Incompressible Viscoelastic Fluid Research Articles

Blow-up criterion for the 3-D inhomogeneous incompressible viscoelastic rate-type fluids with stress-diffusion

<p>In this paper, we investigate the blow-up criterion of an evolutionary partial differential equation system controlling the flows of incompressible viscoelastic rate-type fluids with stress-diffusion, where the extra stress tensor describing the elastic response of the fluid is purely spherical. By utilizing this criterion, the global well-posedness of the system can be readily obtained. Despite being a physical simplification, this model exhibits features that necessitate novel mathematical approaches to tackle the technically complex structure of the associated internal energy, as well as the more complicated forms of the corresponding entropy and energy fluxes. The paper provides the first rigorous proof of the existence of a global solution to the model under small initial data.</p>

Global well-posedness of the three-dimensional free boundary problem for viscoelastic fluids without surface tension

Global well-posedness of the three-dimensional free boundary problem for viscoelastic fluids without surface tension

Linear instability of a resting state of the magnetohydrodynamic flows of polymeric fluid in a cylindrical channel (generalized Vinogradov–Pokrovski model)

We study a linear stability of a resting state for flows of incompressible viscoelastic fluid in an infinite cylindrical channel under the influence of an external uniform magnetic field directed parallel to the cylinder axis (we use a generalized rheological Vinogradov–Pokrovski model as mathematical model) in a class of axisymmetric periodic along the axial variable flows. We establish that for some values of the parameters in the case of an absolute conductivity bm=0, the magnetic field can substantially lessen the real part of an exponent for perturbations of the radial velocity component, which is the main element of the instability development. For general case bm≠0, we justify the possibility of removing the instability based on the performed calculations.

Local well-posedness of a viscoelastic fluid model for reactive polymers

In this paper, we study the Cauchy problem of the two-species incompressible viscoelastic fluid of Oldroyd-B system, which involving a reaction effect between two species of polymers. We prove the local existence with initial data in [Formula: see text] in a classical solution framework, and then provide a blow-up criteria. We concentrate on the a priori estimate, by using the energy method. In particular, the variant system in a general formulation is also studied, and the corresponding local well-posedness is established.

Numerical spectral approach for studying activation energy behavior in viscoelastic fluid flow through non-Darcian medium

The work examines the effects of MHD incompressible viscoelastic fluid under nonlinear thermal radiation while flowing in a non-Darcy porous medium. The utilization of the Darcy-Brinkmann-Forchheimer model has thus been implemented in the formulation of the momentum equation. The study posits the existence of a chemical phenomenon which involves elements A and B as two chemical species. The diffusion coefficient of chemical species exhibits inequality when considered for viscoelastic fluid. Numerical solutions are generated using SRM, spectral relaxation technique for governing flow problems. The current algorithm is formulated and implemented using the computational software MATLAB. The results exhibit a considerable degree of agreement with formerly established numerical outcomes within the framework of a specific scenario. The observations from this study provide evidence that chemical species B operates as a catalyst in a subsurface environment that is oriented horizontally. As a result, the connection between the homogeneous-heterogeneous scheme can be observed in the context of isothermal cubic autocatalytic occurrences and processes of the first order, subsequently. The utilization of the heterogeneous reaction parameter offers notable advantages in reducing the concentration of the bulk-fluid while simultaneously enhancing the concentration of the catalyst situated over the surface. The current findings contribute to the exploration of the computational study of diffusivities in MHD viscoelastic fluid flow. Specifically, this research inquires the effects of nonlinear thermal radiation and homogeneous-heterogeneous reactions.

Inverse Problems for Heat Convection System for Incompressible Viscoelastic Fluids

Inverse Problems for Heat Convection System for Incompressible Viscoelastic Fluids

Global unique solutions for the 2-D inhomogeneous incompressible viscoelastic rate-type fluids with stress-diffusion

<p>We establish the global unique solution for the 2-D inhomogeneous incompressible viscoelastic rate-type fluids with stress-diffusion by employing the standard energy method and the standard compactness arguments.</p>

Homogenization of motion equations for medium consisting of elastic material and incompessible Kelvin-Voigt fluid

We consider an initial-boundary problem describing the motion of a two-phase medium with a periodic structure. The first phase of the medium is an isotropic elastic material and the second phase is an incompressible viscoelastic Kelvin-Voigt fluid. This problem consists of second and fourth order partial differential equations, conditions of continuity of displacements and stresses at the phase boundaries, and homogeneous initial and boundary conditions. Using the Laplace transform method, we derive a homogenized problem, which is an initial boundary value problem for the system of fourth order partial integro-differential equations with constant coefficients. The coefficients and convolution kernels of the homogenized equations are found by using solutions of auxiliary periodic problems on the unit cube. In the case of a layered medium, the solutions of the periodic problems are written explicitly, and this allows us to find analytic expressions for the homogenized coefficients and convolution kernels. In particular, we establish that the type and properties of the homogenized convolution kernels depend on the volume fraction of the fluid layers inside the periodicity cell.

