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Many microorganisms propel themselves through complex media by deforming their flagella. The beat is thought to emerge from interactions between forces of the surrounding fluid, the passive elastic response from deformations of the flagellum and active forces from internal molecular motors. The beat varies in response to changes in the fluid rheology, including elasticity, but there are limited data on how systematic changes in elasticity alter the beat. This work analyses a related problem with fixed-strength driving force: the emergence of beating of an elastic planar filament driven by a follower force at the tip of a viscoelastic fluid. This analysis examines how the onset of oscillations depends on the strength of the force and viscoelastic parameters. Compared to a Newtonian fluid, it takes more force to induce the instability in viscoelastic fluids, and the frequency of the oscillation is higher. The linear analysis predicts that the frequency increases with the fluid relaxation time. Using numerical simulations, the model predictions are compared with experimental data on frequency changes in the bi-flagellated alga Chlamydomonas reinhardtii. The model shows the same trends in response to changes in both fluid viscosity and Deborah number and thus provides a possible mechanistic understanding of the experimental observations.

We investigate the cross-diffusion on MHD mixed convective thermo-solutal transport in viscoelastic fluid from a nonlinear stretching sheet. The novelty of the work is the analytical evaluation of the nonlinear stretching sheet in a porous medium with a variable magnetic parameter and radiative flux. Also, thermo-solutal transport of a mixed convective flow is analyzed with Dufour and Soret effects in the presence of the chemical reaction, heat source/sink. The governing PDEs are reduced into ODEs by similarity variables. ODEs were tackled analytically using the homotopy analysis method (HAM). The analysis is carried out up to the 15th order of approximation. HAM contains an h-curve, allowing a flexible method of controlling the series solution convergence area. Graphs and tables are plotted to analyze the influence of different parameters on the fluid. Rates of heat and mass flux are depicted using tables. Our results indicate that the increasing viscoelastic flow enhances the boundary layer, and the thermal boundary layer reduces as radiation enhances. The numerical demonstrations of the wall drag coefficient, Nusselt number and Sherwood number have been tabulated. The growing parameters are taken as 0. 5 ≤ M ≤ 2. 0 , 0. 1 ≤ Ri ≤ 0. 7 , 0. 3 ≤ K 0 ≤ 0. 9 , 0. 5 ≤ f w ≤ 2. 0 , 1 ≤ Rd ≤ 4 , 0. 3 ≤ Pr ≤ 0. 9 and 0. 5 ≤ K 2 ≤ 2. 0. [ABSTRACT FROM AUTHOR]

Much attention has been focused on viscoelastic microfluidics which can be widely used for the focusing and separation of particles/cells in continuous flows without any external force or energy. In this study, we demonstrate that microparticles can be separated by the elasto-inertial focusing and the concentration gradient of viscoelastic fluid in a microchannel with a rhombic cross-sectional shape. We have already presented a simple and robust fabrication method for microchannel with the rhombic cross-section, which was used for particle focusing in viscoelastic polyethylene oxide (PEO) solution. Using the fabricated microfluidic device, we observed the behavior of particles by size in viscoelastic fluids with various concentration gradients and presented their focusing and separation. Separation experiments were performed on 12, 5.0, and 2.1 µm particles, and the optimal separation conditions were sought according to flow rate, sample-to-sheath flow rate ratio, and PEO concentration gradient. [ABSTRACT FROM AUTHOR]

In this article, von Kárman MHD viscoelastic fluid flow with second-grade model through a heated permeable disk on electric field is examined thoroughly. The effects of viscous dissipation and elasticity on fluid motion around the disk, temperature and space-dependent heat source/sink are also examined. Governing partial differential equations are transmitted into ordinary differential equations with similarity functions. Later, nonlinear system of ordinary differential equations was solved with the help of Galerkin finite element method. Accuracy and validity of the method were noticed by comparing our results with the previous literature. Simulations are performed in order to capture the dynamics of the physical situations against the variation of the pertinent parameters. Nature of heat flux and stresses of the physical parameters are discussed. Physical influence of heat flux, heat transfer is exhibited graphically at the surface of disk and increases when the values of Prandtl number are increased, whereas there is a decreasing trend in the rate of heat transfer when the value of Eckert number is increased. [ABSTRACT FROM AUTHOR]

Roll coating is a popular method for applying a thin coating film to a continuous substrate, such as paper or foil. This study aims to investigate analytically the fluid flow through counter rotating rolls using a non-Newtonian model. The governing equation for the constitutive of the Oldroyd-B as a non-Newtonian fluid with momentum equation has been discovered. The nondimensionalizing of the fluid flow equations is done by using suitable dimensionless parameters. The equations are then simplified by using Lubrication Approximation Theory (LAT) to obtain the solution for various quantities. Analytical solutions for the velocity distribution, pressure and pressure gradients have been obtained by regular perturbation method. Numerical integration has been used to calculate separation point, coating thickness, separation force and power input of the fluid. The effect of involved parameter such as Weissenberg number We and viscosity on velocities, pressure gradient and pressure is presented in a variety of graphs and several other results are shown in tables. It has been observed that as the modified capillary number N C a 2 increases, the separation point moves toward the nip region, whereas the coating thickness declines. It has been witnessed that the We serves as the controlling parameter for flow rate, pressure distribution and power input, whereas for the coating thickness, the separation force increases, which are important for coating industries. [ABSTRACT FROM AUTHOR]

