Weissenberg Number Research Articles

Effects of dilute low molecular weight poly(ethylene oxide) solutions in immiscible radial viscous fingering instabilities

We experimentally study the effects of normal stress differences in the immiscible radial viscous fingering instability in a Hele–Shaw cell. Dilute low molecular weight poly(ethylene oxide) (PEO) solutions are used as the displaced fluid to focus on elastic effects without shear-thinning behavior. The molecular weight of PEO is varied to investigate the effects of normal stress differences. The experimental observations reveal that nonmonotonic and opposing effects are evident depending on the molecular weight of the PEO and the stage of the radial viscous fingering evolution. Decreases in the PEO molecular weight reduce the number of fingers and widen the finger width in the early stage. However, the increase in the PEO molecular weight promotes tip splitting and narrows finger width in the early stage but suppresses tip splitting in the intermediate stage. Weissenberg numbers are estimated at different stages of radial viscous fingering instabilities. Tip splitting occurs at the highest Weissenberg number covered in this study and suppression of tip splitting is observed at intermediate Weissenberg numbers. At low Weissenberg numbers, we observe an increased finger width and a reduced number of fingers.

Kinetic Energy Budget in Turbulent Flows of Dilute Polymer Solutions

Direct numerical simulation of a turbulent pipe flow of a realistic solution of 108\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^8$$\\end{document} polymers, modelled as finitely extensible nonlinear elastic (FENE) dumbbells, and directly momentum coupled with the incompressible Navier–Stokes equations, are performed by means of an Eulerian-Lagrangian approach. Besides the drag reduction, the polymers significantly modify mean and turbulent kinetic energy budgets. The polymer backreaction to the solvent reduces the Reynolds stress and thus decreases the turbulent production and, at large Weissenberg number, the polymers act as a source of turbulent kinetic energy for y+>40\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$y^+> 40$$\\end{document}, leading to an increase in the dissipation. This effect is peculiar to large Weissenberg polymers and it is particularly apparent at a small Reynolds number. At a smaller Weissenberg number, the effect of the polymers remains confined in the buffer layer, with the kinetic energy budget not significantly altered elsewhere.

Direct simulation of viscoelastic-viscoelastic emulsions in sliding bi-periodic frames using Cahn–Hilliard formulation

In this study, a direct numerical simulation technique is proposed for 2-D droplet emulsions in simple shear flow with viscoelastic-viscoelastic liquid systems. To treat the multi-drop problem without wall effects, the sliding bi-periodic frame is combined with the Cahn–Hilliard equation in the DEVSS/DG (Discrete Elastic-Viscous Split Stress/Discontinuous Galerkin method) finite element framework. We employ the Galerkin weak formulation for flows of an Oldroyd-B fluid in a creeping regime with the Cahn–Hilliard equations. Sliding bi-periodic frame constraints for velocity, phase variable, and chemical potential are implemented by Lagrangian multipliers. We discuss the bulk rheology, morphological development, and effect of the viscoelasticity of emulsions through numerical analysis of single-, two-, and multi-drop problems. We report that increasing Weissenberg number orients the droplet in the flow direction, and the breakup time exhibits non-monotonic behavior similar to drop deformation. The coalescence of two drops is observed to be accelerated with the presence of viscoelasticity due to an extensional flow and normal stress difference. The bulk rheology is found to be consistent with prior experimental data from multi-drop problems. For the first time, the sliding bi-periodic frame has been implemented with the combination of the DEVSS/DG finite element method and the Cahn–Hilliard equation in the absence of wall effects, which is essential for understanding industrially important droplet emulsions.

