Search

In this paper, the rise behaviors of Taylor bubbles are investigated in sudden/gradual tubes filled with viscoelastic media via grid adaptive direct numerical simulations (DNS). The exponential Phan–Thien–Tanner (PTT) constitutive model is used to describe the viscoelastic rheological characteristics, and the phase interface is captured via the volume of fluid (VOF) method. The effects of tube structure (diameter ratio and structural angle) and fluid elasticity (expressed by the Weissenberg number Wi) on bubble dynamics have been studied. Our results indicate that bubbles are prone to rupture in the expansion tubes, mainly due to the dual effects of the wall and the elastic relaxation. The fluid elasticity suppresses the jet effect in a sudden expansion tube. Meantime, as the structural angle or the diameter ratio increases, the wall effect is weakened on axial or radial scales, inhibiting the bubble rupture. A large structure angle attenuates the wall effect, while changes in the diameter ratio slow down the radial momentum transfer near the wall region, both of which favor bubble integrity. We also obtain an exponential relationship between the critical rupture time and the structure angle. The dynamical Taylor bubbles can be operated by the structure of the tube and surrounding fluid viscoelasticity, which is of great significance in chemical engineering applications involving complex non-Newtonian fluids. [ABSTRACT FROM AUTHOR]

The combined effect of second sound and the viscoelasticity is examined using the classical stability analysis on the onset of rotating porous medium ferroconvection. Local thermal equilibrium is assumed between the solid matrix and fluid. Present problem is examined by an analytical approach by considering the pertinent boundary conditions. Normal mode analysis technique is utilized for obtaining the critical values for both instabilities namely stationary and oscillatory. We noticed that the oscillatory mode of instability is favored over the stationary mode of instability. We found that magnetic forces, second sound, nonlinearity in magnetization, Vadasz number, stress relaxation due to viscoelasticity and Taylor-Darcy number are in favour of advancing oscillatory porous medium ferroconvection whereas strain retardation postpone the outset of oscillatory porous medium ferroconvection. Convection cell size effects by different parameters and the oscillation’s frequency are also noted. This problem shall have significant feasible technological applications wherein viscoelastic magnetic fluids are involved.

In this paper we consider the vanishing viscosity limit of solutions to the initial boundary value problem for the compressible viscoelastic equations in the half space. When the initial deformation gradient does not degenerate and there is no vacuum initially, we establish the uniform regularity estimates of solutions to the initial-boundary value problem for the three-dimensional compressible viscoelastic equations in the Sobolev spaces. Then we justify the vanishing viscosity limit of solutions of the compressible viscoelastic equations based on the uniform regularity estimates and the compactness arguments. Both the no-slip boundary condition and the Navier-slip type boundary condition on velocity are addressed in this paper. On the one hand, for the corresponding vanishing viscosity limit of the compressible Navier-Stokes equations with the no-slip boundary condition, it is impossible to derive such uniform energy estimates of solutions due to the appearance of strong boundary layers. Consequently, our results show that the deformation gradient can prevent the formation of strong boundary layers. On the other hand, our results also provide two different kinds of boundary conditions suitable for the well-posedness of the initial-boundary value problem of the elastodynamic equations via the method of vanishing viscosity. Finally, it is worth noting that we take advantage of the Lagrangian coordinates to study the vanishing viscosity limit for the fixed boundary problem in this paper. [ABSTRACT FROM AUTHOR]

The stress singularity is determined using matched asymptotics for complete flow of a White–Metzner (WM) fluid around a re-entrant corner. The model is considered in the absence of a solvent viscosity, with power-law forms for the relaxation time and polymer viscosity. In this form, the model shares the same stress singularity as the upper convected Maxwell (UCM) model, but its wall boundary layers may be thinner or thicker than those for UCM depending upon the relative difference in the power-law exponents. If the exponent for the relaxation time is greater than that for the polymer viscosity, the boundary layer is narrower, whilst it is thicker if the polymer viscosity exponent exceeds that of the relaxation time. When the exponents are the same, the WM boundary layer thickness is the same size as that for UCM. A self-similar solution is derived for the stress and velocity fields and matched to both upstream and downstream boundary layers. Restrictions on the sizes of the power-law exponents are also given for validity of this solution. [ABSTRACT FROM AUTHOR]

Reduced-order models (ROMs) have been widely adopted in fluid mechanics, particularly in the context of Newtonian fluid flows. These models offer the ability to predict complex dynamics, such as instabilities and oscillations, at a considerably reduced computational cost. In contrast, the reduced-order modelling of non-Newtonian viscoelastic fluid flows remains relatively unexplored. This work leverages the sparse identification of nonlinear dynamics (SINDy) algorithm to develop interpretable ROMs for viscoelastic flows. In particular, we explore a benchmark oscillatory viscoelastic flow on the four-roll mill geometry using the classical Oldroyd-B fluid. This flow exemplifies many canonical challenges associated with non-Newtonian flows, including transitions, asymmetries, instabilities, and bifurcations arising from the interplay of viscous and elastic forces, all of which require expensive computations in order to resolve the fast timescales and long transients characteristic of such flows. First, we demonstrate the effectiveness of our data-driven surrogate model to predict the transient evolution and accurately reconstruct the spatial flow field for fixed flow parameters. We then develop a fully parametric, nonlinear model capable of capturing the dynamic variations as a function of the Weissenberg number. While the training data are predominantly concentrated on a limit cycle regime for moderate [Formula: see text], we show that the parametrized model can be used to extrapolate, accurately predicting the dominant dynamics in the case of high Weissenberg numbers. The proposed methodology represents an initial step in applying machine learning and reduced-order modelling techniques to viscoelastic flows.

