths necessary for break-up increase with elasticity. Dilatational viscosity scales with the ratio, κ ∗ , the surface viscosity (divided by the droplet radius) to the bulk viscosity, and can extend the deformation time. Extended times are described by a time rescaling proportional to κ ∗ . [ABSTRACT FROM AUTHOR]

Fungal pellets are hierarchical systems that can be found in an ample variety of applications. Modeling transport phenomena in this type of systems is a challenging but necessary task to provide knowledge-based processes that improve the outcome of their biotechnological applications. In this work, an upscaled model for total mass and momentum transport in fungal pellets is implemented and analyzed, using elements of the volume averaging and adjoint homogenization methods departing from the governing equations at the microscale in the intracellular and extracellular phases. The biomass is assumed to be composed of a non-Newtonian fluid and the organelles impervious to momentum transport are modeled as a rigid solid phase. The upscaled equations contain effective-medium coefficients, which are predicted from the solution of adjoint closure problems in a three-dimensional periodic domains representative of the microstructure. The construction of these domains was performed for Laccaria trichodermophora based on observations of actual biological structures. The upscaled model was validated with direct numerical simulations in homogeneous portions of the pellets core. It is shown that no significant differences are observed when the dolipores are open or closed to fluid flow. By comparing the predictions of the average velocity in the extracellular phase resulting from the upscaled model with those from the classical Darcy equation (i.e. , assuming that the biomass is a solid phase) the contribution of the intracellular fluid phase was evidenced. This work sets the foundations for further studies dedicated to transport phenomena in this type of systems. [Display omitted] • An effective-medium model for fluid flow in fungal pellets was implemented. • Laccaria trichodermophora pellets were characterized and used for modeling. • The model was validated with direct numerical simulations. • Flow through the dolipore does not significantly affect momentum transport. • Classical Darcy's law is not applicable for this type of system. [ABSTRACT FROM AUTHOR]

We propose a finite-element formulation for simulating multi-component flows occupying the same domain with spatially varying concentrations. Each constituent is assumed to behave as an incompressible Newtonian fluid, and solutions are sought for the velocities and volume fractions of each phase, as well as the common pressure. Stabilization terms are derived within the framework of the variational multiscale method based on an approximation of the finite-element residual to achieve control of the pressure and volume fractions. We utilize the concept of term-by-term stabilization in conjunction with orthogonal subgrid scales, thus incorporating only those terms of the residual essential to obtain stability and projecting them on a space orthogonal to the finite element space. The resulting system of equations is solved in a monolithic manner, requiring a small number of nonlinear iterations. Several benchmark tests have been performed to confirm the stability and optimal asymptotic convergence rates for linear and higher-order elements using the proposed formulation. • First stabilized FEM for dispersed flows based on orthogonal subgrid scales. • Term-by-term stabilization requires few additional terms in the weak form. • Optimal error convergence despite approximate residual owing to orthogonal subgrid scales. • New approach to considering the algebraic constraint on the volume fractions. • Monolithic solution requires few iterations using Picard's scheme or Newton's method. [ABSTRACT FROM AUTHOR]

This study aims to analyze the dynamics of a thin Newtonian liquid film on a uniformly heated compliant substrate. We consider the violation of time-reversal symmetry in the liquid, resulting in an additional non-zero term in the liquid stress tensor. Using the long-wave expansion technique, we derive a set of coupled equations governing the film thickness and substrate deformation, accounting for inertia, surface tension, thermocapillarity, and odd viscosity. Through linear stability analysis and spatiotemporal simulations, we observe that the compliant substrate enhances instability, while wall heating exacerbates it. However, the introduction of odd viscosity effectively suppresses these instabilities, as confirmed by the agreement between simulation and theoretical predictions. • Analyzed dynamics of thin film flow along a heated compliant substrate. • Liquid's time-reversal symmetry is broken and this leads to odd viscosity inclusion. • Compliant substrates and wall heating amplify surface wave instability. • Odd viscosity reduces instability. [ABSTRACT FROM AUTHOR]

In this paper we prove a Liouville type theorem for the stationary equations of a non-Newtonian fluid in R 3 with the viscous part of the stress tensor A p (u) = div (| D (u) | p − 2 D (u)) , where D (u) = 1 2 (∇ u + (∇ u) ⊤) and 9 5 < p < 3. We consider a weak solution u ∈ W l o c 1 , p (R 3) and its potential function V = (V i j) ∈ W l o c 2 , p (R 3) , i.e. ∇ ⋅ V = u. We show that there exists a constant s 0 = s 0 (p) such that if the L s mean oscillation of V for s > s 0 satisfies a certain growth condition at infinity, then the velocity field vanishes. Our result includes the previous results [5,6] as particular cases. [ABSTRACT FROM AUTHOR]