The onset of convection in a porous medium saturated by the Oldroyd-type viscoelastic fluid, heated and salted from below, is investigated by incorporating the effects of chemical reactions on boundaries and externally imposed magnetic fields with non-equilibrium temperature conditions. The normal mode technique is used to perform linear stability analysis. The whole study is divided into two parts: (i) the parametric study for stability analysis in the oscillatory case and (ii) the stability analysis with the comparative study between different boundary conditions for controlling parameters for the limited case (in the stationary case, the viscoelastic effect is missing). These boundary surfaces are: (a) realistic bounding surfaces (i.e., rigid–free and free–rigid (R/R, R/F and F/R)) and (b) non-realistic bounding surface, i.e., free–free (F/F). For studying the viscoelastic fluid behavior, i.e., effect of the viscoelastic parameters (i.e., relaxation parameter (λ 1) ) and retardation parameter (λ 2) , we discussed the oscillatory state on free–free boundary surfaces. To analyze the consequences of different controlling parameters, numerical computation has been performed, and the results are illustrated in graphical form. For oscillatory convection, the minimum of the critical Rayleigh number drops as the relaxation parameter ( λ 1) , solute Rayleigh number (RaS) and Lewis number (Le) increase while it increases as the retardation parameter ( λ 2) , Chadrashekhar number (Q) and interphase heat transfer coefficient ( τ) increase. In comparative study for stationary convection, the graphs demonstrate that while the critical Rayleigh number reduces as the value of Damk o ¨ hler number ( χ) grows, it increases along with increase in Chandrashekhar number (Q), interphase heat transfer coefficient ( τ) and Lewis number (Le). [ABSTRACT FROM AUTHOR]

[Display omitted] Harnessing electrical energy from salinity gradients, particularly for powering micro and nanoscale devices, has become a focal point of recent research attention, due to its renewable and biocompatible nature. Much of the reported research in that direction revolves around optimizing the membrane architecture and the charge distribution to maximize the induced electric potential, with no particular emphasis on the fluid rheology. However, many of the modern miniature systems, typically the bio-inspired ones, concern fluids with complex rheological characteristics, where the results for Newtonian solvents may not trivially apply. Here, we hypothesize that the interplay between interfacial electro-mechanics and the fluid rheology can influence the effectiveness of salinity-gradient-modulated electrokinetics significantly – an aspect that has largely remained overlooked. Here we report the first experiments supplemented by a theoretical model that unveil how that the addition of polymers in a solvent modulates the salinity gradient – induced electric potential in a microfluidic channel. Our theoretical framework considers the simplified Phan-Thien Tanner (sPTT) constitutive model, which represents the viscoelastic characteristics of fluids. Experiments were conducted with combined pressure driven and salinity gradient driven flow through microchannel involving dilute solutions of polyethylene oxide (PEO) of different molecular weights and concentrations to successfully validate the theoretical approach. Our findings indicate that the induced electrical potential increased non-linearly with the saline concentration ratio across the microchannel, as compared traditional linear response. Our results demonstrate how the elasticity of fluid may enable realizing an optimal benefit to this effect, by arresting the viscous resistance and uplifting the elastic response via utilizing polymeric inclusions of high relaxation times. These results provide specific insights on preferential windows of augmenting the induced streaming potential by harnessing the viscoelastic nature of the solution and the imposed salt concentration, bearing critical implications in miniature energy harvesting and desalination technology. [ABSTRACT FROM AUTHOR]

In this paper, the impact of slip condition, radiation, constant heat and mass flux subjected to chemical reaction on an unsteady viscoelastic periodic flow is investigated. Further, the effect of an inclined magnetic field, heat source and diffusive thermodynamics of incompressible and electrically conductive fluid are also analyzed. The governing non-linear partial differential equations are solved by perturbation method. The final expressions for flow variables and their corresponding gradients at lower plate y = 0 are furnished. It is observed that the diffusive thermo effect Df improves the velocity and reduces skin friction for large values, an angle of inclination ψ and heat source parameter Q enhance velocity while the viscoelastic parameter decreases the same. Df and Q have opposite effects on temperature and subsides the heat transfer for enlarged values, and it is also noted that the effects of Re, Sc, and Kr increase the mass transfer as seen in the plotted graphs. Additionally, the effect of non-dimensional parameters Gr, Re, Pe, N and H on flow variables and their gradients at y = 0 are portrayed by graph’s and subsequently discussed in detail. [ABSTRACT FROM AUTHOR]

This study examines the gravitational instability of a finitely conducting magnetized viscoelastic fluid, under the influence of radiation pressure within the framework of a generalized hydrodynamic fluid model. The general dispersion relation, valid for strongly and weakly coupled fluids under kinetic and hydrodynamic limits respectively, is derived using normal mode analysis for a transverse wave propagation mode. The obtained Jeans instability criteria, in terms of critical Jeans wavenumbers under both limits, are modified by the presence of radiative effects, viscoelastic compressional speed, and Alfvén wave velocity. The findings highlight that viscoelastic compressional speed and radiative pressure slow the Jeans instability's growth rate, exerting a stabilizing effect on the initiation of gravitational collapse. The present investigation provides valuable insights into the role of radiative mechanisms in the gravitational collapse within the strongly coupled region of molecular cloud clumps. [ABSTRACT FROM AUTHOR]

In this research, we look at the rate of heat and mass transfer in an MHD viscoelastic (Walter's liquid-B model) nanofluid over a stretching sheet when that sheet is subject to heat generation/absorption and thermal radiation. According to the mathematical configuration, the current flow problem follows the fundamental laws of motion and heat transfer. The governing equations have been converted to nonlinear ordinary differential (ODEs) equations using similarity transformations. Using the homotopy analysis method (HAM), we have obtained the numerical solution to the resulting nonlinear ODEs and their associated boundary conditions. The behavior of the problem's resultant equations under the impact of various flow factors is examined graphically, which ensures that the rate of heat transfer reduces with an elevation in the Brownian motion parameter and improves with an increase in the thermophoresis parameter. Greater viscoelastic and stretching parameter values accelerate velocity slip. The nanofluid's viscoelasticity minimizes local skin friction, Nusselt, and Sherwood numbers. It is noticed that the slip parameter substantially influences flow velocity. The momentum boundary layer thickness diminished and the thermal boundary layer thickness flourished as the velocity slip factor enhanced. The general conclusions obtained in this article provide an opportunity to understand the importance of this fluid flow. [ABSTRACT FROM AUTHOR]