This study explores the influence of thermal radiation and heat source on magnetized flow micropolar nanofluid through a Stretchable Sheet in the presence of mobile microbes. The presence of microorganisms adds a biological dimension to the problem, affecting fluid dynamics and heat transfer, which are central to this investigation. To motivate the problem, the flow is induced by a Darcy porous exponentially stretching sheet with generalized boundary conditions. A regression analysis is conducted to analyze the interplay of various parameters on the flow and heat transfer characteristics. Additionally, similarity transformations are implemented to transform the set of partial differential equations (PDEs) into a set of ordinary differential equations (ODEs). The resulting equations are solved numerically using the shooting approach via the bvp4c platform in Matlab. The regression model quantifies the impact of each parameter and their interactions on the flow field, temperature distribution, and Darcy effects. Furthermore, the impact of involved parameters on flow, energy, volumetric concentration, density of microbes, and micro-rotations distribution are analyzed and discussed through graphs, literature, and tables. The findings of this research are crucial for various engineering, industrial, and pharmaceutical applications, including biofilm formation, geothermal energy extraction, and wastewater treatment processes.

[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]

The combined effect of second sound and the viscoelasticity is examined using the classical stability analysis on the onset of rotating porous medium ferroconvection. Local thermal equilibrium is assumed between the solid matrix and fluid. Present problem is examined by an analytical approach by considering the pertinent boundary conditions. Normal mode analysis technique is utilized for obtaining the critical values for both instabilities namely stationary and oscillatory. We noticed that the oscillatory mode of instability is favored over the stationary mode of instability. We found that magnetic forces, second sound, nonlinearity in magnetization, Vadasz number, stress relaxation due to viscoelasticity and Taylor-Darcy number are in favour of advancing oscillatory porous medium ferroconvection whereas strain retardation postpone the outset of oscillatory porous medium ferroconvection. Convection cell size effects by different parameters and the oscillation's frequency are also noted. This problem shall have significant feasible technological applications wherein viscoelastic magnetic fluids are involved. [ABSTRACT FROM AUTHOR]

Elastic turbulence is an efficient heat transfer method at microscale. In this work, we conduct a systematic investigation on the flow and heat transfer performances of viscoelastic polymer solutions in microchannels with chip arrays by means of high-fidelity numerical simulations. Focusing on the effects of fluid elasticity [i.e. polymer relaxation time (λ)] and flow Reynolds number (Re), we find that the synergistic interplay between inertial and elastic forces is strategically exploited to amplify convection, thereby facilitating an enhanced heat transfer performance. For highly elastic fluid, the Nusselt number (Nu) can be improved by 76.13 % compared to that of less elastic fluid, while the pressure drop is reduced appropriately. In addition, as the fluid elasticity increases, the pressure drop decreases and eventually converges to a constant. In the zone of elastic turbulence, the fluid reinforces the convective heat transfer, which can be ascribe to the deformation of long-chain polymer molecules. Particularly, we consider the effect of temperature-dependent λ on the heat transfer performance. Our results demonstrate that the increased temperature-dependent λ decreases the value of Nu, and the variation between values of variable and constant λ is reduced with increasing Re or λ. Hence, in some cases of large fluid elasticity or high Re, it is possible to safely ignore the impact of temperature-dependent λ with an acceptable accuracy. The present work provides important insights into the enhanced heat transfer via elastic turbulence, which could guide the applications in the field of chip cooling.

Electrothermal pumping is a recently trending method to force highly conductive fluids in a wide range of microfluidics applications with biological processes. Although most polymer fluids (biological and synthetic) are highly conductive exhibiting viscoelastic rheological properties that are relevant to biomedical applications, their behavior under the effect of electrothermal force has not yet been studied. To this aim, the PTT model (non-linear rheological constitutive equation) and electrothermal equations are implemented in the developed OpenFOAM solver. The effect of rheological characteristics of the fluids on the physical parameters such as velocity, elastic behavior, and vortices strength of electrothermal flow are investigated through the viscoelastic non-dimensional numbers. According to the results, electrothermal outlet velocity decreases by 726% as the retardation ratio (β number) increases from 0.2 to 0.9 and increases by 107% as the Weissenberg number raises from 0.001 to 10. Investigating all non-dimensional numbers simultaneously leads to the conclusion that higher electrothermal velocity is achieved by viscoelastic fluids with lower viscosity and higher relaxation time. This fact is useful for choosing the proper fluid for a particular application. As a practical example, 3000 ppm polyethylene oxide solution results in higher velocity in electrothermal flow compared to the 5% polyvinylpyrrolidone and 2000 ppm xanthan gum solution.

Capillary invasion of liquid is a spontaneous phenomenon that occurs at length scales smaller than the capillary length. By means of capillary action, numerous applications have been developed. We investigate the time-dependent displacement of a Newtonian oil using viscoelastic polyethylene oxide solutions. The setup implies a capillary tube in a horizontal configuration that was partially prefilled with oil. We emphasize the prefilling liquid’s role in the dynamics of the system and show the influence of the displacing liquid’s viscoelastic properties. We find significant changes in the capillary regime as the displacing liquid’s viscoelastic properties change.

In this paper, we consider the optimal time decay rates of the higher order spatial derivatives of global solution for the three-dimensional compressible Oldroyd-B model, which was derived independently by Barrett-Lu-Süli [Commun. Math. Sci., 15(5): 1265–1323, 2017] via micro–macro analysis of the compressible Navier–Stokes–Fokker–Planck system. We show that under $ H^3 $ H 3 framework, the third-order spatial derivatives of global small solution of the compressible Oldroyd-B model decay at the rate $ (1+t)^{-\frac 94} $ (1 + t) − 9 4 instead of $ (1+t)^{-\frac 74} $ (1 + t) − 7 4 stated by Wang-Wen [Math. Models Methods Appl. Sci., 30(1): 139–179, 2020]. This decay rate is optimal in the sense that it coincides with that of solutions to heat equation. [ABSTRACT FROM AUTHOR]