[Display omitted] Hypothesis: Thin liquid films are important in many scientific fields. In particular, films with both the surface layers exposed to a different fluid phase, known as freestanding films, are relevant in the ambit of foams and emulsions. Hence, there is a great interest in developing novel techniques allowing to form large and stable freestanding liquid films and to follow their dynamics. Experiments: We develop a novel opto-mechanical tool allowing to perform and study the preparation and the capillary leveling flow of axisymmetric bare freestanding liquid films. The tool is composed by a customized motorized iris diaphragm and by an innovative joint imaging setup combining digital holography and white light color interferometry that enables real-time measurement of film thickness over a large field of view. The dynamics of films made of a model Newtonian fluid, i.e., high-viscosity silicone oil, is studied. Direct numerical simulations and a hydrodynamic model based on the lubrication theory are used to support the experimental results. Findings: Iris opening induces the formation of large circular freestanding films with a stepped profile. Once iris opening is stopped, the films undergo a capillary leveling flow tending to flatten their profile. The leveling flow follows the theoretical scaling given by Ilton et al. [1]. We prove through numerical simulations that an equi-biaxial extensional flow occurs at the film center. Furthermore, we observe the formation and dynamics of dimples in bare freestanding films for the first time. [ABSTRACT FROM AUTHOR]

In this paper, we establish the well-posedness for the third grade fluid equation perturbed by a multiplicative white noise. This equation describes the motion of a non-Newtonian fluid of differential type with relevant viscoelastic properties. We are faced with a strongly nonlinear stochastic partial differential equation supplemented with a Navier slip boundary condition. Taking the initial condition in the Sobolev space H 2 , we show the existence and the uniqueness of the strong (in the probability sense) solution in a two dimensional and non axisymmetric bounded domain. [ABSTRACT FROM AUTHOR]

For the stability of the non-Newtonian fluid equation ∂ u ∂ t − div (a (x) | ∇ u | p − 2 ∇ u) − ∑ i = 1 N b i (x) D i u + c (x , t) u = f (x , t) , where a (x) | x ∈ Ω > 0 , a (x) | x ∈ ∂ Ω = 0 and b i (x) ∈ C 1 (Ω ‾) , we know that the degeneracy of a (x) may make the usual Dirichlet boundary value condition overdetermined and only a partial boundary value condition is expected. How to depict the geometric characteristic of the partial boundary value condition has been a long-time standing open problem. In this study, an optimal partial boundary value condition has been proposed, and the stability of weak solutions based on this partial boundary value condition is established. When the rate of the diffusion coefficient decays to zero, we explore how it affects the stability of weak solutions. [ABSTRACT FROM AUTHOR]

During the flow of non-Newtonian fluids in porous media, the relationships between macroscopic quantities are governed by extremely complex microscopic fluid dynamics resulting from solid-fluid interactions. Consequently, the Darcy-scale viscosity exhibited by a shear-thinning fluid depends on the injection velocity, contrarily to the case of Newtonian fluids. In the present work, pore network modelling is used to investigate the relationships between local and macroscopic viscosities during the flow of shear-thinning fluids in 3D porous media. Special efforts are devoted to 1) identifying the influence of the viscosity exhibited by the fluid within the constrictions of the preferential flow paths on the value of Darcy-scale viscosity and 2) proposing an analytical expression to upscale viscosity from the local viscosity values. To go further, the reduction in average hydraulic tortuosity stemming from the directional nature of shear-thinning behavior in 3D porous media will also be quantified. The results of the present study show that Darcy-scale viscosity can be accurately calculated as the flow-rate weighted average of local viscosities in the investigated media. Moreover, the velocity maps provided by the proposed pore network flow simulations are suitable to assess hydraulic tortuosity reduction as compared to the flow of a Newtonian fluid. [ABSTRACT FROM AUTHOR]