An exact similarity solution is worked out for fluid motion in the vicinity of a cylindrical surface in an electrically conducting viscoelastic fluid obeying the Jeffrey model. Cylindrical surface expands axially with linear velocity and has a prescribed surface temperature. The present analysis focuses on the partial slip assumption which gives rise to a nonlinear case Robin-type (mixed) boundary condition in axial velocity. In contrast to a previously published study (J. Mech., vol 31, pp. 69–78, 2015) which only reported local similarity solutions in no-slip case, the present work provides an exact similarity analysis by defining a quadratic surface temperature. The effects of the magnetic field and Joule heating on the momentum and thermal transport phenomena are also scrutinized. A numerical routine is used to solve the equation accurately for a wide range of fluid parameters, including ranges that could not be handled by previous approximate analytical methods that were limited to the no-slip limit. The influences of viscoelasticity and partial slip on the flow behavior are investigated, and the coefficient of skin friction for a Jeffrey fluid is calculated. Obtained results are consistent with the previously published works under special situations. The case of flat surface, which can be obtained as a limiting case of the model, is not even explored in the past. [ABSTRACT FROM AUTHOR]

This study presents a new intelligent computing method based on the Levenberg–Marquardt back-propagation-based supervised neural network (LMB-SNN) for the flow of Oldroyd 4-constant fluid in the forward roll coating process (OFC-FRCP). The mathematical formulations for OFC-FRCP are converted into ordinary differential equations using lubrication approximation theory (LAT) and suitable dimensionless parameters. The analytic expressions for velocity distribution, pressure and pressure gradients have been obtained using Adomian's Decomposition Method (ADM) for several situations. The fluid's separation point and coating thickness are then calculated using integration. The reference dataset for LMB-SNN has been obtained by ADM for multiple scenarios by adjusting various physical variables. The neural network's training, testing and validation are carried out in parallel to minimize the mean-squared error function (MSEF). The proposed LMB-SNN's effectiveness was confirmed by analyzing the MSEF, error histograms and regression plots. The precision of the method is verified by the close agreement between numerical outputs and dataset values. The intelligent numerical results computed using ADM and LMB-SNN are presented in various graphs and tables. The method's accuracy is demonstrated by the numerical outputs closest to the built and dataset values at levels between 1 0 − 9 and 1 0 − 1 2 . [ABSTRACT FROM AUTHOR]

This article is concerned with the boundary layer formations over a deforming plane heated surface in a viscoelastic fluid having temperature-dependent physical properties. Viscoelastic fluid obeys a well-accepted Jeffrey fluid model that characterizes both relaxation and retardation times phenomena. Mathematical modeling is performed by considering exponential variations in viscosity, thermal conductivity, relaxation time, and retardation time with temperature. Transport equations are formulated under the aforesaid assumption and are solved for self-similar solutions using a numerical scheme. Solutions are utilized to generate streamlines and isotherms in both Newtonian and viscoelastic fluids. The momentum and thermal layers are specifically scrutinized for various controlling parameters. Illustrative results are included reflecting the consequences of variable physical properties on the induced viscoelastic fluid motion and accompanying heat transfer. In addition, skin friction factor for Jeffrey fluid with variable properties is evaluated and described. [ABSTRACT FROM AUTHOR]

The separation of particles such as cells and bacteria in viscoelastic fluids has significant applications in biomedical fields. At present, one of the main challenges that limit the application of microfluidic technology is to separate particles in the viscoelastic fluids with different rheological properties. For instance, most existing microfluidic devices can only work in the fluid with a specific rheological property, resulting in the requirement of time-consuming design, manufacturing, testing, and optimization of different devices to separate particles in the fluids with different rheological properties. In this work, a novel hybrid three-stage microfluidic device that was made up of a micropore structure and two gradually contracted microchannels was designed to achieve efficient continuous separation of particles in the viscoelastic fluid over a wide range of rheological properties (0.07 < El < 340.41). Different separation strategies including first focusing, then initial separation, and then precise separation (FISPS) and initial separation and then precise separation (ISPS) were found. The separation strategy ISPS occurred at El < 0.14 while the separation strategy FISPS occurred at El > 8.43. In addition, the transformation of the separation mechanism from ISPS to FISPS was found under different flow conditions in the fluid with the transitional rheological properties (0.21 < El < 1.10). The effect of the flow rate and the rheological property of the fluid on microparticle separation were systematically studied by the experiment. With simple structure, easy operation, high separation efficiency, the present microfluidic device would have great potentials in the biomedical and clinical applications, such as the separation of cells for different patients. [ABSTRACT FROM AUTHOR]

