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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 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]

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]

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]

[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]

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]

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]

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]

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 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]

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]

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]

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]

In this paper we develop and implement anisotropic radial basis function methods for simulating the dynamics of ice sheets and glaciers. We test the methods on two problems: the well-known benchmark ISMIP-HOM B that corresponds to a glacier size ice and a synthetic ice sheet whose geometry is inspired by the EISMINT benchmark that corresponds to a continental size ice sheet. We illustrate the advantages of the radial basis function methods over a standard finite element method. We also show how the use of anisotropic radial basis functions allows for accurate simulation of the velocities on a large ice sheet, which was not possible with standard isotropic radial basis function methods due to a small ratio between the typical thickness and length of an ice sheet. Additionally, we implement a partition of unity method in order to improve the computational efficiency of the radial basis function methods. [ABSTRACT FROM AUTHOR]

We consider the system of equations describing the flow of incompressible fluids in bounded domain. In the considered setting, the Cauchy stress tensor is a monotone mapping and has asymptotically (s − 1) -growth with the parameter s depending on the spatial and time variable. We do not assume any smoothness of s with respect to time variable and assume the log-Hölder continuity with respect to spatial variable. Such a setting is a natural choice if the material properties are instantaneous, e.g. changed by the switched electric field. We establish the long time and the large data existence of weak solution provided that s ≥ 3 d + 2 d + 2. [ABSTRACT FROM AUTHOR]

Non-Newtonian fluids are present in most manufacturing industry processes. Computational models used to describe the rheological behavior of such materials can be costly due to the non-linear behavior of the viscosity. This work presents a parametrized projection-based model reduction approach to address time-dependent generalized Newtonian fluids in a computational framework. We develop our discrete formulation using three ingredients: an offline-online setting for the model reduction based on a proper orthogonal and Tucker decompositions, the finite element method for the discretization of the spatial domain and finite differences for the temporal integration, and the variational multiscale approach as a stabilization technique for both the full and reduced order models. We also evaluate the reduced method with some numerical tests, where the first part involves testing the accuracy of the model reduction method for time as a single parameter of the dynamic reduced problem. The second part involves the solution of parametrized time-dependent reduced problems with the Reynolds number and the power-law index of the fluid as the varying parameters. [ABSTRACT FROM AUTHOR]

Interactions between starch and nonstarch components have attracted enormous attention, but limited information is available on the interactions between starch and alkaloids. To elucidate the interaction mechanism between Fuzi total alkaloids (FTA) and Fuzi starch, Fuzi starch-FTA complexes with different FTA concentrations (0, 1, 3, and 5 g/100 g Fuzi starch) were prepared, and their structural characteristics, physicochemical properties, and rheological behaviors were investigated. Fourier transform infrared spectroscopy results demonstrated that FTA interact with starch via hydrogen bonding. Moreover, the addition of FTA increased the formation of a short-range ordered structure. X-ray diffraction results confirmed the existence of hydrogen bonding and suggested that the relative crystallinity of Fuzi starch decreases with the presence of FTA. Furthermore, FTA elevated the solubility of Fuzi starch and reduced its swelling power, coagulability, gelatinization temperature, and enthalpy change. Based on rheological analyses, Fuzi starch-FTA complexes exhibited non-Newtonian fluid properties and a typically weak gel rheological behavior. After adding FTA, the shear stress, viscosity, and storage/loss modulus of Fuzi starch decreased. Overall, our work enriches the theory of starch-alkaloid interactions and provides data to support investigation into the future applications of Fuzi starch. • The isolated Fuzi starch contains 34.67 g/100 g of amylose. • FTA interact with Fuzi starch via hydrogen bonding. • FTA promote the formation of a short-range ordered structure of Fuzi starch. • FTA reduce the swelling power, coagulability, and enthalpy change of Fuzi starch. • FTA reduce the shear stress, viscosity, and storage/loss modulus of Fuzi starch. [ABSTRACT FROM AUTHOR]