Large-amplitude oscillatory shear flow from general rigid bead-rod theory

Oscillatory shear flow, performed at small-amplitude, interrogates polymeric liquids in their equilibrium states. The fluid responds in sinusoidal shear stress waves whose amplitude and phase lead depend on the dimensionless frequency (called the Deborah number). By contrast, this same flow field, performed at large-amplitude, probes departures from the equilibrium state, and the fluid responds with shear stress in the form of a Fourier series, whose component amplitudes and phase leads depend on both the dimensionless frequency (called the Deborah number) and the dimensionless shear rate amplitude (called the Weissenberg number). The physics of these departures from equilibrium in an oscillatory shear flow may be explained by (i) chain disentanglement or (ii) motion along the polymer chain axes (called reptation) or (iii) macromolecular orientation. Of these radically different and yet otherwise equally effective approaches, only (iii) allows the macromolecular structure to be varied arbitrary so that the effect of molecular architecture on the rheology can be explored. Though much has been written about a large-amplitude oscillatory shear flow, we understand little about the role of molecular structure on the measured behaviors, and this has limited its usefulness. In this work, we explain the higher harmonics of both the shear stress (first and third), the first normal stress differences (zeroth, second, and fourth), and the second normal stress differences (zeroth and second) arriving at analytical expressions for all three. These expressions, written in dimensionless form, express the dimensionless rheological responses in large-amplitude oscillatory shear flow in terms of the ratio of the two principal macromolecular moments of inertia. To get these expressions, we derive the first five terms of the orientation distribution function, by solving the general diffusion equation in Euler coordinates. We then integrate in phase space with this orientation result to arrive at our expression for the first seven terms of the polymer contribution to the extra stress tensor. From this tensor, we next write down the Fourier coefficients for the shear stress responses, and the normal stress difference responses, in large-amplitude oscillatory shear flow for a suspension of macromolecules sculpted from a rigid bead-rod structure of any arbitrary axisymmetric shape.

Hyperbolic Tangent Fluid Model for Stagnation Flow of Hybrid Nanofluid Over a Stretching Sheet

The problem of hyperbolic tangent fluid model for stagnation flow of hybrid nanofluid over a stretching sheet is investigated. Constitutive relation of an incompressible hyperbolic tangent model as well as consideration of thermal radiation and Newtonian heating is taken into account. The boundary layer problem is formulated to nonlinear partial differential equations which is then transformed into ordinary differential equations by using similarity transformation. The equations including the boundary conditions are solved numerically using bvp4c in the MATLAB software. A comparison with previous findings shows an excellent agreement. The effect of governing parameters such as power law index, Weissenberg number, suction/injection, radiation and Biot number is investigated. The changes in the value of volume fraction of diamond and silicon dioxide are also analyzed. Characteristics for the significant variables are graphically presented and the numerical results are tabulated. The velocity behavior is significantly influenced by the volume fraction of diamond and silicon dioxide and other physical parameters. Meanwhile, the temperature is influenced by the radiation parameter. This study provides conclusive evidence that increasing the volume fraction of diamond nanoparticles significantly enhances the heat transfer rate. The increment by 0.1 (10%) of the volume fraction of diamond nanoparticles increases the heat transfer rate approximately by 3%. These findings underscore the potential of integrating these nanoparticles to improve thermal performance across diverse applications.

Second law analysis on Ree-Eyring nanoliquid and Darcy Forchheimer flow through a significant stratification in the gyrotactic microorganism