Microfluidic devices have gained popularity in recent years due to their low cost and simplicity. Cell focusing linked with cell counting and cell separation used in clinical tests and point-of-care devices stands towards the top of every list of microfluidic applications. To focus and manipulate particles in a Newtonian medium, inertial microfluidics has been widely used. There is a requirement to replace a significantly more efficient approach given various particle-focusing positions near the channel walls recorded by inertial microfluidics. Here, the synergetic effect of elastic and inertial forces in relatively low-concentration viscoelastic fluids was investigated numerically. Utilizing particle-focusing behavior in straight and serpentine channels with different corner angles, by applying the numerical results obtained using the developed direct numerical simulation method (DNS) for elastic and inertial forces, we created a microchannel with a remarkable performance. As the flow regime transitions to elasto-inertial, where inertial forces are comparable to elastic forces in a straight microchannel, particles tend to concentrate at the channel centerline. As the flow rate increases, however, particle defocusing develops, and shear gradient lift forces ultimately overcome elastic forces in the channel's central region. Given that fluid flows at a higher velocity in the serpentine channel with a corner angle of 75° than in other channels, the Dean drag force induced by secondary flow serves to reduce particle defocusing rate at a given flow rate, making this channel a desirable platform for Elasto-inertial microfluidics. Particle focusing in a vertical direction was noticed as a benefit of elasto-inertial microfluidics, regardless of the geometry or flow rate of the particles passing through the channel. Finally, the impact of particle diameter on focusing behavior was studied. As particle diameter decreases, focusing width decreases and the focusing band shifts to the left side of the cross-section. We expect that the numerical evaluation of using viscoelastic medium in complex geometries can contribute to accelerate the three dimensional particle-focusing mechanism and enhance the efficiency of microdevices for cell and particle manipulation.

The combined heat and mass transfer, the so-called thermosolutal convective problem, has become an attractive field of research in many diversified areas. In this paper, for the first time, oscillatory flow analysis has been carried out for triple diffusive viscoelastic fluid flow in a porous medium. A comprehensive model is developed for the modified Darcy–Brinkman–Oldroyd-B fluid, porous medium, Boussinesq approximation, heat and mass transfer across a finite temperature and concentration difference in the chemical potential of two salts. Triple diffusive viscoelastic fluid flows through porous media have grown significantly as this situation occurs in more than a few applications such as improved oil recovery filtration, liquid complex molding, solidification of liquid crystals, cooling of metallic plate in a bath, exotic lubricants and colloidal solutions, polymer processing, chemical and bioengineering industries, among others. The governing coupled nonlinear partial differential equations with boundary constraints represent the modeled flow problem. In addition, these equations are converted into non-dimensional form by employing suitable non-dimensionalizing quantities. The impacts of the pertinent parameters and related dimensionless numbers on the dimensionless velocity, temperature, concentrations, shear stress, heat and mass transfer are examined for both suction and injection cases. It has been found that when the injection level on the heated plate is increased, the shear rate increases for each channel plate. Furthermore, we recognized that the viscoelastic parameters exhibit an opposite kind of behavior on the velocity, temperature, and concentrations fields. [ABSTRACT FROM AUTHOR]

Bacteria exhibit swimming behavior through the rotation of helical flagellar filaments, a common mode of propulsion for artificial micro-swimmers as well. However, most studies have focused on helical filaments with a uniform radius, leaving limited research on filaments with nonuniform radii. This paper presents a simulation of the hydrodynamics of a rotating helical filament with a nonuniform radius. The degree of nonuniformity is characterized by a radius ratio, β. Using the OpenFOAM platform, a simulation module for non-Newtonian Stokes flow was developed and integrated. The kinematics of the filament were predefined by fixing either the pitch or the helical angle, in addition to the helical radius. Thrust acting on the filament were analyzed with regards to the helical radius ratio, rotation speed, and fluid viscoelasticity. Certain modifications were made to apply the resistive force theory (RFT) to filaments with nonuniform helical radii. Results revealed that when the pitch was fixed, the thrust of the helix varied non-monotonically with the radius ratio, with excessive ratios leading to increased resistance. In contrast, helices with fixed helical angles exhibited an increasing thrust with a higher radius ratio. The thrust was greater in Newtonian fluids compared to non-Newtonian fluids, and the propulsion of the helix was influenced by the Deborah number. As the Deborah number approached zero, the thrust of viscoelastic swimming speed approached that of viscous swimming speed. For small, β (, β =1 and 4), the ratio of the thrust in viscoelastic fluid to the thrust in viscous fluid was always less than unity. At, β = 9, elasticity hindered propulsion at low De (De<1.5), while the opposite was observed at high De (De>1.5). A new approach was proposed to evaluate the impact of viscoelasticity on the helix, it was expected that the new calculation method can reduce the computational effort effectively. [ABSTRACT FROM AUTHOR]

Electrohydrodynamic (EHD) conduction pumping can be applied in many macroscopic devices accompanied by a high electric field intensity (106 V/m). Microscale flow generation has become increasingly important with the widespread development of thermal management devices, which are currently used to cool high heat flux sources with small surface areas and are found in a variety of electronic, controlled heat transfer, and aerospace scenarios. Additionally, the magnitude of the applied voltage can be significantly reduced in micropumping, resulting in power savings and a reliable method for flow generation. In this study, we examine the dynamic characteristics of a conduction micropump embedded within a rectangular microchannel, showing the effects of Coulombic driving forces, different channel heights, polymer elasticity, and viscosity ratios. The results show that electric power consumption can vary by two orders of magnitude for increasing channel height. As the polymer concentration increases, the maximum velocity decreases significantly and can reach 50% of that of the unadded polymer with a plunger-like distribution. The flow rate depends linearly on the polymer concentration, but exhibits non-monotonic curve with the polymer elasticity. It means that the flow rate performance of the micro-pump can be kept controllable by tuning the viscosity ratio, providing some suggestions for some regulated flow applications. [ABSTRACT FROM AUTHOR]