We provide existence of very weak solutions and a-priori estimates for steady flows of non-Newtonian fluids when the right-hand sides are not in the natural existence class. This includes stress laws that depend non-linearly on the shear rate of the fluid like power-law fluids. To obtain the a-priori estimates we make use of a refined solenoidal Lipschitz truncation that preserves zero boundary values. We provide also estimates in (Muckenhoupt) weighted spaces which permit us to regain a duality pairing, which than can be used to prove existence. Our estimates are valid even in the presence of the convective term. They are obtained via a new comparison method that allows to "cut out" the singularities of the right hand side such that the skew symmetry of the convective term can be used for large parts of the right hand side. [ABSTRACT FROM AUTHOR]

A finite difference scheme is used to develop a numerical method to solve the flow of an unbounded viscoelastic fluid with zero to moderate inertia around a prolate spheroidal particle. The equations are written in prolate spheroidal coordinates, and the shape of the particle is exactly resolved as one of the coordinate surfaces representing the inner boundary of the computational domain. As the prolate spheroidal grid is naturally clustered near the particle surface, good resolution is obtained in the regions where the gradients of relevant flow variables are most significant. This coordinate system also allows large domain sizes with a reasonable number of mesh points to simulate unbounded fluid around a particle. Changing the aspect ratio of the inner computational boundary enables simulations of different particle shapes ranging from a sphere to a slender fiber. Numerical studies of the latter particle shape allow testing of slender body theories. The mass and momentum equations are solved with a Schur complement approach allowing us to solve the zero inertia case necessary to isolate the viscoelastic effects. The singularities associated with the coordinate system are overcome using L'Hopital's rule. A straightforward imposition of conditions representing a time-varying combination of linear flows on the outer boundary allows us to study various flows with the same computational domain geometry. For the special but important case of zero fluid and particle inertia we obtain a novel formulation that satisfies the force- and torque-free constraint in an iteration-free manner. The numerical method is demonstrated for various flows of Newtonian and viscoelastic fluids around spheres and spheroids (including those with large aspect ratio). Good agreement is demonstrated with existing theoretical and numerical results. • A finite difference method for viscoelasticity and moderate inertia around spheroids. • Prolate spheroidal coordinates efficiently resolve particle surface and large gradients. • L'Hopital rule eliminates coordinate system generated singularity. • Novel decomposition of equations allows satisfying exact integral constraints directly. • Using Schur complement reduction momentum equation is solved without time marching. [ABSTRACT FROM AUTHOR]

We studied experimentally the breakup of liquid bridges made of aqueous solutions of Poly(acrylic acid) between two separating solid surfaces with freely moving contact lines. For polymer concentrations higher than a certain threshold (~ 30 ppm), the contact line on the surface with the highest receding contact angle fully retracts before the liquid bridge capillary breakup takes place at its neck. This means that all the liquid remains attached to the opposing surface when the surfaces are separated. This behavior occurs regardless of the range of liquid volume and stretching speed studied. Such behavior is very different from that observed for Newtonian liquids or non-Newtonian systems where contact lines are intentionally pinned. It is shown that this behavior stems from the competition between thinning of bridge neck (delayed by extensional thickening) and receding of contact line (enhanced by shear thinning) on the surface with lower receding contact angle. If the two surfaces exhibit the same wetting properties, the upper contact line fully retracts before the capillary breakup due to the asymmetry caused by gravity, and, therefore, all the liquid remains on the lower surface. [ABSTRACT FROM AUTHOR]

The anomeric configuration (α or β) of n -hexadecyl- d -maltopyranoside (C 16 G 2) has been shown to affect the morphology of the micelle, from elongated for α-C 16 G 2 to worm-like micelles for β-C 16 G 2. The entanglement of worm-like micelles often leads to strong modifications of the rheological behavior of the system and, as such, the anomeric configuration of C 16 G 2 could also provide the possibility of controlling this. Furthermore, mixing these surfactants are hypothesized to result in mixed micelles allowing to finely tune the rheology of a system containing these sustainable surfactants. The rheology of α- and β-C 16 G 2 , and mixtures of those, was determined by rotational and oscillatory rheology at different temperatures and surfactant concentrations. Micelle structure and composition for these systems were characterized using contrast variation small-angle neutron scattering and small-angle X-ray scattering. The results from these were connected in order to elaborate a molecular understanding of the rheological response of the system. The self-assembly of these surfactants have been found to result in different rheological properties. β-C 16 G 2 show a high viscosity with a non-Newtonian viscoelastic behavior, which was linked to the formation of worm-like micelles. In contrast, α-C 16 G 2 self-assembled into short cylindrical micelles, resulting in a Newtonian fluid with low viscosity. Furthermore, mixtures of these two surfactants lead to systems with intermediate rheological properties as a result of the formation of micelles with intermediate morphology to those of the pure anomers. These results also show that the rheological properties of the system can be tuned to change the micelle morphology, which in turn depends on the anomeric configuration of the surfactant. Also, surfactant concentration, temperature of the system, and micelle composition for surfactant mixtures provide control over the rheological properties of the system in a wide temperature range. Therefore, these results open new possibilities in the development of sustainable excipients for formulation technology, where the characteristics of the system can be easily tailored through geometric variations in the monomer structure whilst maintaining the chemical composition of the system. [ABSTRACT FROM AUTHOR]