PurposeThe modern day has seen an increase in the prevalence of the improvement of high-performance thermal systems for the enhancement of heat transmission. Numerous studies and research projects have been carried out to acquire an understanding of heat transport performance for their functional application to heat conveyance augmentation. The idea of this study is to inspect the entropy production in Darcy-Forchheimer Ree-Eyring nanofluid containing bioconvection flow toward a stretching surface is the topic of discussion in this paper. It is also important to take into account the influence of gravitational forces, double stratification, heat source–sink and thermal radiation. In light of the second rule of thermodynamics, a model of the generation of total entropy is presented.Design/methodology/approachIncorporating boundary layer assumptions allows one to derive the governing system of partial differential equations. The dimensional flow model is transformed into a non-dimensional representation by applying the appropriate transformations. To deal with dimensionless flow expressions, the built-in shooting method and the BVP4c code in the Matlab software are used. Graphical analysis is performed on the data to investigate the variation in velocity, temperature, concentration, motile microorganisms, Bejan number and entropy production concerning the involved parameters.FindingsThe authors have analytically assessed the impact of Darcy Forchheimer's flow of nanofluid due to a spinning disc with slip conditions and microorganisms. The modeled equations are reset into the non-dimensional form of ordinary differential equations. Which are further solved through the BVP4c approach. The results are presented in the form of tables and figures for velocity, mass, energy and motile microbe profiles. The key conclusions are: The rate of skin friction incessantly reduces with the variation of the Weissenberg number, porosity parameter and Forchheimer number. The rising values of the Prandtl number reduce the energy transmission rate while accelerating the mass transfer rate. Similarly, the effect of Nb (Brownian motion) enhances the energy and mass transfer rates. The rate of augments with the flourishing values of bioconvection Lewis and Peclet number. The factor of concentration of microorganisms is reported to have a diminishing effect on the profile. The velocity, energy and entropy generation enhance with the rising values of the Weissenberg number.Originality/valueAccording to the findings of the study, a slip flow of Ree-Eyring nanofluid was observed in the presence of entropy production and heat sources/sinks. There are features when the implementations of Darcy–Forchheimer come into play. In addition to that, double stratification with chemical reaction characteristics is presented as a new feature. The flow was caused by the stretching sheet. It has been brought to people's attention that although there are some investigations accessible on the flow of Ree-Eyring nanofluid with double stratification, they are not presented. This research draws attention to a previously unexplored topic and demonstrates a successful attempt to construct a model with distinctive characteristics.

Analytical study of viscoelastic fluid during forward roll coating process under lubrication approximation theory

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 [Formula: see text] 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.

Effect of nonlinear thermal radiation and homogeneous-heterogeneous reactions on peristaltic propulsion of Johnson-Segalman fluid

The basic aim of this research is to investigate the main features of the peristaltic flow of Johnson-Segalman fluid in a curved flow channel in the presence of a homogeneous-heterogeneous reaction. The fluid is considered electrically conducting with a radial magnetic field effect. The constitutive relation for energy is formulated with the addition of viscous dissipation and nonlinear thermal radiation. The slip and flexible wall boundary conditions are taken into consideration. The lubrication technique is used for the mathematical the modelling of the problem. The solution of the resulting nonlinear system of ODE’s is computed numerically through NDSolve command of Mathematica, and graphical results are prepared for flow variables. It has been clearly noticed that flow is accelerated in the planer medium as compared to the curved channel, and the velocity of the fluid increases with a larger Weissenberg number. Moreover, the thermal profile has an inverse relation to the parameters, i.e., radiation, temperature ratio, and curvature. Furthermore, it is also observed that the magnitude of heat transfer coefficient rises significantly when a comparatively less curved channel is utilized, however, a reduction in concentration profile is witnessed in this case. Alternative impact of homogeneous and heterogeneous reactions on concentration profile are observed through graphical results. Application of the study include the usage of peristaltic pump in chemical industry and in pharmacology industry for the purpose of drug deliveries.

Extensional rheometry of mobile fluids. Part II: Comparison between the uniaxial, planar, and biaxial extensional rheology of dilute polymer solutions using numerically optimized stagnation point microfluidic devices

Part I of this paper [Haward et al., J. Rheol. 67, 995–1009 (2023)] presents a three-dimensional microfluidic device (the optimized uniaxial and biaxial extensional rheometer, OUBER) for generating near-homogeneous uniaxial and biaxial elongational flows. Here, in Part II, the OUBER device is employed to examine the uniaxial and biaxial extensional rheology of model dilute polymer solutions, compared with measurements made under planar extension in the optimized-shape cross-slot extensional rheometer [OSCER, Haward et al. Phys. Rev. Lett. 109, 128301 (2012)]. In each case, micro-particle image velocimetry is used to measure the extension rate as a function of the imposed flow conditions, and excess pressure drop measurements enable estimation of the tensile stress difference generated in the fluid via a new analysis based on the macroscopic power balance for flow through each device. Based on this analysis, for the most dilute polymer sample tested, which is “ultradilute”, the extensional viscosity is well described by Peterlin’s finitely extensible nonlinear elastic dumbbell model. In this limit, the biaxial extensional viscosity at high Weissenberg numbers (Wi) is half that of the uniaxial and planar extensional viscosities. At higher polymer concentrations, although the fluids remain dilute, the experimental measurements deviate from the model predictions, which is attributed to the onset of intermolecular interactions as the polymer chains unravel in the extensional flows. Of practical significance (and fundamental interest), elastic instability occurs at a significantly lower Wi in uniaxial extensional flow than in either biaxial or planar extensional flow, thereby limiting the utility of this flow type for extensional viscosity measurement.