A relative motion model was used to numerically simulate the phenomenon of particle aggregation in shear thinning fluids. To understand the shear thinning effects on particle mechanical properties in microfluidics, the shear thinning matching was performed with viscoelastic and non-viscoelastic fluids. The research results indicate that, shear thinning characteristics can significantly alter the mechanical properties of particles. In non-viscoelastic fluids, shear thinning can cause the aggregation position of particles to move towards the wall, and has an incentive effect on the aggregation speed of particles. In viscoelastic fluids, the occurrence of shear thinning will bring a decrease of the fluid elasticity, resulting in particle convergence from the center to the wall. [ABSTRACT FROM AUTHOR]

We consider a system of PDEs that model a viscoelastic fluid with damping mechanism. In ℝ 3 {\mathbb{R}^{3}} , we construct some new local energy bounds that enable us to improve several ϵ-regularity criteria for the Caffarelli–Kohn–Nirenberg theorem for weak solutions of this system. [ABSTRACT FROM AUTHOR]

Viscoelastic fluids exhibit complex viscous and elastic behavior and are found in nature and industries like polymer solutions and biological fluids. This research is devoted to the examination of the heat and mass flow characteristics of viscoelastic fluids with heightened viscous effects relative to elasticity. Mathematical models are crucial for understanding and predicting their responses to mechanical stresses. The models are based on spring and dashpot elements and vary in arrangement to capture behavioral dominance. In this study, a spring in parallel with one dashpot and a second dashpot in series creates a viscoelastic three-element viscous model for the fluid. This model is employed in transport equations to analyze the heat and mass flow properties of a viscoelastic fluid across a variable thickness sheet. The numerical Runge-Kutta (RK) technique is used to find the solutions to these equations. The influence of viscosity on the outcomes is shown to be more significant than other parameters. Additionally, there is a 22% and 137% enhancement in the Nusselt number and entropy generation rate, respectively, at $\mu = 0.005.$μ=0.005. [ABSTRACT FROM AUTHOR]

In this paper, a novel analytical approach based on nonlocal strain gradient theory is proposed to investigate small-scale effects on the radial vibration of isotropic spherical nanoparticles interacting with a viscoelastic fluid. The viscoelastic fluid is assumed to be compressible and takes into account both compressional and shear relaxation processes. The frequency equation is derived by imposing the fluid-nanosphere interface continuity conditions. To demonstrate the validity and accuracy of the approach, a comparison is made with the literature results in some particular cases, which shows a good agreement. Numerical examples are finally conducted to reveal the significance of small-scale effects in the radial vibrations, which need to be included in the nonlocal strain gradient model of submerged spherical nanoparticles. It is found that the vibration behavior greatly depends on the nanosphere size, nonlocal parameter, strain gradient parameter and glycerol-water mixture. Particularly, the small-scale effects play a very pronounced role when the spherical gold nanoparticle radius is smaller than 3 nm. Thus, the obtained frequency equation is very useful to interpret the experimental measurements of vibrational characteristics of nanospheres submerged in a viscoelastic fluid. [ABSTRACT FROM AUTHOR]

A model of a viscoelastic fluid with a high-order rheological relation and a memory along the trajectories of the velocity field is under consideration. The weak solvability to the corresponding initial-boundary value problem is established. The investigation is based on the approximation of the problem under consideration by a sequence of regularized problems, and the following passage to the limit. The theory of regular Lagrangian flows is used to study trajectories of a non-smooth velocity fields. [ABSTRACT FROM AUTHOR]

The Saffman‐Taylor instability of polymeric fluids flooding through saturated heterogeneous porous media is studied numerically. The displacement of a Newtonian fluid by a viscoelastic liquid is examined using a Hartley transformation and a fourth‐order Adams‐Bashforth technique. The flow is assumed to be miscible, and the Carreau‐Yasuda equation is used to model the shear‐thinning viscometric functions. The effects of different rheological properties and domain parameters on flow instability are studied in detail. It is found that a channeling regime is possible as the main difference between displacements through homogeneous and heterogeneous media. [ABSTRACT FROM AUTHOR]

Aim: This paper presents a numerical simulation of the mixed convective boundary layer (BL) motion of a bio-rheological liquid over an inclined plate under viscous dissipation and Joule heating effects. This is significant because of the various applications of electro-osmotic force, inclined plates, and viscoelastic fluids in the biochemical engineering and industrial domains. Furthermore, the BL flow is controlled by electromagnetic force (EMF). In this study, a non-Newtonian liquid model, called the Jeffrey fluid model, was employed. Method: The rheological equations of the current study are nonlinear partial differential equations (PDEs). By applying a set of similarity transformations, these PDEs become coupled ordinary differential equations (ODEs), which are then solved numerically using the NDSolve method under realistic boundary constraints. Outcomes: Numerical solutions for the velocity profile (f′(ξ)), temperature distribution (Θ(ξ)), skin friction (shearing stress), and Nusselt number (heat transfer rate) were obtained subject to convective boundary constraints. These numerical outcomes are dependent on 12 embedded parameters: Hartmann number (Ha), viscoelastic time relaxation parameter (γ), inclination of the inclined plate with a horizontal line (ω), mixed convection parameter (Ω), electro-osmotic parameter (k), electro-osmotic velocity parameter (Uhs), Prandtl number Pr, Brinkman number (Br), suction/blowing parameter (s), velocity slip parameter (ϱ), Joule heating parameter (Γ), and thermal slip parameter (δ). The authors discussed how these embedded variables affect rheological features through graphs and tables. The numerical solutions of viscous liquids are also discussed, and these outcomes are compared with the numerical solutions of a viscoelastic liquid. The enhancements of the Θ(ξ) and f′(ξ) are largely dependent on the Joule heating parameter, Brinkman number, and Hartmann number. As the Prandtl number increases, diminishing behavior is observed in the Θ(ξ) and f′(ξ). Increasing the magnetic and viscoelastic parameters increases the magnitudes of the skin friction coefficient and local Nusselt number. The validation of the numerical procedure is discussed by recovering the outcomes of research works from the available literature. Significances and applications: This mathematical study has diverse applications in the electromagnetic multiphase processes, magnetic power generators, chemical engineering phenomena, polymer industry systems, and the thermal enhancement of mechanical and industrial processes.