• A hydrophobic-hydrophilic structure was designed on the TiO 2 surface. • Modified TiO 2 with monodispersity could be simply re-dispersed. • The dispersion with low viscosity could be stable at least 60 days at room temperature. • The dispersion showed a rheological property similar to the Newtonian fluids. Stable dispersion of TiO 2 particle is very desirable for its practical applications in various fields. It is a big challenge to stabilize pigment TiO 2 with relatively large size (200–300 nm) in low viscosity (~10 cP) systems. In the current work, we introduced a general strategy using a hydrophobic-hydrophilic structure to achieve single-dispersed TiO 2 particles with long storage stability in low viscosity systems. The modified TiO 2 particles (~250 nm) can be re-dispersed into water/glycol ethers mixture to form single dispersed suspension without any additives. Our study shows that the dispersion can be stable at least 60 days at room temperature and the rheological property is similar to the Newtonian fluids showing an extremely low yield stress at relatively high solid concentration. This work is expected to introduce a new strategy to improve the dispersion stability of the large size nanoparticles in low viscosity systems. [ABSTRACT FROM AUTHOR]

In the hydro-transport of biomass feedstock by pipeline to bio-refineries, the rheology of the biomass slurry directly impacts the specifications and, therefore the cost of pipeline components. In this study, the rheological characteristics of untreated fine wood chip slurries across a broad range of slurry temperatures (5–15 °C) and solids concentrations (3–15 wt% dry-matter) were experimentally studied. Slurry samples were pumped in a closed-circuit pipeline facility where slurry flow longitudinal pressure drops were simultaneously measured. The rheological characteristics of the samples were then measured using a rotational viscometer with a vane-in-cup geometry. At low slurry concentrations (˂6 wt% dry-matter), the biomass slurry exhibited Newtonian behaviour; however, non-Newtonian (shear-thinning) behaviour was seen at higher slurry concentrations. In order to approximate the corresponding rheological parameters, different well-known non-Newtonian viscosity models (power-law, Bingham, Casson, and Herschel-Bulkley) were applied to experimental data. In addition, a new approach for approximating the apparent viscosity of biomass slurries using longitudinal pressure drop measurements was introduced and validated. The method has not been previously applied to non-Newtonian biomass slurries under turbulent flow regimes. • Rheological characteristics of untreated wood chip biomass slurries were studied. • Biomass slurry samples were made off a closed-circuit pipeline facility. • Rotational viscometer with vane-in-cup geometry was used over range of temperatures. • Corresponding rheological parameters were approximated using well-known models. • A pressure drop-based method proposed to approximate viscosity of slurry flows. [ABSTRACT FROM AUTHOR]

We explore the behaviour of global-in-time weak solutions to a class of bead-spring chain models, with finitely extensible nonlinear elastic (FENE) spring potentials, for dilute polymeric fluids. In the models under consideration the solvent is assumed to be a compressible, isentropic, viscous, isothermal Newtonian fluid, confined to a bounded open domain in R 3 , and the velocity field is assumed to satisfy a complete slip boundary condition. We show that as the Mach number tends to zero the system is driven to its incompressible counterpart. [ABSTRACT FROM AUTHOR]

We prove the existence of random dynamical systems and random attractors for a large class of locally monotone stochastic partial differential equations perturbed by additive Lévy noise. The main result is applicable to various types of SPDE such as stochastic Burgers type equations, stochastic 2D Navier-Stokes equations, the stochastic 3D Leray- α model, stochastic power law fluids, the stochastic Ladyzhenskaya model, stochastic Cahn-Hilliard type equations, stochastic Kuramoto-Sivashinsky type equations, stochastic generalized porous media equations and stochastic generalized p -Laplace equations. [ABSTRACT FROM AUTHOR]