Effect of sinusoidal pressure gradient on MHD flow of viscoelastic fluid in a channel

Unsteady Hydro Magnetic oscillatory flow of incompressible viscoelastic fluid in a channel packed with porous material is investigated under the influence of oscillatory pressure gradient. Moreover, the applied magnetic field of moderate strength interacts with electrically conducting fluid, to generate a resistive volumetric body force. In addition to it, viscoelastic fluidity, characterizing the non-Newtonian behavior in conjunction with permeability of the medium as well as sinusoidal sheared flow due to imposed favorable pressure gradient, contribute to the novelty of the study. The previous work was confined to constant motion of the lower plate but the present work includes the sinusoidal motion of the lower plate in addition to the constant motion. The importance lies with the fact that the coupling effect of sinusoidal fluctuation and viscoelastic fluidity go hard in industrial applications, particularly in process industry. The governing equations characterizing the flow are solved analytically. The striking results of this study are: the formation of inverted boundary layer in case of oscillatory lower plate with moderately escalated time span but such instability leading to flow reversal, does not appear in case of constant motion of the lower plate. Hence, it is recommended that for stability of flow and to avoid flow reversal, higher frequency of oscillation as well as larger time span is not desirable. The elastico-viscosity property reduces the volume flow rate which may be useful to control the efflux and differentiates the state of motion (resulting low skin friction) and state of rest (resulting high skin friction) in respect shearing effects at the bounding surfaces.

Inverse problems for nonlinear Navier–Stokes–Voigt system with memory

Inverse problems for nonlinear Navier–Stokes–Voigt system with memory

Effect of fluid viscoelasticity, shear stress, and interface tension on the lift force in lubricated contacts.

We consider a cylinder immersed in viscous fluid moving near a flat substrate covered by an incompressible viscoelastic fluid layer, and study the effect of the fluid viscoelasticity on the lift force exerted on the cylinder. The lift force is zero when the viscoelastic layer is not deformed, but becomes non-zero when it is deformed. We calculate the lift force by considering both the tangential stress and the normal stress applied at the surface of the viscoelastic layer. Our analysis indicates that as the layer changes from the elastic limit to the viscous limit, the lift force decreases with the decrease of the Deborah number (De). For small De, the effect of the layer elasticity is taken over by the surface tension and the lift force can become negative. We also show that the tangential stress and the interface slip velocity (the surface velocity relative to the substrate), which have been ignored in the previous analysis, give important contributions to the lift force. Especially for thin elastic layers, they give dominant contributions to the lift force.

MHD VISCOELASTIC STAGNATION-POINT FLOW AROUND A STRETCHING SHEET WITH INDUCED MAGNETIC FIELD AND VISCOUS DISSIPATION

The present study deals with a steady MHD stagnation-point flow of incompressible viscoelastic fluid in a porous medium around a stretching/shrinking sheet. The influence of induced magnetic field, heat source parameter and viscous dissipation are considered. The resulting nonlinear partial differential equations are solved under suitable boundary conditions using the bvp4c method. The effect of various physical parameters affecting on the flow has been studied. It is observed that the viscoelastic parameter enhances the induced magnetic field profile and temperature profile, whereas fluid velocity reduces. Moreover, the stretch parameter has a significant influence on the fluid velocity. The temperature profile can be improved by increasing the viscoelastic parameter, magnetic parameter, heat source parameter and radiation parameter, while the opposite effect is observed for Eckert number, reciprocal of the magnetic Prandtl number and Prandtl number.

Tangential Shear Stress in Oscillatory Flow of a Viscoelastic Incompressible Fluid in a Plane Channel

Tangential Shear Stress in Oscillatory Flow of a Viscoelastic Incompressible Fluid in a Plane Channel

Akışkanlar Dinamiğinde Oskolkov Denkleminin Tam Çözümleri

Traveling wave solutions of the Oskolkov equation, which is a model describing the dynamics of an 
 incompressible visco-elastic Kelvin-Voigt fluid, are investigated in this study. Complex trigonometric and 
 complex hyperbolic solutions of Oskolkov equation are obtained using the sub equation method. In 
 these obtained solutions, graphs are presented by assigning special values to the parameters. The 
 presented graphics are drawn with a computer package program. Implemented method is powerful 
 and an effective method to achieve the exact solutions of nonlinear partial differential equations
 (NPDEs).