External Gear Pumps are used in various industries to pump non-Newtonian viscoelastic fluids like plastics, paints, inks, etc. For both design and analysis purposes, it is often a matter of interest to understand the features of the displacing action realized by meshing of the gears and the description of the behavior of the leakages for this kind of pumps. However, very limited work can be found in literature about methodologies suitable to model such phenomena. This article describes the technique of modelling external gear pumps that operate with non-Newtonian fluids. In particular, it explains how the displacing action of the unit can be modelled using a lumped parameter approach which involves dividing fluid domain into several control volumes and internal flow connections. This work is built upon the HYGESim simulation tool, conceived by the authors’ research team in the last decade, which is for the first time extended for the simulation of non-Newtonian fluids. The article also describes several comparisons between simulation results and experimental data obtained from numerous experiments performed for validation of the presented methodology. Finally, operation of external gear pump with fluids having different viscosity characteristics is discussed. [ABSTRACT FROM AUTHOR]

The objective of this study was to determine the effect of micronization techniques for particle size reduction from D (v, 0.9) ≥ 800 μm to D (v, 0.9) ≤ 100 μm on the rheological and structural characteristics of tart cherry puree. Commercially frozen cherry puree was thawed and micronized using Megatron MT5000 at 15000 rpm for three cycles (M1, M2, M3; 10 min each) followed by high-pressure homogenization at 200 MPa. The particle size distribution was measured using Malvern laser particle size analyzer and total soluble and insoluble solid contents by using the AOAC official method 20.5 or 30.2. All samples were further characterized for rheology, total solids content and particle morphology. Results showed a significant reduction in apparent viscosities (2.59 Pa s to 0.0144 Pa s) with a reduction in particle size (800 μm–100 μm) and this trend was consistent in different shear rate ranges. The change in serum viscosity followed the similar trend as observed in puree viscosity with micronization. Comparative analysis of the effect of shear rate (0–1000 s −1 ) on viscosity showed an inverse relationship, suggesting a shear thinning behavior of the fluid. This effect on serum viscosity (0.0119 Pa s to 0.0047 Pa s) was found to be higher in the shear rate range of 0–10 s −1 , as opposed to a relatively less reduction from 0.0047 Pa s to 0.0022 Pa s and 0.0015 Pa s at higher shear rates in ranges of 20–100 s −1 and 20 to 1000 s −1 respectively. The viscosity–shear rate changes were approximated by Ostwald-de Waele model (power law relation) for serum and Herschel Bulkley model for puree. The total solid content (14.20 ± 1.10 °Brix) was not significantly affected by particle size reduction. Results of this study provide useful information about the rheological properties of fruit juices/purees, which are influenced by the interactions between the dispersed phase and the serum, and are critical indicators of textural properties, mouth-feel, commercial acceptability, requirements of mixing and transport equipment. [ABSTRACT FROM AUTHOR]

We study the partial regularity of weak solution to a certain class of non-Newtonian fluids (1.1) – (1.3) , the existence of weak solution to such system had been provided by D. Pierre and H. Norbert in [40] . In particular, we prove that the regularity point in Q T is an open set with full measure, and we obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In this paper we confined ourselves to considered the case p = 2 and space dimension d = 2 . [ABSTRACT FROM AUTHOR]

Microfluidic devices have been widely used since 1990s for diverse manipulations of particles (a general term of beads, cells, vesicles, drops, etc.) in a variety of applications. Compared to the active manipulation via an externally imposed force field, the passive manipulation of particles exploits the flow-induced intrinsic lift and/or drag to control particle motion with several advantages. Along this direction, inertial microfluidics has received tremendous interest in the past decade due to its capability to handle a large volume of samples at a high throughput. This inertial lift-based approach in Newtonian fluids, however, becomes ineffective and even fails for small particles and/or at low flow rates. Recent studies have demonstrated the potential of elastic lift in non-Newtonian fluids for manipulating particles with a much smaller size and over a much wider range of flow rates. The aim of this article is to provide an overview of the various passive manipulations, including focusing, separation, washing and stretching, of particles that have thus far been demonstrated in non-Newtonian microfluidics. [ABSTRACT FROM AUTHOR]