Recent green manufacturing demands have boosted the development of new biodegradable lubricants to replace petroleum-based lubricants. In this regard, water-based lubricants have been at the vanguard of recent research for a wide range of industrial applications, including metalworking fluids (MWFs). In this work, we present an experimental investigation on the performance of novel green MWFs based on aqueous nopal mucilage solutions. For this, fully biodegradable solutions with different mucilage concentrations (2.29, 4.58, and 6.85 mg/mL) were evaluated in terms of rheological, tribological, thermal stability, and turning (minimum quantity lubrication) performance and compared to a commercial semisynthetic oil-based MWF (Cimstar 60). Mucilage solutions exhibited viscoelastic shear-thinning behavior, which was enhanced along with mucilage concentration. The solution with the highest mucilage content studied resulted in the lowest wear, friction, and temperature in comparison to the other solutions and neat water in extreme pressure four-ball tests and a similar level of lubricity as compared to the commercial MWF in cutting tests. This performance is associated with the enhanced viscosity and elasticity of the solution, as well as the contents of lipids with fatty acids in the mucilage. Overall, the present results reveal the relevance of the viscoelastic behavior of the lubricant, elasticity in particular, in lubrication processes and point to nopal mucilage as an effective green additive to produce innocuous MWFs. [ABSTRACT FROM AUTHOR]

In this paper, we consider the optimal time decay rates of the higher order spatial derivatives of global solution for the three-dimensional compressible Oldroyd-B model, which was derived independently by Barrett-Lu-Süli [Commun. Math. Sci., 15(5): 1265–1323, 2017] via micro–macro analysis of the compressible Navier–Stokes–Fokker–Planck system. We show that under $ H^3 $ H 3 framework, the third-order spatial derivatives of global small solution of the compressible Oldroyd-B model decay at the rate $ (1+t)^{-\frac 94} $ (1 + t) − 9 4 instead of $ (1+t)^{-\frac 74} $ (1 + t) − 7 4 stated by Wang-Wen [Math. Models Methods Appl. Sci., 30(1): 139–179, 2020]. This decay rate is optimal in the sense that it coincides with that of solutions to heat equation. [ABSTRACT FROM AUTHOR]

Electrothermal pumping is a recently trending method to force highly conductive fluids in a wide range of microfluidics applications with biological processes. Although most polymer fluids (biological and synthetic) are highly conductive exhibiting viscoelastic rheological properties that are relevant to biomedical applications, their behavior under the effect of electrothermal force has not yet been studied. To this aim, the PTT model (non-linear rheological constitutive equation) and electrothermal equations are implemented in the developed OpenFOAM solver. The effect of rheological characteristics of the fluids on the physical parameters such as velocity, elastic behavior, and vortices strength of electrothermal flow are investigated through the viscoelastic non-dimensional numbers. According to the results, electrothermal outlet velocity decreases by 726% as the retardation ratio (β number) increases from 0.2 to 0.9 and increases by 107% as the Weissenberg number raises from 0.001 to 10. Investigating all non-dimensional numbers simultaneously leads to the conclusion that higher electrothermal velocity is achieved by viscoelastic fluids with lower viscosity and higher relaxation time. This fact is useful for choosing the proper fluid for a particular application. As a practical example, 3000 ppm polyethylene oxide solution results in higher velocity in electrothermal flow compared to the 5% polyvinylpyrrolidone and 2000 ppm xanthan gum solution. [ABSTRACT FROM AUTHOR]

The viscoelastic effects on the double diffusive oscillatory flow in a fluid-saturated porous layer are investigated. A modified Darcy–Oldroyd-B model is used to characterize the non-Newtonian fluid behavior flow in a porous layer. Analytic solutions of the dimensionless governing equations of fluid flow are obtained and the effects of the flow parameters on temperature, concentration, velocity profiles, skin friction and rate of heat transfer are discussed and shown graphically. It is interesting to note that skin friction increases on both channel plates as injection increases on the heated plate. Increase in the strain retardation parameter is to decrease the fluid velocity, while an opposite trend is noticed with increasing stress relaxation parameter. The study reiterates that the consideration of viscoelastic fluid is very important in proper considerate of oscillatory flow in double diffusive fluid systems. [ABSTRACT FROM AUTHOR]

We are concerned with the global well-posedness of rate type viscoelastic fluids system (1.1)–(1.2). First, we prove the global existence and decay estimate of solution to (1.1)–(1.2) with stress diffusion near a constant state in H N (R 3) (N ≥ 4). We only assume that the H 3 -norm of initial data is small, but the L 2 -norm of the higher order derivatives can be arbitrary large. If the initial data belongs to homogeneous Sobolev or Besov spaces, we obtain the optimal decay rates of the solution and its higher order derivatives. Next, we establish the local existence of smooth solution to (1.1)–(1.2) without stress diffusion and present a blow-up criterion in R 2. From which and the Bony decomposition, we prove the global existence of smooth solution. [ABSTRACT FROM AUTHOR]

The computation of flows of viscoelastic fluids is expensive compared to standard fluids. Besides degrees-of-freedom for velocity and pressure, the viscoelastic stresses introduce an additional unknown to the system. While adaptive meshing techniques are commonly used for simulations of standard fluids, their application is seldom explored in the context of viscoelastic fluids. In this work, we apply an anisotropic mesh adaptation algorithm to solve the viscoelastic flow problem. Our flow solver is based on a logarithmic reformulation of the viscoelastic constitutive laws, which greatly reduces the stringent stability requirements on the mesh size and allows adaptive meshing in this context. For discretization, we use a stabilized finite element method. We present numerical results for a flow past a cylinder. The adaptive method produces near mesh-independent results up to Weissenberg number Wi = 0.7. Our results indicate that with an anisotropic refinement strategy, fewer mesh elements are needed to maintain the same error level as with an isotropic refinement strategy. In a stick-slip transition flow, we demonstrate the capability of the adaptive method to produce optimal meshes even in the presence of a singularity in the solution. • Robust low-order finite element method to solve the viscoelastic flow problem. • Automatic accurate stress profile predictions in the wake region of a cylinder flow. • Optimal mesh gradation in a Stick-Slip transition flow. [ABSTRACT FROM AUTHOR]