Unsteady blood flow of Carreau fluid in a porous saturated medium with stenosis under the influence of acceleration and magnetic fields: A comprehensive analysis

Blood flow in stenosed arteries is a common cause of cardiovascular diseases, leading to serious health problems. The present study aims to investigate the unsteady Womersley blood flow in a stenosed, porous saturated artery under the influence of acceleration and magnetic fields. The study utilizes a Carreau constitutive equation to model blood rheology and employs the finite difference technique to compute the governing equations under the assumption of unsteady, unidirectional, and laminar flow. The importance of this study lies in its potential to provide a better understanding of the complex behavior of hemodynamic flow in the presence of external fields and porous media, which has significant implications for the control and management of cardiovascular diseases. In particular, the study analyses the impacts of non-dimensional parameters, such as magnetic field, channel permeability, acceleration field, Weissenberg number, and stenosis amplitude, on critical flow variables, such as velocity, resistivity, wall shear stress, and flow rate. Our calculations suggest that a magnetic field is an effective instrument for regulating hemodynamic flow because it increases resistance by up to 8.31% while decreasing flow by up to 8.44%. Channel permeability, on the other hand, improves blood velocity by up to 33.35% while eliminating resistance by up to 23.43%. Furthermore, greater acceleration fields decrease resistivity while increasing velocity, flow rate, and wall shear stress. Additionally, the severity of the stenosis and the Weissenberg number substantially affect flow factors. By raising the stenosis amplitude, resistivity rises, and other flow characteristics diminish, whereas modifying the Weissenberg number causes the reverse effect.

On viscoelastic drop impact onto thin films: axisymmetric simulations and experimental analysis

This study investigates the effect of fluid elasticity on axisymmetric droplets colliding with pre-existing liquid films, using both numerical and experimental approaches. The numerical simulations involve solving the incompressible flow momentum equations with viscoelastic constitutive laws using the finite volume method and the volume of fluid (VOF) technique to track the liquid’s free surface. Here, the Oldroyd-B model is used as the constitutive equation for the viscoelastic phase. Experiments are also performed for dilute viscoelastic solutions with 0.005% and 0.01% (w/w) polyacrylamide in 80:20 glycerin/water solutions, in order to ensure the validity of the numerical solution and to investigate the elasticity effect. The formation and temporal evolution of the crown parameters are quantified by considering the flow parameters, including the fluid’s elasticity. The results indicate that the axisymmetric numerical solutions reasonably agree with the experimental observations. Generally, the fluid’s elasticity can enlarge the crown dimension at different thicknesses of the fluid film. Moreover, at intermediate values of the Weissenberg number, the extensional force in the crown wall can control the crown propagation. Furthermore, the results reveal that the effects of the Weber number and the viscosity ratio on this problem are more significant at higher values of the Weissenberg number.

Analysis of entropy generation in Carreau ternary hybrid nanofluid flow over a stretching sheet

In this study, we consider a steady-state viscous,laminar Carreau ternary-hybrid nanofluid flow over a stretching sheet with first-order slip and Ohmic dissipation.Further, we consider the effects of suction/injection, oblique Lorentz force, and a temperature jump boundary condition. We investigate here how to transport a Carreau ternary hybrid nano-fluid while minimizing the entropy it generates. We analyze in this article the flow of molybdenum disulfide (MoS2), silver (Ag), and multi-wall carbon nanotubes (MWCNT). Carboxymethyl cellulose (CMC-water) is the observed fluid of choice. Several industries could benefit from this research, including those dealing with the equations of the model are converted to a dimensionless form by appropriate similarity transformations. Using a shooting strategy with Runge-Kutta-Fehlberg and Secant methods the velocity and the temperature fields are obtained. The physical quantities such as the fluid flow rate, the temperature, the skin friction, the Nusselt number, the entropy minimization, and the Bejan number are presented graphically and analyzed. In our Carreau ternary hybrid nanofluid model it is found that an increase in the Weissenberg number is to decrease the velocity field. We also noticed a significant effect of the Brinkmann number which has a deleterious effect on the entropy-minimization and Bejan-number profiles.