This paper presents the results of an extensive experimental campaign on the dynamic interactions between an elastic structure and a non-Newtonian fluid. The structure consists of a thin circular cylindrical shell, with the bottom end clamped to a shaking table, and the top end carrying a heavy mass. The fluid is a mixture of water and cornstarch, also known as oobleck. The system dynamics has been analyzed in the presence of different fluid levels (i.e., empty, partially, and full-filled). The experimental modal analysis has been carried out to identify the modal properties of the system. High energy tests have been performed by means of a seismic excitation consisting in a stepped sine sweep, spanning the forcing frequency within the neighborhoods where strong resonance phenomena take place. Different excitation amplitudes have been considered in order to induce phase transitions in the fluid, and the onset of complex dynamics has been detected using Fourier spectra and bifurcation diagrams of the Poincaré maps: when the fluid–solid​ transition occurs, the entangled non-Newtonian fluid rheology results in a complex dynamic scenario where period-doubling cascades, quasiperiodic and chaotic responses can be observed. [ABSTRACT FROM AUTHOR]

To investigate the microstructural evolution dependency on the apparent viscosity in shear-thickening fluids (STFs), a hybrid mesoscale model combined with stochastic rotation dynamics (SRD) and molecular dynamics (MD) is used. Muller-Plathe reverse perturbation method is adopted to analyze the viscosities of STFs in a two-dimensional model. The characteristic of microstructural evolution of the colloidal suspensions under different shear rate is studied. The effect of diameter of colloidal particles and the phase volume fraction on the shear thickening behavior is investigated. Under low shear rate, the two-atom structure is formed, because of the strong particle attractions in adjacent layers. At higher shear rate, the synergetic pair structure extends to layered structure along flow direction because of the increasing hydrodynamics action. As the shear rate rises continuously, the layered structure rotates and collides with other particles, then turned to be individual particles under extension or curve string structure under compression. Finally, at the highest shear rate, the strings curve more severely and get into two-dimensional cluster. The apparent viscosity of the system changes from shear-thinning behavior to the shear-thickening behavior. This work presents valuable information for further understanding the shear thickening mechanism. [ABSTRACT FROM AUTHOR]

We solve the stationary Stokes and Navier–Stokes equations for non-Newtonian incompressible fluids with shear dependent viscosity in domains with outlets containing unbounded cross sections, in the case of shear thickening viscosity. The flux assumes arbitrary given values and the growth of the cross sections are analyzed under different convergence hypotheses, inclusive the growth of Dirichlet's integral of the velocity field is deeply related the convergence hypotheses of such sections. We extend the results of the section 4 of [12, Ladyzhenskaya and Solonnikov] (for Newtonian fluids) to non-Newtonian fluids using the techniques found in [3, Dias and Santos] . [ABSTRACT FROM AUTHOR]