This paper presents a numerical simulation of the tunneling rupture behavior of bubbles in microchannels using OpenFOAM. The fluid properties were characterized by the Giesekus model, and the interface was tracked by the volume of fluid (VOF) method. The effects of relaxation time λ and flow velocity u on the bubble tunneling rupture behavior were examined. The results indicated that the axial length of the bubble first increases and then remains constant as the relaxation time increases. The presence of elastic force accelerates the neck refinement in the pinch-off stage. In viscoelastic fluids, the head of the bubble is closer to the inner wall than in Newtonian fluids, influenced by the first normal stress difference. Furthermore, the tail of the bubble changes from convex to concave, and the time for the bubble to reach the rupture stage accelerates with increasing flow velocity, shortening the bubble rupture cycle. The effect of the bubble rupture period was also scrutinized at various Weissenberg numbers. The results showed that the bubble rupture period increases with the Weissenberg number, indicating that the presence of elasticity slows down the bubble rupture process. [ABSTRACT FROM AUTHOR]

The present investigation analyzes the transient multilayer electro-osmotic flow through an annular microchannel with hydrophobic walls. The fluids are considered immiscible and viscoelastic, following the Maxwell rheological model. In the problem examined, the linearized Poisson–Boltzmann and Cauchy momentum equations are used to determine the electric potential distribution and the flow field, respectively. Here, different interfacial phenomena are studied through the imposed boundary conditions, such as the hydrodynamic slip and specified zeta potentials at solid–liquid interfaces, the velocity continuity, the electroviscous stresses balance, the potential difference, and the continuity of electrical displacements at the interfaces between fluids. The semi-analytic solution uses the Laplace transform theory. In the results, the velocity profiles and velocity tracking show the oscillatory behavior of flow, which strongly depends on the dimensionless relaxation time. Furthermore, the hydrodynamic slip on the channel walls contributes to the release of energy stored in the fluids due to elastic effects at the start-up of the flow. Similarly, other dimensionless parameters are also investigated. This research aims to predict the parallel flow behavior in microfluidic devices under electro-osmotic effects. [ABSTRACT FROM AUTHOR]

Capillary invasion of liquid is a spontaneous phenomenon that occurs at length scales smaller than the capillary length. By means of capillary action, numerous applications have been developed. We investigate the time-dependent displacement of a Newtonian oil using viscoelastic polyethylene oxide solutions. The setup implies a capillary tube in a horizontal configuration that was partially prefilled with oil. We emphasize the prefilling liquid’s role in the dynamics of the system and show the influence of the displacing liquid’s viscoelastic properties. We find significant changes in the capillary regime as the displacing liquid’s viscoelastic properties change. [ABSTRACT FROM AUTHOR]

A numerical study was conducted on the interaction of bubbles with different diameters and arrangements in shear-thinning viscoelastic fluids using OpenFOAM. The Volume of Fluid (VOF) method combined with the surface tension model was used to track the gas–liquid interface, and the rheological properties of the fluid were characterized with the Giesekus model. The numerical results are corresponded with the previous references, verifying the correctness of the simulation method. The influences of the initial bubble diameter, horizontal spacing, and arrangement on the motion state of three parallel bubbles were studied in detail. The flow pattern of the bubble rising was analyzed and compared with the motion state of parallel unequal double bubbles. As the diameter of the bubbles increases, the interaction among three equal size bubbles is changed from coalescence to detachment. Changing the diameter of one of the bubbles will significantly affect the movement of the larger diameter bubble, which is due to the enhancement in kinetic energy. The final state of some arrangement ways is consistent with the phenomenon of unequal double bubbles. The shear thinning effect, the velocity difference between bubbles, and the flow field around bubbles are considered the main reasons that decide the interaction between bubbles. [ABSTRACT FROM AUTHOR]

Elasticity is commonly associated with regular oscillations, which are prevalent in various systems at different scales. However, chaotic oscillations are rarely connected to elasticity. While overdamped chaotic systems have received significant attention, there has been limited exploration of elasticity-driven systems. In this study, we investigate the influence of elasticity on the dynamics of chaotic systems by examining diverse models derived from mechanics, immunology, ecology, and rheology. Through numerical MATLAB simulations obtained by using an ode15s solver, we observe that elasticity profoundly alters the chaotic dynamics of these systems. As a result, we term the underlying equations as the elastic-Lorenz equations. Specifically, we extensively analyze a viscoelastic fluid confined within a closed-loop thermosyphon, considering general heat flux, to demonstrate the impact of the viscoelastic parameter on the model's chaotic behavior. Our findings build upon prior research on the asymptotic behavior of this model by incorporating the presence of a viscoelastic fluid. The results highlight the non-trivial and non-monotonic role of elasticity in understanding the control, or lack thereof, of chaotic behavior across different scales. [ABSTRACT FROM AUTHOR]

In this paper, we consider an initial-value problem for the three-dimensional incompressible Phan-Thien–Tanner (PTT) model. This model is regard to the dynamic mechanical properties of polymeric fluids. We shall mainly investigate two different cases, one is without damping on the stress tensor (i.e. a = 0) and the other is a > 0. Under some suitable assumptions on the initial data, we show that the solutions of the PTT model will blow up in finite time. This result also reveals a special solution. Furthermore, we prove the global existence and the optimal time decay rates of strong solutions to the PTT model when the initial data close enough to this special solution. In particular, it also works for the simpler case of the Oldroyd-B model. [ABSTRACT FROM AUTHOR]