Computation of stagnation coating flow of electro-conductive ternary Williamson hybrid mathrm{GO}-mathrm{AU}-{mathrm{Co}}_{3}{mathrm{O}}_{4}/mathrm{EO} nanofluid with a Cattaneo–Christov heat flux model and magnetic induction

Modern smart coating systems are increasingly exploiting functional materials which combine multiple features including rheology, electromagnetic properties and nanotechnological capabilities and provide a range of advantages in diverse operations including medical, energy and transport designs (aerospace, marine, automotive). The simulation of the industrial synthesis of these multi-faceted coatings (including stagnation flow deposition processes) requires advanced mathematical models which can address multiple effects simultaneously. Inspired by these requests, this study investigates the interconnected magnetohydrodynamic non-Newtonian movement and thermal transfer in the Hiemenz plane's stagnation flow. Additionally, it explores the application of a transverse static magnetic field to a ternary hybrid nanofluid coating through theoretical and numerical analysis. The base fluid (polymeric) considered is engine-oil (EO) doped with graphene left(GOright), gold left(Auright) and Cobalt oxide left(C{o}_{3}{O}_{4}right) nanoparticles. The model includes the integration of non-linear radiation, heat source, convective wall heating, and magnetic induction effects. For non-Newtonian characteristics, the Williamson model is utilized, while the Rosseland diffusion flux model is used for radiative transfer. Additionally, a non-Fourier Cattaneo–Christov heat flux model is utilized to include thermal relaxation effects. The governing partial differential conservation equations for mass, momentum, energy and magnetic induction are rendered into a system of coupled self-similar and non-linear ordinary differential equations (ODEs) with boundary restrictions using appropriate scaling transformations. The dimensionless boundary value problem that arises is solved using the bvp4c built-in function in MATLAB software, which employs the fourth-order Runge–Kutta (RK-4) method. An extensive examination is conducted to evaluate the impact of essential control parameters on the velocity f{^{prime}}left(zeta right), induced magnetic field stream function gradient g{^{prime}}left(zeta right) and temperature theta left(zeta right) is conducted. The relative performance of ternary, hybrid binary and unitary nanofluids for all transport characteristics is evaluated. The inclusion of verification of the MATLAB solutions with prior studies is incorporated. Fluid velocity is observed to be minimized for the ternary mathrm{GO}–mathrm{Au}–{mathrm{Co}}_{3}{mathrm{O}}_{4} nanofluid whereas the velocity is maximized for the unitary cobalt oxide left({mathrm{Co}}_{3}{mathrm{O}}_{4}right) nanofluid with increasing magnetic parameter (beta ). Temperatures are elevated with increment in thermal radiation parameter (Rd). Streamlines are strongly modified in local regions with greater viscoelasticity i.e. higher Weissenberg number (We). Dimensionless skin friction is significantly greater for the ternary hybrid GO–Au–C{o}_{3}{O}_{4}/EO nanofluid compared with binary hybrid or unitary nanofluid cases.

Three dimensional flow of Cross nanofluid over bidirectional moving surface in Darcy-Forchheimer medium with Cattaneo-Christov heat flux