Newtonian liquids, usually used as base oil lubricants, exhibit low viscosity under extreme thermal conditions, needed for the functioning of wind turbines. This is directly affecting the colloidal stability and the tribological properties of the formulations containing additives, such as MoS 2. Here, it was hypothesized that the surface hydrophobization of MoS 2 particles will allow for an increased colloidal stability of the resulting formulations, for temperatures as high as 80 °C. The antifriction properties and the thermal stability of the designed formulations were determined on submicron MoS 2 particles dispersed in poly-α-olefins (PAO) base oils of different dynamic viscosities (from 32 to 1650 mPa·s at 25 °C). The submicron particles of MoS 2 (300–500 nm in diameter) were synthesised by a simple one-pot solvothermal method under mild conditions. The resulting particles were hydrophobized in situ in PAO base oils using alkyltrichlorosilane grafting agents with two chain lengths (C8 and C18). The covalent grafting of alkylsilanes through Mo-O-Si bonds was confirmed by DFT calculations and FT-IR measurements. Turbiscan optical analysis revealed that thermal and colloidal stabilities can be significantly improved depending on oil viscosity and chain length of the grafting agent. The formulations in the PAO65 oil remained highly stable (TSI < 1), even at 80 °C. Herein, we demonstrate the impact of hydrophobization degree on the tribological properties of the lubricants, which, importantly, could reach ultra-low friction coefficients, less than 0.02. [ABSTRACT FROM AUTHOR]

We have examined mixtures of toluene, a Newtonian liquid, with several non-Newtonian liquids (i.e. surfactants) across the full composition range, from pure toluene to pure surfactant, for the purpose of exploring their rheological properties. Surfactants of similar viscosities but significantly different molecular weights were chosen, in order to verify the role of the molecular chain length. We discovered that the classical mixing rule, based on excess activation energy, succeeds for mixtures with shorter molecular chain, but fails for mixtures with longer ones. We suggest here a hypothesis which explains this difference as the result of expanding-collapsing of flexible long-chain molecules in shear flow. In order to support this hypothesis, we applied longitudinal rheology measurements which reproduce such oscillatory effects under the controlled conditions of an ultrasound longitudinal wave. This method confirms that there are qualitative differences in the rheology of these liquids mixtures with short and long molecular chains. [ABSTRACT FROM AUTHOR]

In this paper a fluid-structure interaction problem for incompressible Newtonian fluids is studied. We prove the convergence of an iterative process with respect to the computational domain geometry moving according to a viscoelastic deformation. In our previous joint works on numerical approximation of similar problems we refer to this approach as the global iterative method [1,2]. This iterative approach can be understood as a linearization of the so-called geometric nonlinearity of the underlying model. The proof of the convergence is based on the Banach fixed point Theorem, where the contractivity of the corresponding mapping is shown using the continuous dependence of the weak solution on the given domain deformation. This estimate is obtained by remapping the problem onto a fixed domain and using appropriate divergence-free test functions involving the difference of two solutions. [ABSTRACT FROM AUTHOR]

The association between a hydrophobically modified polysaccharide, gellan gum, with micelles based on a surfactant bearing the same hydrophobic tail as pendant groups was investigated by rheology and small-angle neutron scattering (SANS). Gellan gum grafted with cholesterol groups (20% mol/mol tetrasaccharide unit), GeCh, was mixed with polyoxyethylene cholesteryl ether (ChEO 10), which comprises a cholesterol group as the tail linked to a small polyoxyethylene headgroup, and self-assembles into micelles with an unusual disc-like morphology. The addition of 0.5% polymer to solutions of ChEO 10 induced a remarkable transition from a Newtonian fluid to a predominantly solid-like viscoelastic behaviour, leading to a ×105 increase in zero-shear viscosity (with 5% ChEO 10). Increasing surfactant concentration led to an enhancement of the viscoelasticity, but the elastic modulus G′ reached a plateau around 15% surfactant, attributed to a saturation of the sticker groups. The effect of micellar morphology on the network was studied by adding a small headgroup co-surfactant, triethylene glycol monododecyl ether, to ChEO 10 micelles, which drives their elongation into wormlike micelles. Networks obtained with the long, flexible micelles displayed enhanced solid-like behaviour, with no cross-over between G′ and G″ over the measured range of frequencies, reflecting relaxation times of the order of minutes or hours. The morphology of the gels studied by SANS revealed a scattering dominated by strongly interacting micelles (described by discs of 140 Å diameter and a hydrated ∼38 Å PEO corona) and the presence of micellar clusters induced by the presence of the polymer. The scattering data therefore confirm that the onset of gelation is due to surfactant micelles acting as junction points for the network. [ABSTRACT FROM AUTHOR]