Many industrial flow processes are sensitive to changes in the rheological behaviour of process fluids, and there therefore exists a need for methods that provide online, or inline, rheological characterisation necessary for process control and optimisation over timescales of minutes or less. Nuclear magnetic resonance (NMR) offers a non-invasive technique for this application, without limitation on optical opacity. We present a Bayesian analysis approach using pulsed field gradient (PFG) NMR to enable estimation of the rheological parameters of Herschel-Bulkley fluids in a pipe flow geometry, characterised by a flow behaviour index n , yield stress τ 0 , and consistency factor k , by analysis of the signal in q -space. This approach eliminates the need for velocity image acquisition and expensive gradient hardware. We investigate the robustness of the proposed Bayesian NMR approach to noisy data and reduced sampling using simulated NMR data and show that even with a signal-to-noise ratio (SNR) of 100, only 16 points are required to be sampled to provide rheological parameters accurate to within 2% of the ground truth. Experimental validation is provided through an experimental case study on Carbopol 940 solutions (model Herschel-Bulkley fluids) using PFG NMR at a 1 H resonance frequency of 85.2 MHz; for SNR > 1000, only 8 points are required to be sampled. This corresponds to a total acquisition time of <60 s and represents an 88% reduction in acquisition time when compared to MR flow imaging. Comparison of the shear stress-shear rate relationship, quantified using Bayesian NMR, with non-Bayesian NMR methods demonstrates that the Bayesian NMR approach is in agreement with MR flow imaging to within the accuracy of the measurement. Furthermore, as we increase the concentration of Carbopol 940 we observe a change in rheological characteristics, probably due to shear history-dependent behaviour and the different geometries used. This behaviour highlights the need for online, or inline, rheological characterisation in industrial process applications. [ABSTRACT FROM AUTHOR]

We consider the α -Euler equations on a bounded three-dimensional domain with frictionless Navier boundary conditions. Our main result is the existence of a strong solution on a positive time interval, uniform in α , for α sufficiently small. Combined with the convergence result in [6] , this implies convergence of solutions of the α -Euler equations to solutions of the incompressible Euler equations when α → 0 . In addition, we obtain a new result on local existence of strong solutions for the incompressible Euler equations on bounded three-dimensional domains. The proofs are based on new a priori estimates in conormal spaces. [ABSTRACT FROM AUTHOR]

[Display omitted] • A portable magnetic resonance instrument is used to measure the flow behaviour indices of non-Newtonian fluids. • Velocity induced phase interference leads to a rheological dependence of signal magnitude. • Measured values of the flow behavior indices are in close agreement with literature values. • Various procedures for calibration and data analysis outlined and compared. In this work, we expand on past portable magnetic resonance flow methods and propose a novel method for characterizing circular (laminar) Couette flow of non-Newtonian fluids. Symmetry of the flow system combined with a constant magnetic field gradient leads to phase interference, affecting the signal magnitude, and net phase cancellation when averaging across the excited slice, preventing the use of phase-sensitive methods. Therefore, we utilize the dependence of signal magnitude at variable echo times and shear rates to characterize rheological properties. Theoretical equations governing the velocity distributions of fluids that obey a simple power-law model are used to obtain integral expressions for signal magnitude. Integral expressions can be simplified by approximating a thin excited slice or complete excitation of the Couette cell depending on experimental parameters. With simple data acquisition and analysis procedures employed, our measurements of the flow behavior indices of non-Newtonian xanthan gum dispersions are in close agreement with conventional rheological magnetic resonance measurements. [ABSTRACT FROM AUTHOR]

We perform the stability analysis of bulging localized structures on the wall of a fluid-filled axisymmetric membrane elastic tube. The wall of the tube is assumed to be subjected to localized thinning. The problem has no translational invariance anymore, hence the stability of a bulging wave centered in the point of the localization of imperfection is usual, and not orbital stability up to a shift as in the case of translationally invariant governing equations. Motionless wave solutions of the governing equations having the form of a localized bulging are called throughout the paper aneurysm solutions. We assume that the fluid is subjected to the power law for viscous friction of a non-Newtonian fluid, and also that the viscosity of the fluid does not play a significant role and it can be neglected. The velocity profile remains not constant along the cross section of the tube (even in the absence of the viscosity) because no-slip boundary conditions are performed on the tube walls. Stability is established by demonstrating the non-existence of the unstable eigenvalues with a positive real part of the linearized problem. This is achieved by constructing the Evans function depending only on the spectral parameter, analytic in the right half of the complex plane Ω + and which zeroes in Ω + coincide with the unstable eigenvalues of the problem. The non-existence of zeroes of the Evans function is performed using the argument principle from the analysis of complex variable. Finally, we discuss the possibility of applying of the results of the present analysis to the aneurysm formation in damaged human vessels under the action of the internal pressure. [ABSTRACT FROM AUTHOR]