The main purpose of this study is to present the mathematical modeling of steady three dimensional boundary layer flow of incompressible non-Newtonian Cross nanofluid over a bidirectional stretching surface. The Buongiorno nanofluid model and Cattaneo-Christov heat flux model are also assumed in present work. It is considered that bidirectional stretching sheet is embedded in Darcy-Forchheimer porous media. Additionally, the motion of fluid flow is induced due to the bidirectional stretching surface. Boundary layer theory is invoked to model the basic partial differential equations of current study. The modeled partial differential equations are reduced to ordinary differential equations with the assistance of appropriate transformation and then solved numerically through Runge Kutta Fehlberg scheme along shooting method. The ranges of involved physical parameters in present study can be explained as 0≤βT≤0.08,0≤βC≤0.25,0≤Fr≤6.0,0≤β≤4.0,0≤We₁≤1.0,0≤We₂≤1.5,0≤Nt≤0.4,0.1≤Nb≤1.2,0≤n≤2,0≤δ≤1.2,0.7≤Pr≤6.2,1≤Sc≤7. It is engrossing to reveal that surface mass transfer rate is an aggrandizing function of concentration relaxation parameter but reverse behavior is noticed for enrich thermal relaxation parameter. Additionally, fluid velocities f′(η) and g′(η) reduce due to the improvement of Forchheimer number and porosity parameter. Furthermore, magnitudes of the surface drag forces along x− and y− directions grow for larger approximation of Weissenberg numbers.

Numerical computation of mixed convective entropy optimized in Darcy-Forchheimer flow of Cross nanofluids through a vertical flat plate with irregular heat source/sink

This article seeks to provide multiple solutions for the buoyancy effects and heat transfer flow of non-Newtonian Cross nanofluids past a vertical flat plate in a Darcy-Forchheimer porous medium. The experimental properties of nanofluid are considered in this study. In addition, the entropy generation along with irregular heat source/sink is also incorporated. The complete partial differential equations (PDEs) are converted into a particular set of ordinary differential equations (ODE) employing the proper similarity variables. The consequent nonlinear ODE system is then resolved using the MATLAB function bvp4c for distinctive values of pertaining parameters. The profiles of entropy generation for different physical influential parameters are plotted. The results indicate that the boundary layer separation accelerates due to the superior consequence of the permeability parameter. The shear stress declines due to the Weissenberg number and permeability parameter for both solutions, while the rate of heat transfer uplifts owing to the larger influence of the Weissenberg number and permeability parameter.

Oldroyd-B Model with High Weissenberg Number and Fractional Velocity Dissipation

Oldroyd-B Model with High Weissenberg Number and Fractional Velocity Dissipation

Efekty lepkosprężyste w warunkach nawadniania kolektora szczelinowo-porowego cieczą wodno-polimerową

The work is devoted to the numerical simulation of the flow of simple and viscoelastic (polymer solution) fluids through a fracture by using polymer solutions for enhanced oil recovery from a reservoir. Polymer solutions have viscoelastic properties. Therefore, when polymer solution flows through the slot, we use the well-known Maxwell’s fluid model with the Jaumann derivative to evaluate deformation characteristics of the flow (stream functions, distributions of the longitudinal velocity gradient and normal stress) resulting in the manifestation of abnormal (compared with the behaviour of the ordinary fluid) effects. The case of slow flow is considered. In this case, the inertial terms can be neglected, the velocities, stresses, and stream functions can be written as the decomposition by Weisenberg number, and we can assume that the Weissenberg number is less than one. The determined regularities of viscoelastic (polymer solution) liquid behaviour with longitudinal velocity gradient and the elastic deformations effects manifested in this case have a decisive meaning in understanding the mechanism of anomalously high oil recovery capacity of a reservoir by using water-polymer flooding of the fractured-porous reservoir. Understanding the nature of the effects of elastic deformations under the conditions of water-polymer flooding of the fractured-porous reservoir enables hydrodynamic calculations of the optimal flow of the polymer solution. One of the main issues that need to be solved when developing the technology for increasing oil recovery from formations using polymer solutions is to determine the optimal flow regime in the fractured-porous reservoir. The calculation results verify the ideas obtained from the experimental solution of this problem concerning the strain-stress state of polymer macromolecules (liquid elements) during polymer flow in the inlet area of the fracture in the oil reservoir and confirm the possibility of using numerical analysis of convergent polymer flow for calculating longitudinal velocity gradients in the inlet area of the fracture and can also serve as additional substantiation of the proposed earlier mechanism for increasing oil recovery from reservoirs by using polymer solutions.