Tangential Shear Stress in Oscillatory Flow of a Viscoelastic Incompressible Fluid in a Plane Channel

The problems of oscillatory flow of a viscoelastic incompressible fluid in a plane channel are solved for a given harmonic oscillation of the fluid flow rate. The transfer function (amplitude–phase frequency response) is determined. Using this function, the effect of the acceleration oscillation frequency and the relaxation properties of fluid on the ratio of the tangential shear stress on channel wall to the velocity averaged over the channel cross-section (cross-sectional velocity) is determined. It is shown that the viscoelastic properties of fluid, as well as its acceleration, are the limiting factors for using the quasi-stationary approach. The found formulas for determining the transfer function for viscoelastic fluid flow in the case of non-stationary stream make it possible to determine the dissipations of mechanical energy in a non-stationary flow of the medium which are of importance for calculation of the control of hydraulic and pneumatic systems.

Analysis of small oscillations of a pendulum partially filled with a viscoelastic fluid

<abstract><p>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.</p></abstract>

Sıkıştırılamaz Visko Elastik Kelvin-Voigt Sıvısında Ortaya Çıkan Oskolkov Denkleminin Gezici Dalga Çözümleri

In this manuscript, exact solutions of the Oskolkov equation, which describes the dynamics of incompressible viscoelastic Kelvin-Voigt fluid, are presented. The -expansion method is used to search for these solutions. The dynamics of the obtained exact solutions are analyzed with the help of appropriate parameters and presented with graphics. The applied method is efficient and reliable to search for fundamental nonlinear waves that enrich the various dynamical models seen in engineering fields. It is concluded that the analytical method used in the study of the Oskolkov equation is reliable, valid and useful tool for created traveling wave solutions.

Spectrum and linear Lyapunov instability of a resting state for flows of an incompressible polymeric fluid

Spectrum and linear Lyapunov instability of a resting state for flows of an incompressible polymeric fluid

Unsteady thermally radiative and chemically reactive viscoelastic fluid flow past a vertical porous plate with a heat source

AbstractAn analytical study is performed to investigate the thermal radiation effect on the unsteady two‐dimensional magnetohydrodynamic flow of a viscoelastic incompressible fluid (Walters fluid model) along an infinite hot vertical sheet embedded in a porous medium. Further, the addition of a heat source in the energy equation as well as a chemical reaction in the concentration equation renders the present analysis realistic in the field of engineering and technology. The governing equations of mass, momentum, energy, and concentration are solved with successive perturbation techniques. The effects of pertinent parameters on fluid velocity, temperature, concentration, and bounding surface coefficients are shown graphically and in tabular form. The salient feature of the present study is to impose control on magnetic field strength vis‐à‐vis electromagnetic force by regulating voltage in the electric circuit. The important findings are: the elasticity property of the fluid is more sensitive to heated bounding surface consequently free convection current in enhancing the velocity near the plate than the inherent property viscosity. This outcome contributes to the design requirement to control the flow near the heated surface, higher values of frequency parameters contribute to the attainment of a free stream state in temperature distribution. Besides the aforesaid outcome, the present model is conducive to thinning of boundary layer as the elasticity, magnetic as well as free convection parameters enhance the force coefficients at the bounding surface.

Perturbation based analytical and numerical solutions of non-Newtonian differential equation during reverse roll coating process under lubrication approximation theory

Reverse roll coating process are utilized for the purpose of applying a coating to a substrate or web by utilising different rollers in order to get the required coated surface. As a result of this, reverse roll coating process have found applications in a wide variety of industries, such as those dealing with food and medicine, electronic components, optical and LCD devices, and optical products. The main objective of this paper is to develop the mathematical formulation for the coating of thin film for an incompressible isothermal viscoelastic fluid between two reversely rotating rolls. Through the use of an appropriate dimensionless parameter, Non-dimensional nonlinear ordinary differential equations (ODEs) are derived from governing partial differential equations (PDEs). LAT (lubrication approximation theory) simplifies the dimensionless equations of fluid motion. The expressions for velocity of flow, pressure gradient and flow rate is obtained analytically by using regular perturbation method, while numeric solution of some mechanical parameters such as power input, coating thickness, roll separation force and separation points are calculated. The numerical validation of the analytical solution of the fundamental model of nonlinear constitutive flow laws is done in the Maple environment using the numeric technique which is based on finite difference method. The influence of numerous non-Newtonian parameters such as velocities ratio and Weissenberg number on velocity profiles, pressure gradient, power input, roll separation force, separation points and coating thickness of a non-Newtonian Johnson–Segalman (JS) fluid are explored via graphically and in tabular form. The outcomes demonstrate that on increasing the Weisenberg number and velocities ratio, the coating thickness on web is decreases. For the numerous values of velocities ratio, it is important to note that separation points shifted towards the nip region. In addition, the non-Newtonain parameter have signifcant impact on power input and roll separating force. The maximum coating thickness that is 1.0927 has been observed at the value of separation poin 0.9620. Hence, these factors may help in an efficient coating process and improve the substrate life.