pH-responsive viscoelastic fluids are often achieved by adding hydrotropes into surfactant solutions. However, the use of metal salts to prepare pH-responsive viscoelastic fluids has been less documented. Herein, a pH-responsive viscoelastic fluid was developed by blending an ultra-long-chain tertiary amine, N-erucamidopropyl-N, N-dimethylamine (UC22AMPM), with metal salts (i.e., AlCl3, CrCl3, and FeCl3). The effects of the surfactant/metal salt mixing ratio and the type of metal ions on the viscoelasticity and phase behavior of fluids were systematically examined by appearance observation and rheometry. To elucidate the role of metal ions, the rheological properties between AlCl3− and HCl−UC22AMPM systems were compared. Results showed the above metal salt evoked the low-viscosity UC22AMPM dispersions to form viscoelastic solutions. Similar to HCl, AlCl3 could also protonate the UC22AMPM into a cationic surfactant, forming wormlike micelles (WLMs). Notably, much stronger viscoelastic behavior was evidenced in the UC22AMPM−AlCl3 systems because the Al3+ as metal chelators coordinated with WLMs, promoting the increment of viscosity. By tuning the pH, the macroscopic appearance of the UC22AMPM−AlCl3 system switched between transparent solutions and milky dispersion, concomitant with a viscosity variation of one order of magnitude. Importantly, the UC22AMPM−AlCl3 systems showed a constant viscosity of 40 mPa·s at 80 °C and 170 s−1 for 120 min, indicative of good heat and shear resistances. The metal-containing viscoelastic fluids are expected to be good candidates for high-temperature reservoir hydraulic fracturing. [ABSTRACT FROM AUTHOR]

We consider the free boundary problem of compressible isentropic neo-Hookean viscoelastic fluid equations with surface tension. Under the physical kinetic and dynamic conditions proposed on the free boundary, we investigate the regularity of classical solutions to viscoelastic fluid equations in Sobolev spaces which are uniform in viscosity and justify the corresponding vanishing viscosity limits. The key ingredient of our proof is that the deformation gradient tensor in Lagrangian coordinates can be represented as a parameter in terms of the flow map so that the inherent structure of the elastic term improves the uniform regularity of normal derivatives in the limit of vanishing viscosity. This result indicates that the boundary layer does not appear in the free boundary problem of compressible viscoelastic fluids, which is different from the case studied by Mei et al. (2018) for the free boundary compressible Navier-Stokes system. [ABSTRACT FROM AUTHOR]

We study a model for a fluid showing viscoelastic and viscoplastic behavior, which describes the flow in terms of the fluid velocity and a symmetric deviatoric stress tensor. This stress tensor is transported via the Zaremba-Jaumann rate, and it is subject to two dissipation processes: one induced by a nonsmooth convex potential and one by stress diffusion. We show short-time existence of strong solutions as well as their uniqueness in a class of Leray-Hopf-type weak solutions satisfying the tensorial component in the sense of an evolutionary variational inequality. The global-in-time existence of such generalized solutions has been established in a previous work. We further study the limit when stress diffusion vanishes. In this case, the above notion of generalized solutions is no longer suitable, and we introduce the concept of energy-variational solutions, which is based on an inequality for the relative energy. We derive general properties of energy-variational solutions and show their existence by passing to the nondiffusive limit in the relative energy inequality satisfied by generalized solutions for nonzero stress diffusion.

Article highlights We obtain reliable results for the temporal and spatial discretization for a challenging viscoelastic FSI benchmark. We show good performance for the dual-weighted residual method for pure viscoelastic problems and for viscoelastic FSI. The viscoelasticity has a significant impact on the functionals of interest for the benchmarks and for the human eye.

It is considered the unsteady and incompressible magnetohydrodynamic rotating free convection flow of viscoelastic fluid with simultaneous heat and mass transfer near an infinite vertical oscillating porous plate under the influence of uniform transverse magnetic field and taking Hall current into account. The governing equations of the flow field are then solved by a regular perturbation method for a small elastic parameter. The expressions for the velocity, temperature, and concentration have been derived analytically and also its behavior is computationally discussed with reference to different flow parameters with the help of graphs. The skin friction on the boundary, the heat flux in terms of the Nusselt number, and the rate of mass transfer in terms of the Sherwood number are also obtained and their behavior discussed. The resultant velocity enhances with increasing Hall parameter and rotation parameter. The reversal behavior is observed with increasing viscoelastic parameters. The resultant velocity enhances and experiences retardation in the flow field with increasing radiation parameters, whereas the secondary velocity component increases with increasing rotation parameters. The temperature diminishes as the Prandtl number and/or the frequency of oscillations. The concentration reduces at all points of the flow field with the increase in the Schmidt number. [ABSTRACT FROM AUTHOR]

Viscoelastic fluids are highly challenging from the rheological standpoint, and their discretization demands robust, efficient numerical solvers. Simulating viscoelastic flows requires combining the Navier–Stokes system with a dynamic tensorial equation, increasing mathematical and computational demands. Hence, fractional‐step methods decoupling the calculation of the flow quantities are an attractive option. In consistent fractional‐step schemes, the splitting of the equations is derived from the continuous level, so that neither mass nor momentum balance is sacrificed. Thus, no corrections or velocity projections are needed, resulting in fewer algorithmic steps than other classical approaches. Moreover, consistency guarantees the absence of both numerical boundary layers and splitting errors, enabling high‐order accuracy in space and time. This article introduces the first consistent splitting methods for incompressible flows of viscoelastic fluids, for which arbitrary constitutive laws are allowed. We present the formulation and the algorithm, along with various numerical examples testing their accuracy. First‐, second‐ and third‐order backward‐differentiation schemes are numerically tested, and optimal convergence is confirmed for several spatial and temporal discretizations. Furthermore, good numerical stability is verified in challenging benchmark problems, including steady and time‐dependent solutions. [ABSTRACT FROM AUTHOR]

When a soft glassy colloidal suspension is displaced by a Newtonian fluid in a radial Hele-Shaw geometry, the pattern morphology that develops at the interface is determined by the complex rheology of the former. We had reported in an earlier work [Palak, V. R. S. Parmar, D. Saha and R. Bandyopadhyay, JCIS Open, 6 (2022) 100047] that a range of pattern morphologies characterised by distinctive structural features can be formed by controlling the elasticity of the displaced suspension, the flow rate of the displacing fluid and the interfacial tension of the fluid pair. Interestingly, all the different morphological features can be distinguished in terms of their areal ratios, defined as the ratio of the areas occupied by the fully-developed pattern and the smallest circle enclosing it. In a significant advance to this earlier work, we show here that a systematic study of spatio-temporal pattern growth can reveal important information about pattern selection mechanisms. We analyse the time-evolution of the patterns to reveal interesting correlations between their growth mechanisms and fully-developed morphologies. We believe that such systematic identification of the unique temporal features characterising pattern growth at the interface between an aging viscoelastic clay suspension and a Newtonian fluid can be useful in pre-empting and suppressing the onset and evolution of interfacial instabilities in the displacement of mud and cement slurries.