Bioconvective nonlinear radiative flow of cross nanofluid due to porous oscillating surface with variable thermal conductivity and Cattaneo–Christov model

Present exploration elucidates the bio-convective time-dependent flow of Cross nanoparticles across periodically stretched surface immersed in porous space. Modified diffusion theories are employed to evaluate mass and thermic transference attributes effectively. Aspects of thermic transformation are additionally inspected with nonlinear radiation, variable thermic conductivity and heat generation characteristics. Magnetic consequences are deployed for physical importance. Dimensionless expressions are accomplished with pertinent transformations, and then analytically elucidated by homotopic technique. Physical importance of leading variables on curves of skin friction, temperature, microorganisms and concertation are premediated graphically. Numerical computations are executed to briefly notice the significance of relative variables on local Sherwood, motile density and Nusselt numbers and organized in respective tables. It is acknowledged that velocity curves display declining tendencies for enlarging buoyancy ratio, bio-convective Rayleigh and Weissenberg numbers. The present study accentuated that temperature boosted prominently for heat generation and variable thermic conductivity. The attained outcomes further divulge that concentration display diminishing results for solutal relaxation variable while such declining outcomes ensued in temperature for thermic relaxation variable. Furthermore, microorganism’s curves display declining responses for bio-convective Lewis and Peclet variables. Finally, shear wall force improved for magneto-porous variable but lessened for Weissenberg number.

Triggering of electro-elastic anti-superhydrophobicity during non-Newtonian droplet collision

The present article discusses the electrohydro-dynamics of impacting non-Newtonian dielectric droplets on superhydrophobic (SH) surfaces. The role of important parameters like electric Eotvos number ( Eo e ), Weber number ( We ), dielectric particle concentration ( TiO 2 ) and polymer concentration ( PEG-400 ) were elucidated in this experimental study. Due to the interplay of non-Newtonian effects and electric field, we had observed the suppression of drop rebound on SH surfaces at much lower Eo e compared to its Newtonian counterpart. It has been observed that with an increase in both polymer concentration or dielectric particle concentration, the suppression of drop rebounds was observed at lower Eo e. In order to encapsulate the combined effects of electric field and non-Newtonian dynamics on drop rebound suppression, we have introduced the ‘electro-elastic effect’. Contrary to the common observations of drop rebound on SH surfaces, this electro-elastic effect induces inhibition of drop rebound, thereby resulting in anti-superhydrophobicity. Subsequently, we also established a scaling relationship to show that the rebound suppression is observed as a manifestation of the onset of electro-elastic instability, when a proposed electric Weissenberg number ( Wi e ) exceeds unity. Finally, we demarcated the rebound and rebound suppression regimes of droplet dynamics through a detailed phase map.

Activation energy and convective heat transfer effects on the radiative Williamson nanofluid flow over a radially stretching surface containing Joule heating and viscous dissipation

This article recognizes the time-dependent axisymmetric flow of a non-Newtonian Williamson fluid caused by a radially stretching surface in the presence of nanoparticles in the porous medium. The combined impacts of Joule heating and viscous dissipation on the flow profiles are also discussed. Chemical reaction at the surface is implemented. The convective heat transfer model and Brownian motion are also studied for the electrically conducting nanofluid flow. The Williamson nanofluid flow has been modeled using a set of partial differential equations based on the fundamental conservation laws of mechanics. By using nondimensional quantities, these equations are first transformed into ordinary differential equations. The Galerkin weighted residual method is performed to resolve these equations numerically. Visual displays and detailed descriptions of the impacts of relevant variables on the thermal performance, concentration field, and velocity field are provided. It is noticed that the thermal profile enhances as the values of the Brownian motion parameter and temperature ratio parameter increase while declining when the values of the velocity slip parameter increase. The Biot number, activation energy, and unsteadiness parameters have proportional effects on the concentration profile, but the reaction parameter has inversely proportional effects on the concentration profile. Heat transfer rate increases with increasing the Weissenberg number and velocity slip parameter, drops with increasing the thermophoresis and unsteadiness parameters, and the Arrhenius activation energy. Finally, a comparison of the obtained numerical solution for the porous and nonporous medium are also done graphically and discussed in details.