Viscoelastic Fluid Layer Research Articles

Heat and mass transfer in tri‐layer ependymal ciliary transport with diverse viscosity

AbstractSpecialized cilia known as ependymal cilia help the cerebrospinal fluid, which is important for nutrient delivery and waste elimination, to circulate in the brain. Many species rely on cilia and flagella for fluid movement and motility. Cilia and flagella, for instance, produce propulsive forces that allow unicellular creatures like Paramecium and Euglena to move through their surroundings. Ciliary transport plays a role in the flow of egg cells, or oocytes, via the fallopian tubes in the female reproductive system. The transfer of the egg towards the uterus is facilitated by the synchronized wave‐like motion produced by the cilia lining the fallopian tubes. Like this, ciliary transport in men aids in the passage of sperm cells via the epididymis. Many scientists and researchers are studying the mechanics of cilia motion and the properties of the viscoelastic fluid layer to develop new treatments and applications in biomedical engineering and for some diseases. Motivated by a wide range of biological applications, the objective of this study is to investigate the heat and mass transfer flow of tri‐layered Newtonian fluids flowing with the help of ciliary beating in a Cartesian coordinate. The fluid is incompressible, and fluid layers are not intermixed. The fluid flow with heat and mass transfer is first modelled in wave and then transmuted into fixed. Solutions for temperature profile, velocity distribution, stresses and concentration distribution are obtained. The influence of incipient parameters is displayed with graphs and plotted with the computational software MATHEMATICA 13.0 in the results section. The key findings obtained from graphs show that the maximum magnitude for temperature and velocity is achieved in the middle layer of fluid whereas in the outer layer concentration profile is maximum. It is predicted that this approach will make an essential contribution to the progress and enhancement of various types of drug delivery systems in the biomedical industry and biomechanics.

Viscous correction to the potential flow analysis of Rayleigh–Taylor instability in a Rivlin–Ericksen viscoelastic fluid layer with heat and mass transfer

AbstractThe current investigation focuses on examining viscous corrections for viscous potential flow (VCVPF) analysis concerning the Rayleigh–Taylor instability occurring at the interface of a Rivlin–Ericksen (R–E) viscoelastic fluid and a viscous fluid during the transfer of heat and mass between phases. The R–E model is a fundamental framework in the study of viscoelastic fluids, providing insights into their complex rheological behavior. It characterizes the material's response to both deformation and flow, offering valuable predictions for various industrial and biological applications. Within the framework of viscous potential flow (VPF) theory, viscosity is exclusively accounted for in the normal stress balance equation, disregarding the influence of shearing stress entirely. This study introduces a viscous pressure term into the normal stress balance equation alongside the irrotational pressure, presuming that this addition will improve the discontinuity of tangential stresses at the fluid interface. Through derivation of a dispersion relationship and subsequent theoretical and numerical stability analyses, the stability of the interface is investigated across various physical parameters. Multiple plots are generated using the dispersion relation, and a comparative analysis between VPF and VCVPF is conducted to establish improved stability criteria. The investigation highlights that the combined impact of heat/mass transport and shearing stress serves to delay the instability of the interface.

Shear horizontal wave dispersion in two phase magneto-electro-elastic material loaded with viscoelastic fluid layer

In the present work, an exact analytical approach has been used to study the dispersive behavior of the shear horizontal (SH) wave in magneto-electro-elastic (MEE) material loaded with a viscoelastic fluid. Complex dispersion equations are derived in the cases of electric short magnetic short (ESMS), electric short magnetic open (ESMO), electric open magnetic short (EOMS), and electric open magnetic open (EOMO) boundary conditions by solving the equilibrium equations of MEE material and the Stokes equation of viscoelastic fluid. To validate the present outcomes, the MEE material is changed into piezoelectric and piezomagnetic materials by taking some theoretical assumptions and the outcomes are matched with preexisting results. Effect of volume fraction, wave frequency, substrate thickness and thickness of the fluid layer on phase velocity and attenuation of SH wave have studied. This study may find its applications in better understanding of the surface acoustic wave devices incorporated with viscoelastic fluid layer.

Effect of basic Temperature Gradients on Electrothermal Convection in a Rotating Layer of Viscoelastic (Walter’s B) Fluid Saturated Porous Medium Heated from Below

Combined Effect of Thermal Modulation and Rotation on the Onset of Convection in Walter's B Viscoelastic Fluid Saturated Porous Medium has been investigated. The problem is numerically solved using the Galerkin method after applying linear stability analysis and normal modes. It is possible to derive the dispersion relation while accounting for the effects of wave number, electric Rayleigh number, Darcy number, Taylor number, and thermal electric Rayleigh number. Graphically, the effects of the electric Rayleigh number, Darcy number, Wave number, and Taylor number on the onset of stationary convection have been studied. Under the boundary conditions considered, The kinematic viscoelasticity accounting for rheology of the nanofluid has no effect on the stationary convection for Walters’ (model B’) nanofluids and behaves like an ordinary Newtonian nanofluid.