In this work, the decoupled finite particle coupled with smoothed particle hydrodynamics (DFP-SPH) method is firstly developed to simulate the viscoelastic fluid flow with free surface. A particle shifting technology is introduced to eliminate the tensile instability and nonuniformity of fluid particles. The motivations and embodiments include: (a) the partial derivatives of physical quantities of velocity, density and viscoelastic stress are calculated based on multivariate Taylor series and dominated contributions from diagonal matrices, which avoid the inversion of encountered ill-conditioned matrices potentially and improve the precision of numerical approximation to a certain extent; (b) a particle shifting technology is added to remove the tensile instability and nonuniformity of fluid particles in the frame of proposed DFP-SPH, and the determination of free surface particles is also proceeded in nature; (c) the dynamic boundary particles possessing computational simplicity are introduced and adopted in the proposed method. A moderate uniformization is proposed to eliminate the spatial effect of nonphysical boundary layers. Subsequently, the accuracy, consistency and convergence of present method are investigated on some benchmarks of Newtonian and Oldroyd-B fluids with analytical solutions. The validity of particle shifting technology in DFP-SPH is verified and multiple inter miscible viscoelastic drops impacting on the rigid wall are simulated and analyzed numerically for the capacity of proposed method. The procedure of jet bulking is well demonstrated through using Newtonian and Oldroyd-B models at different Weissenberg numbers, which possesses flexible free surfaces and tangled interfaces of multifluid layers. Numerical results show that the coupled particle model has a good performance on the viscoelastic fluid flow with free surface. [ABSTRACT FROM AUTHOR]

A method for modeling non-Newtonian fluids (dilatants and pseudoplastics) by a power law under the Godunov-Peshkov-Romenski model is presented, along with a new numerical scheme for solving this system. The scheme is also modified to solve the corresponding system for power-law elastoplastic solids. The scheme is based on a temporal operator splitting, with the homogeneous system solved using a finite volume method based on a WENO reconstruction, and the temporal ODEs solved using an analytical approximate solution. The method is found to perform favorably against problems with known exact solutions, and numerical solutions published in the open literature. It is simple to implement, and to the best of the authors' knowledge it is currently the only method for solving this modified version of the GPR model. • Presents a way of modeling power-law non-Newtonian fluids in the GPR framework. • Presents a new numerical scheme for solving this model. • This numerical scheme is extended to work for power-law elasto-plastic materials. [ABSTRACT FROM AUTHOR]

• A new iterative state estimation algorithm for advection dominated flows with non-Gaussian uncertainty description of L ∞ -type. • The algorithm approximates this L ∞ -type bounding set by a union of possibly overlapping localized (in space) ellipsoids. • The resulting local state estimates are stitched together by the iterative d-ADN Schwartz method. • The efficacy of the proposed method is demonstrated with a set of numerical examples. This paper presents a new iterative state estimation algorithm for advection dominated flows with non-Gaussian uncertainty description of L ∞ -type: uncertain initial condition and model error are assumed to be pointwise bounded in space and time, and the observation noise has uncertain but bounded second moments. The algorithm approximates this L ∞ -type bounding set by a union of possibly overlapping ellipsoids, which are localised (in space) on a number of sub-domains. On each sub-domain the state of the original system is estimated by the standard L 2 -type filter (e.g. Kalman minimax filter) which uses Gaussian/ellipsoidal uncertainty description and observations (if any) which correspond to this sub-domain. The resulting local state estimates are stitched together by the iterative d-ADN Schwarz method to reconstruct the state of the original system. The efficacy of the proposed method is demonstrated with a set of numerical examples. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • A new series of trihexyl/trioctylammonium cation based protic ionic liquids (PILs) were synthesized. • Density, speed of sound, viscosity and refractive index of PILs were measured as a function of temperature. • Effect of temperature and alkyl chain length on physicochemical properties has been analyzed. • Low viscosity has been observed for studied PILs and viscosity data correlated using VFT equation. • The lattice potential energy decreased with increase in cation or anion chain length of studied PILs. Abstract A series of trialkylammonium cation and carboxylate anion based room temperature protic ionic liquids (PILs) were synthesized by varying cation alkyl chain length to hexyl, octyl and anion chain length to butanoate, hexanoate, and octanoate. The corresponding ILs are named as trihexylammonium butanoate ([THA][But]), trihexylammonium hexanoate ([THA][Hex]), trihexylammonium octonoate ([THA][Oct]), trioctylammonium butanoate ([TOA][But]), trioctylammonium hexanoate ([TOA][Hex]), and trioctylammonium octonoate ([TOA][Oct]). The thermophysical properties such as density (ρ), speed of sound (u) , viscosity (η) and refractive index (n D) were measured over a wide temperature range. The calculated parameters from experimental data such as thermal expansion coefficient, isentropic compressibility decreased linearly with the number of carbon atoms in cation or anion, whereas they increased with the temperature. Thermogravimetric analysis revealed an increase in the thermal stability of the ILs with the increase in total chain length. The shear-dependent viscosity measurements suggest that all the studied PILs showed fluid nature and Newtonian behavior at 298.15 K. The effect of alkyl chain length of cation or anion and temperature on the physicochemical properties were discussed with respect to the structure of ILs and in correlation with the reported structurally similar ILs. [ABSTRACT FROM AUTHOR]