The classical stability analysis is used to examine the combined effect of viscoelasticity and the second sound on the onset of porous medium ferroconvection. The fluid and solid matrix are assumed to be in local thermal equilibrium. Considering the boundary conditions appropriate for an analytical approach, the critical values pertaining to both stationary and oscillatory instabilities are obtained by means of the normal mode analysis. It is observed that the oscillatory mode of instability is preferred to the stationary mode of instability. It is shown that the oscillatory porous medium ferroconvection is advanced through the magnetic forces, nonlinearity in magnetization, stress relaxation due to viscoelasticity, and the second sound. On the other hand, it is observed that the presence of strain retardation and porous medium delays the onset of oscillatory porous medium ferroconvection. The dual nature of the Prandtl number on the Rayleigh number with respect to the Cattaneo number is also delineated. The effect of various parameters on the size of the convection cell and the frequency of oscillations is also discussed. This problem may have possible implications for technological applications wherein viscoelastic magnetic fluids are involved.

Recent green manufacturing demands have boosted the development of new biodegradable lubricants to replace petroleum-based lubricants. In this regard, water-based lubricants have been at the vanguard of recent research for a wide range of industrial applications, including metalworking fluids (MWFs). In this work, we present an experimental investigation on the performance of novel green MWFs based on aqueous nopal mucilage solutions. For this, fully biodegradable solutions with different mucilage concentrations (2.29, 4.58, and 6.85 mg/mL) were evaluated in terms of rheological, tribological, thermal stability, and turning (minimum quantity lubrication) performance and compared to a commercial semisynthetic oil-based MWF (Cimstar 60). Mucilage solutions exhibited viscoelastic shear-thinning behavior, which was enhanced along with mucilage concentration. The solution with the highest mucilage content studied resulted in the lowest wear, friction, and temperature in comparison to the other solutions and neat water in extreme pressure four-ball tests and a similar level of lubricity as compared to the commercial MWF in cutting tests. This performance is associated with the enhanced viscosity and elasticity of the solution, as well as the contents of lipids with fatty acids in the mucilage. Overall, the present results reveal the relevance of the viscoelastic behavior of the lubricant, elasticity in particular, in lubrication processes and point to nopal mucilage as an effective green additive to produce innocuous MWFs.

Fused deposition modelling is one of the most widely used additive manufacturing techniques and the diffusion of 3D printers has increased in popularity even further in recent times. Since high precision is required in 3D printing, a good control over the extrusion process is necessary. In this regard, a crucial phenomenon to be accounted for is the die or extrudate swell, i.e., the enlargement of the cross-section of the strand when coming out of the printer nozzle. While this phenomenon has been studied in large scale extruders, it has not yet been investigated in depth for 3D printing processes. In this work, the die swell phenomenon observed in a printed PLA filament is studied by experiments and fluid dynamic simulations. A novel, easy-to-use, accurate and fast procedure for measuring the value of the die swell ratio during the printing process is developed, accounting for typical errors related to a non-constant strand diameter and possible oscillations of the filament with respect to the extrusion direction. As the printing velocity is increased, a linearly increasing swelling ratio is observed at low printing speeds. The trend flattens at moderate speed values. A sudden increase is found at high printing velocities. The swelling ratio measured with the proposed technique is compared with the results of multi-mode viscoelastic simulations at different temperatures. A fair agreement between the experimental measurements and the numerical predictions is found for printing velocities that are typically employed in commercial 3D printers, supporting the reliability of the developed procedure. [ABSTRACT FROM AUTHOR]

• Induced charge electroosmosis in complex electrochemical scenarios concomitant with multi-ion and polymer rheology. • Asymmetric flow patterns and altered energy /interfacial-force distributions. • Kinetic energy changes due to diverse viscosity ratios and shear-thinning dependencies. • New flow instability features and spectral decay indices due to the addition of polymer molecules. • The strong coupling of electrokinetic transport and fluid flow phenomena in electrochemical interfaces. Induced charge electroosmosis (ICEO) can assist lab-on-a-chip devices and macromolecular separation involving interface, multi-ion species, and solution properties. To supplement the mechanistic insights into the ICEO phenomenon in complex electrochemical scenarios, we numerically address electrokinetic ion transport–fluid flow coupling regulated by multi-ion species and polymer macromolecular rheology around a polarized cylinder. The physics of the ICEO are analysed from multiple perspectives, including the azimuthal velocity, flow type, energy distribution, interfacial ion transport, and electroelastic instability. The main findings are as follows: (1) Deviations under neutral pH conditions (multi-ion species) cause flow field asymmetry and alter the input energy distribution (PE) in the tight double layer. Polymers greatly modify the interfacial force features in ion-enriched regions, as identified by the first stress difference (N 1). (2) The kinetic energy vs. viscosity ratio (β) represents the nonlinear enhancement curve E k = 0.011 * exp (β / 0.64) - 0.0138 due to the weakened effective viscosity R vis . In addition, shear thinning notably lifts the charge density and salt concentration at the cylinder surface, which boosts the PE. (3) Quadrupolar vortex modes impact the positive correlation between β and the ion current (J total) at different pH levels, resulting in less ion current dependence for small β. A low enhancement efficiency occurs at 10-4 ≤ α (molecular anisotropy) ≤ 0.1, whereas a high efficiency exists at α > 0.1. Electroelastic instabilities are confirmed by the spatiotemporal evolution of the velocity fluctuation, with a broadband structural power-law decline in the power spectral density. These results allow microdevice mixing manipulation and disclose non-Newtonian barrier of electrokinetic dynamics. [ABSTRACT FROM AUTHOR]