Effect of Temperature Gradients and DC Electric Field on Electrothermal Convection in a Rotating Layer of Walter's-B Fluid Saturated Porous Media

Thermal convection in fluid-saturated porous media has diverse applications across geothermal energy utilisation, thermal insulation engineering, grain storage and understanding geodynamic processes. The thermal convection's physics is crucial for optimising the thermofluid system, improving energy efficiency, and enhancing our understanding of natural phenomena. The study examines how the initiation of electrothermal convection in a rotating viscoelastic fluid layer (Walter's B) is influenced by basic temperature gradients and a uniform vertical DC electric field, considering three different types of velocity boundary conditions: free-free, rigid-rigid, and lower rigid and upper free. By applying an electric field to a fluid, studying electrothermal convection helps engineers design effective cooling systems for electronics. The eigenvalue problem is solved by using the Galerkin technique. The Galerkin method is a widely used numerical technique for solving eigenvalue problems. The DC electric field effect exhibits a more stabilising effect for free-free boundaries than rigid and rigid-rigid boundaries. Moreover, the linear temperature profile exhibits a more stabilising effect than the parabolic temperature profile. The control of electrothermal convection on the system with the impact of other physical parameters is also discussed.

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.

Stability of natural convection in a vertical layer of Navier-Stokes-Voigt fluid

The stability of natural convection in a vertical layer of viscoelastic fluid confining between rigid-isothermal side walls held at different temperatures is investigated numerically using the Chebyshev collocation method. The viscoelastic behavior is modelled by means of a constitutive equation encompassing the Navier-Stokes-Voigt fluid or the Kelvin-Voigt fluid of order zero. The onset of convective instability is examined by linearizing the governing equations for the perturbations and an appropriate extension of Squire's theorem is given making a case to consider only two-dimensional perturbation stability equations. The numerical solution of the stability eigenvalue problem leads to the determination of the neutral stability condition. The dependence of the Kelvin-Voigt parameter on the critical stability parameters and also on the Prandtl number at which the point of transition from stationary to travelling-wave mode occurs is thoroughly analysed. The Kelvin-Voigt parameter shows an important role on the travelling-wave mode instability where it inducts both stabilizing and destabilizing effects on the base flow depending on the values of Prandtl number, while its impact on the stationary mode is found to be very weak. Furthermore, the streamlines and isotherms of the perturbation modes presented herein demonstrate the development of complex dynamics at the critical state. The results of a Newtonian fluid are obtained as a particular case.

Impact of heat and mass transport on Rayleigh–Taylor instability of Walter’s B viscoelastic fluid layer

Impact of heat and mass transport on Rayleigh–Taylor instability of Walter’s B viscoelastic fluid layer

Oscillatory convection in viscoelastic ferrofluid layer: Linear and non-linear stability analyses

The problem of ferroconvection in a viscoelastic fluid layer is studied with the aim to investigate oscillatory motions. In this article, a stability analysis for both linear and nonlinear systems is carried out. In the linear stability analysis, the expressions for steady and oscillatory Rayleigh numbers are obtained and the effects of magnetic as well as viscoelastic parameters on the onset of viscoelastic ferromagnetic convection are investigated numerically. From the analysis, we found that the magnetic number (M_1), the stress relaxation time (lambda_1) and the nonlinearity of magnetization (M_3) have destabilizing influences on the onset of ferroconvection, whereas the strain retardation time (lambda_2) has stabilizing influence. In the weakly nonlinear stability analysis, the formula for heat transfer rate in terms of the Nusselt number is derived for oscillatory convection. From the analyses, we found that for increasing values of the magnetic number, stress relaxation time and nonlinearity of magnetization, the heat transfer rate rises, whereas it decreases for larger values of the strain retardation time. Moreover, the pitchfork bifurcation analysis yields that in order to reach the stable positions, the value of amplitude increases as the stress relaxation time increases, whereas a reverse trend is observed for the strain retardation time.