Abstract Present work concerns the pulsatile blood flow of two-fluid model through porous blood vessels under the effect of radially varying viscosity. Blood is modeled as two-phase fluid model consisting a core region by non-Newtonian (Herschel-Bulkley) fluid and a plasma region modeled as Newtonian fluid. No slip condition has been used on wall and pressure gradient is taken as periodic function of time. Up to first order approximate solutions of governing equations are obtained using perturbation approach. A comparative analysis for relative change in flow resistance between our model and previously studied single and two-fluid models without porous layer near wall has also been done. The wall of the blood vessel is composed by a thin Brinkman (porous) layer. The stress jump condition has been imposed on fluid-porous interface. Analytical expressions for the velocity profile, flow rate, wall shear stress and flow resistance have been obtained for different regions and the effect of plasma layer thickness, varying viscosity, yield stress, permeability and viscosity ratio parameter on the flow variables are pictorially discussed. It is perceived that values of flow rate for two-fluid model with porous region near wall is higher in comparison to two-fluid model without porous region near wall. Present study reveals a significant impact of glycocalyx layer on blood flow through blood vessels with a porous layer near wall. Highlights • In the present work, pulsatile nature of blood flow of two-fluid model through porous blood vessels under the effect of radially varying viscosity has been done. • The combined effect of plasma layer thickness (and hence porous layer thickness), varying viscosity parameters, permeability and viscosity ratio parameter on hemodynamical quantities have been pictorially analyzed and compared with constant viscosity model. • The viscosity ratio parameter (and hence porosity of arterial wall) affects the plug core radius (and hence the yield plane location). • Due to presence of porous region near wall, there is slight phase difference in flow rate and flow resistance between two-fluid model with and without porous region near wall which completely agrees with Tiwari and Deo [A. Tiwari, S. Deo, Pulsatile flow in a cylindrical tube with porous walls: Applications to blood flow, Journal of Porous Media 16(4) (2013) 335-340] approach. • The outcome of above work shows a significant impact of the viscosity ratio parameter and permeability arising due to existence of glycocalyx layer near wall on various hemodynamical quantities such as rate of flow and resistance offered against the flow. [ABSTRACT FROM AUTHOR]

Graphical abstract Abstract Extending previous electrokinetic analyses based on a Newtonian fluid to power-law fluids, we investigate the behaviors of the ion current rectification (ICR) and the ion selectivity S of a conical nanopore having a pH-regulated surface. The bulk salt concentration C bulk , the solution pH, and the power-law index n are examined in detail for their influences on these behaviors. We show that the ICR ratio for the case where pH is lower than the isoelectric point (IEP) of the nanopore surface is different both quantitatively and qualitatively from that for the case where pH > IEP. The relative magnitude of the ICR ratio as n varies depends largely on the level of C bulk. In contrast, S (pH < IEP) is qualitatively similar to that for S (pH > IEP), where | S | decreases with increasing C bulk and/or decreasing n. In addition, S is very sensitive to n , for example, a decrease of n from 1.0 (Newtonian fluid) to 0.9 (pseudoplastic fluid) can yield a 245% increase in S at C bulk = 100 mM. Implying that the performance of ion separation can be improved by tuning the fluid viscosity. Mechanisms are proposed for explaining the observed behaviors in the ICR ratio. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider stochastic second grade fluids driven by Lévy noise on a bounded domain of R 2. Global existence and uniqueness of strong probabilistic solutions are established, which improves the existing corresponding results for martingale solutions in literature. [ABSTRACT FROM AUTHOR]