Implicit integration of the viscous term can significantly improve performance in computational fluid dynamics for highly viscous fluids such as lava. We show improvements over our previous proposal for semi-implicit viscous integration in Smoothed Particle Hydrodynamics, extending it to support a wider range of boundary models. Due to the resulting loss of matrix symmetry, a key advancement is a more robust version of the biconjugate gradient stabilized method to solve the linear systems, that is also better suited for parallelization in both shared-memory and distributed-memory systems. The advantages of the new solver are demonstrated in applications with both Newtonian and non-Newtonian fluids, covering both the numerical aspect (improved convergence thanks to the possibility to use more accurate boundary model) and the computational aspect (with excellent strong scaling and satisfactory weak scaling). • No symmetry required in the linear system associated to the implicit viscous term. • A variant of BiCGSTAB is used to solve the system. • The variant is more robust numerically, converges easily even in single precision. • The variant is efficient when parallelized on both shared- and distributed- memory. [ABSTRACT FROM AUTHOR]

Gliding bacteria are an assorted group of rod-shaped prokaryotes that adhere to and glide on certain layers of ooze slime attached to a substratum. Due to the absence of organelles of motility, such as flagella, the gliding motion is caused by the waves moving down the outer surface of these rod-shaped cells. In the present study we employ an undulating surface model to investigate the motility of bacteria on a layer of non-Newtonian slime. The rheological behavior of the slime is characterized by an appropriate constitutive equation, namely the Carreau model. Employing the balances of mass and momentum conservation, the hydrodynamic undulating surface model is transformed into a fourth-order nonlinear differential equation in terms of a stream function under the long wavelength assumption. A perturbation approach is adopted to obtain closed form expressions for stream function, pressure rise per wavelength, forces generated by the organism and power required for propulsion. A numerical technique based on an implicit finite difference scheme is also employed to investigate various features of the model for large values of the rheological parameters of the slime. Verification of the numerical solutions is achieved with a variational finite element method (FEM). The computations demonstrate that the speed of the glider decreases as the rheology of the slime changes from shear-thinning (pseudo-plastic) to shear-thickening (dilatant). Moreover, the viscoelastic nature of the slime tends to increase the swimming speed for the shear-thinning case. The fluid flow in the pumping (generated where the organism is not free to move but instead generates a net fluid flow beneath it) is also investigated in detail. The study is relevant to marine anti-bacterial fouling and medical hygiene biophysics. [ABSTRACT FROM AUTHOR]

Since non-Newtonian fluid behavior are not uncommon in practice, especially in modern applications of colloid and interface science, assessment of how serious is the deviation of the existing results for Newtonian fluids due to fluid nature is highly desirable and necessary. Here, we extend previous analyses for the diffusiophoresis of a particle in a Newtonian fluid to that in a non-Newtonian fluid choosing Carreau fluids as an example. Results gathered reveal that due to the shear-thinning property of the fluid considered, the difference between the particle mobility in a Carreau fluid and that in the corresponding Newtonian fluid can be on the order of 100%. In addition, this difference has a local minimum as the thickness of double layer varies. [ABSTRACT FROM AUTHOR]