On the competition of transverse and longitudinal modes of Marangoni convection in a three-dimensional layer of viscoelastic fluid

Within the vast array of applications encompassed by viscoelastic fluids, some lack of knowledge seems to affect the non-linear behavior of Marangoni convection when its typical initial unicellular and steady states are taken over by more complex flow configurations. These still hide a not-fully understood competition of complex and diverse physical mechanisms that determine the prevailing macroscopic behavior. In the present study, relevant insights are sought from consideration of the classical differentially heated rectangular layer of liquid with adiabatic bottom and top free surface. It is shown that, for increasing values of the Marangoni number and/or the elasticity parameter, this problem offers a multifaceted spectrum of different outcomes depending on the non-trivial interplay established between two distinct categories of disturbances (transverse and longitudinal). These are studied using a diversity of model types in which some processes are on or off to discern selectively their effect in the laminar state and their contribution to the evolution of the system toward chaos. The characteristic marks by which the ensuing elastic turbulence can be distinguished from the companion Kolmogorov counterpart are highlighted through analysis of the emerging scaling laws in the velocity spectrum and the sensitivity of these to the intensity of the driving force and the considered elasticity level. It is shown that these two forms of turbulence can coexist in the considered problem.

Modified stability analysis of double‐diffusive convection in viscoelastic fluid layer saturating porous media

AbstractThe present analysis mathematically investigates the thermohaline convection problem in viscoelastic fluid layer saturating porous media by utilizing the modified Boussinesq approximation. By performing linear stability analysis, the Darcy–Rayleigh numbers for stationary and oscillatory modes of convection are derived. The effects of different parameters describing the problem are studied numerically. In nonlinear stability analysis, the heat and mass transfer rates in the form of Nusselt and Sherwood numbers, respectively, are obtained for oscillatory convection using the derived Ginzburg–Landau equation. From the results, it is observed that overstability is the preferred mode of instability in linear stability. It is found that in linear double‐diffusive convection problems, the stress relaxation imparts a destabilizing effect whereas the strain retardation time, the coefficient of specific heat variation due to temperature, and the concentration gradient have a stabilizing effect on the system's stability. The numerical values of heat and mass transfer rates varied with the coefficient of specific heat showing that the heat transport decreases while the mass transport increases. Also, the stress relaxation time, the concentration gradient, and the gravity modulation's amplitude increase while the strain retardation time decreases the heat and mass transfer rates. The wavelength of oscillations remains unaltered with the variation of specific heat variation due to temperature. The modulation frequency does not affect the heat/mass transfer rate; though, the wavelength of oscillations decreases with increasing frequency.

Gravitational Modulation Effect on Double-Diffusive Oscillatory Convection in a Viscoelastic Fluid Layer

The complex Ginzburg-Landau model has been employed to derive the temporal amplitude of convection in a viscoelastic fluid layer under gravity modulation. The finite amplitude is based on a weakly nonlinear thermal convection. The perturbation technique is applied to simplify the nonlinear system of partial differential equations into a non-autonomous amplitude equation. Heat and mass transfer obtained in terms of the Nusselt and Sherwood numbers, and the corresponding results are presented for the small amplitude of modulation. The moderate values of amplitude and frequencies of gravity modulation are considered, their effect is to enhance the heat and mass transfer in the layer. Thus, the modulation plays dual role in heat and mass transfer. The variations of Nusselt and Sherwood numbers with slow time becomes rapid on either increasing the parameters Rs, Pr, λ, δ or decreasing the parameters Γ, ε, Ω. Each parameter effect has been presented graphically with their effect on Nu and Sh. Further, it is found that an oscillatory mode of convection enhances the heat and mass transfer than a stationary mode.

Triple diffusive convection in a viscoelastic Oldroyd-B fluid layer

The stability of a triply diffusive viscoelastic fluid layer in which the fluid density depends on three stratifying agencies possessing different diffusivities is investigated. The viscoelastic fluid is modeled by means of the Oldroyd-B constitutive equation. Analytical expressions are obtained for steady and oscillatory onset by carrying out the linear instability analysis and the crossover boundary between them is demarcated by identifying a codimension-two point in the viscoelastic parameters plane. The occurrence of disconnected closed oscillatory neutral curve lying well below the stationary neutral curve is established for some values of governing parameters indicating the requirement of three critical values of thermal Rayleigh number to specify the linear instability criteria. However, the possibility of quasiperiodic bifurcation from the motionless basic state is not perceived and this is in contradiction to the case of inelastic couple stress and Newtonian fluids. The corresponding weakly nonlinear stability of stationary and oscillatory modes has been carried out using a perturbation method. The cubic Landau equations are derived and the stability of bifurcating solution is discussed. The viscoelastic parameters influence the stability of stationary bifurcation despite their effect is not felt on the stationary onset. The stationary and oscillatory finite amplitude solution is found to bifurcate either subcritical or supercritical depending on the choice of governing parameters. The effect of Prandtl number and viscoelastic parameters on stationary and oscillatory convection modes of heat and mass transfer is analyzed.