Graphical abstract Abstract The time evolution of a coating layer of liquid on an inclined circular cylindrical substrate is studied experimentally and theoretically. For small-diameter cylinders, the motion of Newtonian liquids, driven by the combined influences of surface tension and gravity, is analyzed using the long-wave or "lubrication" approximation. Computed time-dependent solutions of the lubrication model are in general agreement with our experimental observations. Starting from a slightly-perturbed uniform coating, the full family of evolving flows is shown to depend only on three dimensionless parameters: the inclination angle of the cylinder from the vertical direction, the Bond number representing the ratio of gravity to surface tension effects, and a nondimensional measure of the initial coating thickness. Typically flow is initiated by the well-known Rayleigh-Plateau instability followed by drainage, and also wave propagation if the cylinder is not horizontal. Steady propagation of ring-like structures can occur as well as eventual overtaking, merging and reformation of the rings. We demonstrate that volumetric transport is maximized if the cylinder axis is inclined to, rather than aligned with, the direction of gravity. Results are relevant to the understanding, and potential optimization, of small-scale liquid transport. Such problems arise in the natural and industrial worlds. [ABSTRACT FROM AUTHOR]

Highlights • To our knowledge, this is the first numerical work for the investigations of Newtonian vesicle dynamics in Oldroyd-B fluid. • The inclination angle and tank-treading frequency of the N/O fluid case are comparably smaller than the ones in N/N fluid. • In matched viscosity N/O fluid, the vesicle inclination angle in TT regime decreases with increasing Weissenberg number. • In unmatched viscosity N/O fluid, most surprisingly, the negative inclination angle is found in TT regime. • The inertia enables the vesicle to undergo TT-TB-TT transition as the Reynolds number increases. Abstract In this paper, a two-dimensional immersed boundary method is developed to simulate the dynamics of Newtonian vesicle in viscoelastic Oldroyd-B fluid under shear flow. The viscoelasticity effect of extra stress is well incorporated into the immersed boundary formulation using the indicator function. Our numerical methodology is first validated in comparison with theoretical results in purely Newtonian fluid, and then a series of numerical experiments is conducted to study the effects of different dimensionless parameters on the vesicle motions. Although the tank-treading (TT) motion of Newtonian vesicle in Oldroyd-B fluid under shear flow can be observed just like in Newtonian fluid, it is surprising to find that the stationary inclination angle can be negative without the transition to tumbling (TB) motion. Moreover, the inertia effect plays a significant role that is able to turn the vesicle back to positive inclination angle through TT-TB-TT transition as the Reynolds number increases. To the best of our knowledge, this is the first numerical work for the detailed investigations of Newtonian vesicle dynamics suspended in viscoelastic Oldroyd-B fluid. We believe that our numerical results can be used to motivate further studies in theory and experiments for such coupling vesicle problems. [ABSTRACT FROM AUTHOR]

In this work, transient movement of a vertically falling soluble spherical particle in a non-Newtonian medium is perused. It is supposed that the particle mass diminishes owing to its solubility in the fluid, and thus particle size will be diminished by a linear function. The governing nonlinear differential equation is solved analytically using Collocation Method (CM). The impacts of the effective parameters of this study are examined on the velocity and acceleration. Further, the positions of the particle are portrayed graphically at every 1 s time trend. Also, the limiting cases are gained and are found to be in good compromise with the numerical and literature results. The outcomes portray that the particle with a larger rate of diameter diminution moving with larger velocity rather than smaller diameter particle. [ABSTRACT FROM AUTHOR]

Abstract We consider a symmetric restricted three-body problem on surfaces M κ 2 of constant Gaussian curvature κ ≠ 0 , which can be reduced to the cases κ = ± 1. This problem consists in the analysis of the dynamics of an infinitesimal mass particle attracted by two primaries of identical masses describing elliptic relative equilibria of the two body problem on M κ 2 , i.e., the primaries move on opposite sides of the same parallel of radius a. The Hamiltonian formulation of this problem is pointed out in intrinsic coordinates. The goal of this paper is to describe analytically, important aspects of the global dynamics in both cases κ = ± 1 and determine the main differences with the classical Newtonian circular restricted three-body problem. In this sense, we describe the number of equilibria and its linear stability depending on its bifurcation parameter corresponding to the radial parameter a. After that, we prove the existence of families of periodic orbits and KAM 2-tori related to these orbits. [ABSTRACT FROM AUTHOR]