This study investigates the complex dynamics of a viscoelastic fluid subjected to magneto-hydrodynamics over a stretching sheet, incorporating the Cattaneo–Christov heat flux model. This model is especially advantageous for explaining heat transfer in materials possessing significant thermal conductivity, where the conventional Fourier’s law might not be precise. The investigation revolves around evaluating how the thermal relaxation time affects the boundary layer and how both thermal radiation and viscous dissipation influence the thermal field. The significance of this research lies in its contribution to understanding the intricate behavior of such fluids in the presence of magnetic fields and non-Fourier heat conduction. The primary objective is to analyze the impact of viscoelasticity, magnetohydrodynamics, and Cattaneo–Christov heat flux on the flow and heat transfer characteristics over the stretching sheet. The research methodology involves the application of mathematical models and numerical techniques, particularly the use of the shifted Chebyshev polynomials of the sixth-order approximation and spectral collocation technique. The major conclusion of the study underscores the significant influence of viscoelasticity, magnetic field, and Cattaneo–Christov heat flux on the transport properties of the fluid, providing valuable insights for applications in various engineering and industrial contexts. Certain notable results arising from the current issue indicate that heat transfer is more pronounced for the viscoelastic factor and magnetic parameter, whereas the thermal relaxation parameter exhibits the opposite trend. In addition, the inclusion of the Cattaneo–Christov term enhances our comprehension of thermal behavior.

The lubrication phenomenon plays a novel role in the chemical industries, manufacturing processes, extrusion systems, thermal engineering, petroleum industries, soil sciences, etc. Owing to such motivated applications, the aim of the current work is to predict the assessment of heat and mass transfer analysis for non-Newtonian nanomaterial impinging over a lubricated surface. The flow is subject to the oblique stagnation point framework. The lubricated phenomenon is observed due to viscoelastic nanofluid. The impacts of chemical reaction are also endorsed. The fundamental conservation laws are utilized to model the flow problem and similarity transformation are used to transform the governing system of partial differential equations into ordinary differential equations. A thin layer of power law lubricant is used to enhance the lubrication features. The numerical object assessment regarding the simulation process is captured by implementing the Keller Box scheme. The physical characterization endorsing the thermal fluctuation with flow parameters is inspected.

The injection of a fluid into another fluid causes a spatiotemporal pattern along the injection front. Viscous fingering is a well-known example when the replaced material is a viscous fluid. Notably, most fluids are, in reality, viscoelastic, i.e., they behave as an elastic solid over short timescales. For this reason, it is important to study the situation when the replaced fluid is viscoelastic. In this study, we observed a dynamics of fluids when an incompressible organic liquid was injected into an oleophilic Hele-Shaw cell filled with an aqueous viscoelastic fluid made of a wormlike micellar solution. We found extensive tip splitting of the injection front, which led to thin fingers with a characteristic size comparable to four times the cell thickness. We examined the material properties and suggest that the thin fingering pattern observed in our system is due to the delamination of viscoelastic fluid from the bottom substrate surface. Our result shows that the effect of interfacial energy in the existing solid layer should be considered in the injection process. [ABSTRACT FROM AUTHOR]

Log-Conformation Representation (LCR) method effectively enhances the stability of viscoelastic fluid flow driven by a cavity at high Wi numbers. However, its stability is relatively poor under low viscosity ratio conditions. In this study, three momentum equation stabilization algorithms (Both-Sides-Diffusion, Discrete Elastic Viscous Split Stress-Vorticity, and velocity–stress coupling) were tested and compared in OpenFOAM to assess their stabilizing effects on the LCR method under low viscosity ratio conditions. The evaluation was based on changes in average kinetic energy and the maximum critical time step. The results indicate that the different momentum equation stabilization algorithms improve the numerical oscillations observed in the numerical simulation of low viscosity ratio cavity-driven flow to varying extents. This enables a reduction in the viscosity ratio that can be stably simulated by 0.03 to 0.15. Furthermore, these cases using the momentum equation stabilization algorithms require time steps that are 33% to 100% shorter than those of the original cases. This demonstrates the promoting effect of the additional diffusion term in the momentum equation on stability under low viscosity ratio conditions. The combination of LCR and velocity–stress coupling was used to analyze the impact of viscosity ratios on velocity, logarithmic conformation tensor, and average kinetic energy. As the viscosity ratio decreases, the contribution of fluid elasticity increases, resulting in more pronounced variations in velocity and stress. However, the viscosity ratio has little effect on the stress boundary layer at the top cover and corners. Under conditions with the same Wi number, the average kinetic energy decreases as the viscosity ratio decreases until stability is achieved. [ABSTRACT FROM AUTHOR]