The present investigation analyzes the transient multilayer electro-osmotic flow through an annular microchannel with hydrophobic walls. The fluids are considered immiscible and viscoelastic, following the Maxwell rheological model. In the problem examined, the linearized Poisson–Boltzmann and Cauchy momentum equations are used to determine the electric potential distribution and the flow field, respectively. Here, different interfacial phenomena are studied through the imposed boundary conditions, such as the hydrodynamic slip and specified zeta potentials at solid–liquid interfaces, the velocity continuity, the electroviscous stresses balance, the potential difference, and the continuity of electrical displacements at the interfaces between fluids. The semi-analytic solution uses the Laplace transform theory. In the results, the velocity profiles and velocity tracking show the oscillatory behavior of flow, which strongly depends on the dimensionless relaxation time. Furthermore, the hydrodynamic slip on the channel walls contributes to the release of energy stored in the fluids due to elastic effects at the start-up of the flow. Similarly, other dimensionless parameters are also investigated. This research aims to predict the parallel flow behavior in microfluidic devices under electro-osmotic effects.

In this paper, we initially study the behavior of the resolvent family associated with the abstract equation u ′ = A u + ∫ 0 t K (t - s) u (s) d s , in abstract interpolation scales, which has a self-interest. Next, we prove the study the abstract semilinear equation u ′ = A u + ∫ 0 t K (t - s) u (s) d s + ∫ 0 t g (t - s , u (s)) d s + f (t , u) , t > 0 , for critical nonlinearities f and g, by means of the ϵ -regular solutions introduced by Arrieta and Carvalho [7]. We prove a result on the existence, a type of uniqueness, and continuous dependence upon the initial data of the solutions, and results on its prolongation, robustness of the continuous dependence, and a blow-up alternative. As applications, we prove the solvability of three interesting partial differential equations with memory and critical nonlinearities. [ABSTRACT FROM AUTHOR]

We present a new and efficient phase‐field solver for viscoelastic fluids with moving contact line based on a dual‐resolution strategy. The interface between two immiscible fluids is tracked by using the Cahn‐Hilliard phase‐field model, and the viscoelasticity incorporated into the phase‐field framework. The main challenge of this approach is to have enough resolution at the interface to approach the sharp‐interface methods. The method presented here addresses this problem by solving the phase field variable on a mesh twice as fine as that used for the velocities, pressure, and polymer‐stress constitutive equations. The method is based on second‐order finite differences for the discretization of the fully coupled Navier–Stokes, polymeric constitutive, and Cahn–Hilliard equations, and it is implemented in a 2D pencil‐like domain decomposition to benefit from existing highly scalable parallel algorithms. An FFT‐based solver is used for the Helmholtz and Poisson equations with different global sizes. A splitting method is used to impose the dynamic contact angle boundary conditions in the case of large density and viscosity ratios. The implementation is validated against experimental data and previous numerical studies in 2D and 3D. The results indicate that the dual‐resolution approach produces nearly identical results while saving computational time for both Newtonian and viscoelastic flows in 3D. [ABSTRACT FROM AUTHOR]

Viscoelastic microfluidics leverages the unique properties of non-Newtonian fluids to manipulate and separate micro- or submicron particles. Channel geometry and dimension are crucial for device performance. Traditional rigid microfluidic devices require numerous iterations of fabrication and testing to optimize these parameters, which is time-consuming and costly. In this work, we developed a flexible microfluidic device using ultra-stretchable and biocompatible Flexdym material to overcome this issue. Our device allows for simultaneous modification of channel dimensions by external stretching. We fabricated a stretchable device with an initial square microchannel (30 μm × 30 μm), and the channel aspect ratio can be adjusted from 1 to 5 by external stretching. Next, the effects of aspect ratio, particle size, flow rate, and poly(ethylene oxide) (PEO) concentration that make the fluid viscoelastic on particle migration were investigated. Finally, we demonstrated the feasibility of our approach by testing channels with an aspect ratio of 3 for the separation of both particles and cells.

Reduced-order models (ROMs) have been widely adopted in fluid mechanics, particularly in the context of Newtonian fluid flows. These models offer the ability to predict complex dynamics, such as instabilities and oscillations, at a considerably reduced computational cost. In contrast, the reduced-order modelling of non-Newtonian viscoelastic fluid flows remains relatively unexplored. This work leverages the sparse identification of nonlinear dynamics (SINDy) algorithm to develop interpretable ROMs for viscoelastic flows. In particular, we explore a benchmark oscillatory viscoelastic flow on the four-roll mill geometry using the classical Oldroyd-B fluid. This flow exemplifies many canonical challenges associated with non-Newtonian flows, including transitions, asymmetries, instabilities, and bifurcations arising from the interplay of viscous and elastic forces, all of which require expensive computations in order to resolve the fast timescales and long transients characteristic of such flows. First, we demonstrate the effectiveness of our data-driven surrogate model to predict the transient evolution and accurately reconstruct the spatial flow field for fixed flow parameters. We then develop a fully parametric, nonlinear model capable of capturing the dynamic variations as a function of the Weissenberg number. While the training data are predominantly concentrated on a limit cycle regime for moderate W i , we show that the parametrized model can be used to extrapolate, accurately predicting the dominant dynamics in the case of high Weissenberg numbers. The proposed methodology represents an initial step in applying machine learning and reduced-order modelling techniques to viscoelastic flows., Competing Interests: We declare we have no competing interests., (© 2024 The Author(s).)

Elasticity is commonly associated with regular oscillations, which are prevalent in various systems at different scales. However, chaotic oscillations are rarely connected to elasticity. While overdamped chaotic systems have received significant attention, there has been limited exploration of elasticity-driven systems. In this study, we investigate the influence of elasticity on the dynamics of chaotic systems by examining diverse models derived from mechanics, immunology, ecology, and rheology. Through numerical MATLAB simulations obtained by using an ode15s solver, we observe that elasticity profoundly alters the chaotic dynamics of these systems. As a result, we term the underlying equations as the elastic-Lorenz equations. Specifically, we extensively analyze a viscoelastic fluid confined within a closed-loop thermosyphon, considering general heat flux, to demonstrate the impact of the viscoelastic parameter on the model’s chaotic behavior. Our findings build upon prior research on the asymptotic behavior of this model by incorporating the presence of a viscoelastic fluid. The results highlight the non-trivial and non-monotonic role of elasticity in understanding the control, or lack thereof, of chaotic behavior across different scales.