Overall (U) and fluid-to-particle heat-transfer coefficients (h fp ) in canned particulates (Nylon spheres) suspended in non-Newtonian fluid (CMC dispersions) undergoing reciprocation agitation thermal processing was evaluated in a pilot-scale reciprocating retort. Five influencing process variables affecting U and h fp were selected. A CCRD and a 3 × 3 × 2 full-factorial design of experiments were used to relate the coefficients U and h fp to the various process variables viz . reciprocation frequency; reciprocation amplitude; temperature; liquid viscosity and headspace. U and h fp varied in the range 524–1124 W/m 2o C and 549–1610 W/m 2o C respectively. Analysis of variance showed frequency, amplitude, liquid viscosity, headspace and temperature to be significant factors for h fp , and frequency, amplitude and liquid viscosity for U (p < 0.001). Increasing the reciprocation frequency from 1 to 4 Hz almost doubled the value of both the heat transfer coefficients. Similarly increasing the reciprocation amplitude from 5 to 25 cm, resulted in 30–35% increase in the values of heat transfer coefficients. Overall with increase in temperature, frequency, amplitude, and headspace, associated h fp and U values also increased, but with increasing liquid viscosity, both h fp and U showed a decrease. Finally, optimization of processing conditions was carried out to minimize quality losses due to particle motion (agitation intensity) and thermal damage (severity of thermal processing). [ABSTRACT FROM AUTHOR]

We consider a general model for a non-Newtonian fluid of second grade which is capable of describing shear thinning and shear thickening effects. The model incorporates parameters m and n which are varied to account for which effect, shear thinning or thickening, is desired in the tangential and normal shear rate directions, although here we restrict attention to the shear thickening case. By constructing a generalized energy-like equation and manipulating this we show that the solution may exhibit finite-time blow up if the initial data are regular enough for the solution to exist for a sufficiently long time. The nature of the blow up, or nonexistence, behavior depends critically on the normal stress coefficients α 1 and α 2 , and on the parameters m and n . [ABSTRACT FROM AUTHOR]

This work deals with the accuracy of non-Newtonian Lattice Boltzmann simulations. Previous work for Newtonian fluids indicate that, depending on the numerical value of the dimensionless collision frequency Ω, additional artificial viscosity is introduced, which negatively influences the accuracy. Since the non-Newtonian fluid behavior is incorporated through appropriate modeling of the dimensionless collision frequency, a Ω dependent error E Ω is introduced and its influence on the overall error is investigated. Here, simulations with the SRT and the MRT model are carried out for power-law fluids in order to numerically investigate the accuracy of non-Newtonian Lattice Boltzmann simulations. A goal of this accuracy analysis is to derive a recommendation for an optimal choice of the time step size and the simulation Mach number, respectively. For the non-Newtonian case, an error estimate for E Ω in the form of a functional is derived on the basis of a series expansion of the Lattice Boltzmann equation. This functional can be solved analytically for the case of the Hagen–Poiseuille channel flow of non-Newtonian fluids. With the help of the error functional, the prediction of the global error minimum of the velocity field is excellent in regions where the E Ω error is the dominant source of error. With an optimal simulation Mach number, the simulation is about one order of magnitude more accurate. Additionally, for both collision models a detailed study of the convergence behavior of the method in the non-Newtonian case is conducted. The results show that the simulation Mach number has a major impact on the convergence rate and second order accuracy is not preserved for every choice of the simulation Mach number. [ABSTRACT FROM AUTHOR]

Many foods are suspensions of solid particles randomly distributed in a non-Newtonian polymeric fluid. The rheological properties of high molecular weight poly(ethylene oxide) (PEO) and carboxymethyl cellulose (CMC) suspensions by adding micro-metric solid particles such as fibres or spheres were studied. The particle volume fraction, Φ , was varied between 0 and 0.4. Their rheological properties were obtained after fitting a Cross model. Rheological behaviour of the solutions was compared with rheological behaviour of food reported in the literature. For PEO and CMC solutions with spherical particle, the behaviour of the normalized steady shear viscosity, μ / μ 0 , as function of the fraction volume was compared with a Thomas model. However, for PEO the multibody interactions were not well represented and for CMC suspensions, μ / μ 0 seems to be lineal with Φ. To observe and explain more the influence of the particle concentrations on the rheological behaviour, dynamic rheological measurements (upon verification of the linearity limit) were also performed. A transition from a dominantly viscous fluid to a dominantly elastic material was observed when Φ was increased. [ABSTRACT FROM AUTHOR]