AbstractThe drag and heat transfer characteristics of an isothermal sphere in a FENE-P-type viscoelastic fluid have been studied in the steady axisymmetric flow regime. The governing equations, namely, mass, momentum, and energy equations, together with FENE-P type viscoelastic constitutive equations, have been solved using the finite volume method based opensource CFD code OpenFOAM over the following ranges of conditions: Reynolds number, 1≤Re≤100; Prandtl number, 1≤Pr≤50; Weissenberg number, 0​≤Wi≤10 and polymer extensibility parameter, 10≤L2≤500 for a fixed value of the polymer viscosity ratio of β=0.5. At low Reynolds numbers, fluid viscoelasticity causes an upward and downward shifting in the axial velocity profiles with reference to that in a Newtonian fluid along the upstream and downstream axis of the sphere, respectively. However, such a shift progressively diminishes with the increasing Reynolds number. Furthermore, a “velocity overshoot” and/or a “negative wake” is also observed in a viscoelastic polymer solution at low Reynolds numbers, and this is accentuated with the increasing Weissenberg number. The separation of boundary layers is seen to be suppressed with the increasing Weissenberg number. The drag coefficient decreases with the Reynolds number irrespective of the fluid type and the corresponding dependence on the Weissenberg number is found to be non-monotonic depending upon the values of Re and L2. The average Nusselt number always increases with the increasing values of Re, Pr, and Wi and with the decreasing value of L2. A limited number of simulations have also been carried out to show the effect of the temperature-dependent viscosity of the fluid on the flow dynamics and heat transfer characteristics. Finally, simple correlations for the drag coefficient and average Nusselt number are presented which not only capture the functional dependence but also can be used for the interpolation of the present results for the intermediate values of the governing parameters in a new application. [ABSTRACT FROM AUTHOR]

The oscillating flow of the viscoelastic fluid‐saturated porous layer has been useful in many areas, including the petroleum, chemical, and bioengineering industries. It is studied using the modified Darcy‐Oldroyd‐B model in this article. The exact solution is obtained utilizing a simpler and more reasonable method. According to this velocity solution, the time‐velocity profile of one kind of viscoelastic fluid is analyzed. From the analysis, it was found that the flow behaves like the Newton fluid when the oscillating frequency is low, and the flow reversal occurs when the oscillating frequency is high. Further, velocity, temperature, shear stress, and the rate of heat transfer are exponential solutions that are obtained and analyzed for different values of known physical parameters. Finally, we recognize that the relaxation and retardation parameters in this model act in the opposite manner. [ABSTRACT FROM AUTHOR]

The process of solid propellant production, which is the most widely used high-energy material, has garnered significant attention from researchers. However, there have been relatively few studies on its processing, due to the unique nature of the casting process. This paper aims to further analyze the pouring process of the propellant slurry. Initially, we obtained a sample of the propellant slurry and measured its rheological parameters using a rotary rheometer. From the analysis of the experimental results, we derived the viscosity parameters and the yield values of the propellant slurry. Subsequently, we simulated the pouring process, setting the slurry parameters based on the data obtained from the rheological measurement experiment. The simulation results demonstrated that the flower plate significantly impacts upon the cutting and separating effect on the slurry during pouring. Upon leaving the flower plate, the slurry descends onto the core mold platform under the influence of gravity, gradually flowing along the edge of the core mold. Although there may be some small voids in the pouring process, the voids will disappear completely at the end of pouring. A comparison with the actual pouring situation revealed a higher consistency between the simulation results and reality, thus establishing the reliability of the simulation method as a reference for analyzing the pouring process. [ABSTRACT FROM AUTHOR]

We have exploited the Oldroyd-B model to explain the appearance of stationary and oscillatory convection in a viscoelastic magnetic fluid saturating a porous horizontal layer heated from below. The analytical expressions of the Rayleigh number corresponding to each convection are determined as a function of dimensionless parameters. We note that the appearance of steady convection does not depend on the viscoelastic properties of the fluid. Using numerical simulations, we analysed the stabilising effect of each dimensionless parameter on the evolution of the convection and on the size of the convection cells formed. We note that in the oscillatory convection case, the values of the Darcy number, the parameter characterising the permeability of the medium, are low compared to those of stationary convection. The behaviour of the critical frequency for oscillatory convection is studied. The possibility of co-dimension-2 bifurcation is discussed and the boundary between the oscillatory and stationary convections is found. [ABSTRACT FROM AUTHOR]

We investigate the impact of radiation parameter on MHD flow of a viscoelastic fluid over a vertical surface. The Hall effect and induced magnetic field (i.m.f) are applied. The model equations are solved analytically. The nature of pertinent parameters affecting velocity, i.m.f, temperature and concentration are analyzed. The novelty of the research is in investigating the impacts of radiation effect and i.m.f along with Hall current on the flow field. Important findings are: with the rise in thermal radiation, i.m.f falls in primary flow direction, whereas the reverse trend is noticed for secondary flow direction. We also found that radiation effect increases the fluid temperature and both the components of velocity profiles. The expressions of skin friction, current density, Nusselt and Sherwood number over the magnetized vertical surface (m.v.s) are computed and assessed graphically. It is also found that as the Nusselt number rises, skin friction on primary flow accelerates to maximum value then decelerates and current density on secondary flow accelerates with rise in the thermal radiation, whereas skin friction on secondary flow and current density on primary flow decelerate with increase in thermal radiation.

This paper focuses on the spectral analysis of equations that describe the oscillations of a heavy pendulum partially filled with a homogeneous incompressible viscoelastic fluid. The constitutive equation of the fluid follows the simpler Oldroyd model. By examining the eigenvalues of the linear operator that describes the dynamics of the coupled system, it was demonstrated that under appropriate assumptions the equilibrium configuration remains stable in the linear approximation. Moreover, when the viscosity coefficient is sufficiently large the spectrum comprises three branches of eigenvalues with potential cluster points at $ 0 $, $ \beta $ and $ \infty $ where $ \beta $ represents the viscoelastic parameter of the fluid. These three branches of eigenvalues correspond to frequencies associated with various types of waves.