A numerical study was conducted on the interaction of bubbles with different diameters and arrangements in shear-thinning viscoelastic fluids using OpenFOAM. The Volume of Fluid (VOF) method combined with the surface tension model was used to track the gas–liquid interface, and the rheological properties of the fluid were characterized with the Giesekus model. The numerical results are corresponded with the previous references, verifying the correctness of the simulation method. The influences of the initial bubble diameter, horizontal spacing, and arrangement on the motion state of three parallel bubbles were studied in detail. The flow pattern of the bubble rising was analyzed and compared with the motion state of parallel unequal double bubbles. As the diameter of the bubbles increases, the interaction among three equal size bubbles is changed from coalescence to detachment. Changing the diameter of one of the bubbles will significantly affect the movement of the larger diameter bubble, which is due to the enhancement in kinetic energy. The final state of some arrangement ways is consistent with the phenomenon of unequal double bubbles. The shear thinning effect, the velocity difference between bubbles, and the flow field around bubbles are considered the main reasons that decide the interaction between bubbles.

pH-responsive viscoelastic fluids are often achieved by adding hydrotropes into surfactant solutions. However, the use of metal salts to prepare pH-responsive viscoelastic fluids has been less documented. Herein, a pH-responsive viscoelastic fluid was developed by blending an ultra-long-chain tertiary amine, N-erucamidopropyl-N, N-dimethylamine (UC22AMPM), with metal salts (i.e., AlCl3, CrCl3, and FeCl3). The effects of the surfactant/metal salt mixing ratio and the type of metal ions on the viscoelasticity and phase behavior of fluids were systematically examined by appearance observation and rheometry. To elucidate the role of metal ions, the rheological properties between AlCl3− and HCl−UC22AMPM systems were compared. Results showed the above metal salt evoked the low-viscosity UC22AMPM dispersions to form viscoelastic solutions. Similar to HCl, AlCl3 could also protonate the UC22AMPM into a cationic surfactant, forming wormlike micelles (WLMs). Notably, much stronger viscoelastic behavior was evidenced in the UC22AMPM−AlCl3 systems because the Al3+ as metal chelators coordinated with WLMs, promoting the increment of viscosity. By tuning the pH, the macroscopic appearance of the UC22AMPM−AlCl3 system switched between transparent solutions and milky dispersion, concomitant with a viscosity variation of one order of magnitude. Importantly, the UC22AMPM−AlCl3 systems showed a constant viscosity of 40 mPa·s at 80 °C and 170 s−1 for 120 min, indicative of good heat and shear resistances. The metal-containing viscoelastic fluids are expected to be good candidates for high-temperature reservoir hydraulic fracturing.

We consider the system of partial differential equations governing two-dimensional flows of a robust class of viscoelastic rate-type fluids with stress diffusion, involving a general objective derivative. The studied system generalizes the incompressible Navier–Stokes equations for the fluid velocity v and pressure p by the presence of an additional term in the constitutive equation for the Cauchy stress expressed in terms of a positive definite tensor B . The tensor B evolves according to a diffusive variant of an equation that can be viewed as a combination of corresponding counterparts of Oldroyd-B and Giesekus models. Considering spatially periodic problem, we prove that for arbitrary initial data and forcing in appropriate L 2 spaces, there exists a unique globally defined weak solution to the equations of motion, and more regular initial data and forcing launch a more regular solution with B positive definite everywhere. [ABSTRACT FROM AUTHOR]

Elasto-inertial turbulence (EIT), a new turbulent state found in polymer solutions with viscoelastic properties, is associated with drag-reduced turbulence. However, the relationship between EIT and drag-reduced turbulence is not currently well-understood, and it is important to elucidate the mechanism of the transition to EIT. The instability of viscoelastic fluids has been studied in a canonical wall-bounded shear flow to investigate the transition process of EIT. In this study, we numerically deduced that an instability occurs in the linearly stable viscoelastic plane Couette flow for lower Reynolds numbers, at which a non-linear unstable solution exists. Under instability, the flow structure is elongated in the spanwise direction and regularly arranged in the streamwise direction, which is a characteristic structure of EIT. The regularity of the flow structure depends on the Weissenberg number, which represents the strength of elasticity; the structure becomes disordered under high Weissenberg numbers. In the energy spectrum of velocity fluctuations, a steep decay law of the structure's scale towards a small scale is observed, and this can be recognized as a ubiquitous feature of EIT. The existence of instability in viscoelastic plane Couette flow supports the idea that the transitional path toward EIT may be mediated by subcritical instability. [ABSTRACT FROM AUTHOR]

Polymer components are shaped mostly out of the molten state. As in the case of semi-crystalline polymers, crystallization can be suppressed by shock cooling, thermal process design allows to influence the solid bodies properties. A simulation approach that enables to predict these properties based on a forecast of crystallinity is presented in this paper. The main effects to consider and possibilities of modeling and simulation are discussed. A detailed description of how to create an experimental foundation using dynamic scanning calorimetry (DSC) and a rheometer is provided. Suppression of crystallization is modeled by a novel phenomenological approach, based on data over a large band of cooling rates. Special focus is put on parameter identification and extension of insufficient DSC data. The mechanical behavior is modeled using a weighted approach based on a nonlinear-thermoviscoelastic model for the molten state and a highly viscous Newtonian model for the solid state. Parameterization of both models is highlighted. An implementation in OpenFOAM is documented, emphasizing specific methods that were applied. Results of simulations for a simplified profile extrusion and injection molding case are presented. Basic relationships are forecasted correctly by the method, and important findings are presented for both processes. [ABSTRACT FROM AUTHOR]