Many small organisms self-propel in viscous fluids using travelling wave-like deformations of their bodies or appendages. Examples include small nematodes moving through soil using whole-body undulations or spermatozoa swimming through mucus using flagellar waves. When self-propulsion occurs in a non-Newtonian fluid, one fundamental question is whether locomotion will occur faster or slower than in a Newtonian environment. Here we consider the general problem of swimming using small-amplitude periodic waves in a viscoelastic fluid described by the classical Oldroyd-B constitutive relationship. Using Taylor׳s swimming sheet model, we show that if all travelling waves move in the same direction, the locomotion speed of the organism is systematically decreased. However, if we allow waves to travel in two opposite directions, we show that this can lead to enhancement of the swimming speed, which is physically interpreted as due to asymmetric viscoelastic damping of waves with different frequencies. A change of the swimming direction is also possible. By analysing in detail the cases of swimming using two or three travelling waves, we demonstrate that swimming can be enhanced in a viscoelastic fluid for all Deborah numbers below a critical value or, for three waves or more, only for a finite, non-zero range of Deborah numbers, in which case a finite amount of elasticity in the fluid is required to increase the swimming speed. [ABSTRACT FROM AUTHOR]

We prove a version of the negative norm theorem in Orlicz–Sobolev spaces. A study of boundedness properties of the Bogovskiĭ operator between Orlicz spaces is a crucial step, of independent interest, in our approach. Applications to the problem of pressure reconstruction for non-Newtonian fluids governed by constitutive laws, which are not necessarily of power type, are presented. A key inequality for a numerical analysis of the underlying elliptic system is also derived. [ABSTRACT FROM AUTHOR]

We describe forced drainage experiments of foams made with model surfactant solutions with different surface rheology. We analyze the origin of two distinct drainage transitions reported in the literature, between regimes where the bubble surfaces are mobile or rigid. We propose that both transitions are related to the surface shear viscosity and to its shear thinning behavior. Shear thinning could also account for the huge discrepancies between measurements reported in the literature. The role of surface tension gradients, i.e. Marangoni effect, could not possibly explain the behavior observed with the different solutions. [ABSTRACT FROM AUTHOR]

We present a hybrid particle-mesh method for numerically solving the hydrodynamic equations of incompressible active polar viscous gels. These equations model the dynamics of polar active agents, embedded in a viscous medium, in which stresses are induced through constant consumption of energy. The numerical method is based on Lagrangian particles and staggered Cartesian finite-difference meshes. We show that the method is second-order and first-order accurate with respect to grid and time-step sizes, respectively. Using the present method, we simulate the hydrodynamics in rectangular geometries, of a passive liquid crystal, of an active polar film and of active gels with topological defects in polarization. We show the emergence of spontaneous flow due to Fréedericksz transition, and transformation in the nature of topological defects by tuning the activity of the system. [ABSTRACT FROM AUTHOR]

Hypothesis The process of dried blood spot sampling involves simultaneous spreading and penetration of blood into a porous filter paper with subsequent evaporation and drying. Spreading of small drops of blood, which is a non-Newtonian liquid, over a dry porous layer is investigated from both theoretical and experimental points of view. Experiments and theory A system of two differential equations is derived, which describes the time evolution of radii of both the drop base and the wetted region inside the porous medium. The system of equations does not include any fitting parameters. The predicted time evolutions of both radii are compared with experimental data published earlier. Findings For a given power law dependency of viscosity of blood with different hematocrit level, radii of both drop base and wetted region, and contact angle fell on three universal curves if appropriate scales are used with a plot of the dimensionless radii of the drop base and the wetted region inside the porous layer and dynamic contact angle on dimensionless time. The predicted theoretical relationships are three universal curves accounting satisfactorily for the experimental data. [ABSTRACT FROM AUTHOR]