Present article aims at developing similarity solutions for heat transportation in swirling flow of viscoelastic fluid (obeying Jeffrey model) generated by an infinite porous rotating surface. The resulting thermal energy equation comprising frictional heating and Ohmic dissipation terms is mainly focused. Relevant equations simplified under boundary layer approximations have been solved analytically by a powerful homotopy based analytical scheme, while numerical solutions are constructed by a reliable MATLAB solver bvp4c. For homotopy based series solutions, total squared residual of the system is evaluated, and it is found to decline for increasing order of approximations. Both applied methods are shown to be in compliance with each other for wide range of viscoelastic fluid parameters. Computed solutions are utilized to understand the combined influence of viscoelasticity and viscous dissipation on heat transport phenomena associated with the Von-Kármán configuration. Subtle fluid dynamics entities such as resisting torque and Nusselt number are computed and elaborated. Results predict that the torque required by the disk drastically reduces when viscoelastic fluid assumption is applied. However, cooling rate of the disk in Newtonian fluid is better than that in viscoelastic fluid. Present results are found in agreement with that of the previous studies in a limiting situation.

The injection of a fluid into another fluid causes a spatiotemporal pattern along the injection front. Viscous fingering is a well-known example when the replaced material is a viscous fluid. Notably, most fluids are, in reality, viscoelastic, i.e., they behave as an elastic solid over short timescales. For this reason, it is important to study the situation when the replaced fluid is viscoelastic. In this study, we observed a dynamics of fluids when an incompressible organic liquid was injected into an oleophilic Hele–Shaw cell filled with an aqueous viscoelastic fluid made of a wormlike micellar solution. We found extensive tip splitting of the injection front, which led to thin fingers with a characteristic size comparable to four times the cell thickness. We examined the material properties and suggest that the thin fingering pattern observed in our system is due to the delamination of viscoelastic fluid from the bottom substrate surface. Our result shows that the effect of interfacial energy in the existing solid layer should be considered in the injection process.

In this paper, we propose a novel, simple and accurate analytical study based on nonlocal elasticity theory to forecast small-scale effects on the radial vibration of anisotropic gold nanospheres submerged in viscoelastic fluid (VEF). Eringen's model is used to determine the motion equation for anisotropic nanospheres, with the fluid assumed to be viscoelastic and compressible. The frequency equation is derived by imposing the fluid-nanosphere interface continuity conditions. A comparison with the literature results is conducted to demonstrate the validity and correctness of this analysis, which indicates a very good agreement. The importance of small-scale effects in the radial vibration, which need to be included in the nonlocal elasticity model of submerged nanospheres, is eventually revealed by numerical examples. It is discovered that the nanosphere size, nonlocal parameter, and glycerol–water mixture have a significant impact on the vibration behaviors. Our results show that the small scale is crucial for the radial vibration of gold nanoparticles when the gold nanosphere is smaller than 5. 5 nm. Thus, the resulting frequency equation is very useful to interpret experimental measurements of the vibration characteristics of submerged gold nanospheres in VEF. [ABSTRACT FROM AUTHOR]

This article is devoted to the investigation of the weak solvability to the initial boundary value problem, which describes the viscoelastic fluid motion with memory. The memory of the fluid is considered not at a constant position of the fluid particle (as in most papers on this topic), but along the trajectory of the fluid particle (which is more physical). This leads to the appearance of an unknown function z, which is the trajectory of fluid particles and is determined by the velocity v of a fluid particle. However, in this case, the velocity v belongs to L 2 (0 , T ; V 1) , which does not allow the use of the classical Cauchy Problem solution. Therefore, we use the theory of regular Lagrangian flows to correctly determine the trajectory of the particle. This paper establishes the existence of weak solutions to the considered problem. For this purpose, the topological approximation approach to the study of mathematical hydrodynamics problems, constructed by Prof. V. G. Zvyagin, is used. [ABSTRACT FROM AUTHOR]

The existence of weak solutions of the initial-boundary value problem for the equations of motion of a viscoelastic fluid with memory along trajectories of a nonsmooth velocity field and with an inhomogeneous boundary condition is proved. The study relies on Galerkin-type approximations of the original problem followed by passage to the limit based on a priori estimates. The theory of regular Lagrangian flows is used to examine the behavior of trajectories of a nonsmooth velocity field. [ABSTRACT FROM AUTHOR]

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In this study, we investigated the particle separation phenomenon in a microchannel with a T-shaped cross-section, a unique design detailed in our previous study. Utilizing a co-flow system within this T-shaped microchannel, we examined two types of flow configuration: one where a Newtonian fluid served as the inner fluid and a viscoelastic fluid as the outer fluid (Newtonian/viscoelastic), and another where both the inner and outer fluids were Newtonian fluids (Newtonian/Newtonian). We introduced a mixture of three differently sized particles into the microchannel through the outer fluid and observed that the co-flow of Newtonian/viscoelastic fluids effectively separated particles based on their size compared with Newtonian/Newtonian fluids. In this context, we evaluated and compared the particle separation efficiency, recovery rate, and enrichment factor across both co-flow configurations. The Newtonian/viscoelastic co-flow system demonstrated a superior efficiency and recovery ratio when compared with the Newtonian/Newtonian system. Additionally, we assessed the influence of the flow rate ratio between the inner and outer fluids on particle separation within each co-flow system. Our results indicated that increasing the flow rate ratio enhanced the separation efficiency, particularly in the Newtonian/viscoelastic co-flow configuration. Consequently, this study substantiates the potential of utilizing a Newtonian/viscoelastic co-flow system in a T-shaped straight microchannel for the simultaneous separation of three differently sized particles. [ABSTRACT FROM AUTHOR]