Mathematical study of the small oscillations of a spherical layer of viscoelastic fluid about a rigid spherical core in the gravitational field

Mathematical study of the small oscillations of a spherical layer of viscoelastic fluid about a rigid spherical core in the gravitational field

Double‐diffusive convection in a rotating viscoelastic fluid layer

AbstractThe linear instability and a weakly nonlinear stability of a rotating double‐diffusive convection in a viscoelastic fluid layer are investigated. An Oldroyd‐B constitutive equation is used to describe the rheological behavior of the viscoelastic fluid. Several remarkable departures from those of single‐diffusive and double‐diffusive viscoelastic fluid systems are explored by performing the linear instability analysis. Under certain conditions, it is observed that (i) a non‐rotating double diffusive viscoelastic fluid layer becomes destabilized by rotation, (ii) a rotating viscoelastic fluid layer gets destabilized by the addition of heavy solute to the bottom of the layer, (iii) disconnected closed convex oscillatory neutral curve from the stationary neutral curve exists, and (iv) three critical thermal Rayleigh numbers are required to specify the linear instability criteria, as opposed to a single critical value. The nature of linear instability characteristics for Oldroyd‐B, Maxwell and Newtonian fluids is found to be contradictory for the identical values of governing parameters. By performing a weakly nonlinear stability analysis, a cubic Landau equation for the amplitude corresponding to stationary convection is derived and the stability of bifurcating equilibrium solution is discussed. The viscoelastic parameters influence the stability of stationary bifurcation despite their effect is not felt on the stationary onset. The influence of various parameters on heat and mass transfer is also elucidated.

Fingering instability in Marangoni spreading on a deep layer of polymer solution

Spreading on the free surface of a complex fluid is ubiquitous in nature and industry, such as drug delivery, oil spill, and surface treatment with patterns. Here, we report on a fingering instability that develops during Marangoni spreading on a deep layer of the polymer solution. In particular, the wavelength depends on the molecular weight and concentration of the polymer solution. We use the transmission lattice method to characterize the free surface morphology during spreading and the finger height at the micron scale. We use the Maxwell model to explain the spreading radius, which is dominated by elasticity at small time scales and by viscous dissipation at large time scales. In a viscous regime, with consideration of shear thinning, the spreading radius follows the universal 3/4 power law. Our model suggests a more generalized law of the spreading radius than the previous laws for Newtonian fluids. Furthermore, we give a physical explanation on the origin of the fingering instability as due to normal stresses at high shear rates generating a high contact angle, providing a necessary condition for the fingering instability. The normal stress also generates the elastic deformation at the leading edge and so selects the wavelength of the fingering instability. Understanding the spreading mechanism on a layer of viscoelastic fluid has a particular implication in airway drug delivery and surface coating.

English

English

Marangoni instability in a heated viscoelastic liquid film: Long-wave versus short-wave perturbations.

We investigate the Marangoni instability in a thin layer of viscoelastic fluid, confined between its deformable free surface and a substrate of low thermal conductivity. Following a theoretical analysis, we study the stability of the present system for the case when the fluid layer is subjected to heating from below. Here, we use the Maxwell model to depict the rheology of the viscoelastic fluid. Linear stability analysis of the quiescent base state reveals that, in addition to the conventional short-wave mode, a long-wave instability can also emerge in this system. We demonstrate the appearance of both the long-wave monotonic and oscillatory instabilities in such a system. We study this long-wave mode analytically using the scaling k∼sqrt[Bi] (k is the wave number and Bi is the Biot number), whereas the short-wave mode is examined numerically. The influential role of elasticity of the fluid and the other involved parameters on the stability of the system is aptly discussed, and their ranges are identified within which a particular instability mode gets critical.

Effect of cross-diffusion on the stability of a triple-diffusive Oldroyd-B fluid layer

The onset and stability of a triple cross-diffusive viscoelastic fluid layer is investigated. The rheology of viscoelastic fluid is approximated by the nonlinear Oldroyd-B constitutive equation which encompasses Maxwell and Newtonian fluid models as special cases. By performing the linear instability analysis, analytical expression for the occurrence of stationary and oscillatory convection is obtained. The numerical results show that the elasticity and cross-diffusion effects reinforce together in displaying complex dynamical behavior on the system. The presence of cross-diffusion is found to either stabilize or destabilize the system depending on the strength of species concentration as well as elasticity of the fluid and also alters the nature of convective instability. The disconnected closed oscillatory neutral curve lying well below the stationary neutral curve is observed to be convex in its shape in contrast to quasiperiodic bifurcation from the quiescent basic state noted in the case of Newtonian fluids. This striking feature is attributed to the viscoelasticity of the fluid. By performing a weakly nonlinear stability analysis, the stability of bifurcating solution is discussed. It is worth reporting that the viscoelastic parameters significantly influence the stability of stationary bifurcation though the stationary onset is unaffected by viscoelasticity. Besides, subcritical instability is occurs and the critical Rayleigh number at which such an instability is possible decreases in the presence of cross-diffusion terms. The results of Maxwell and Newtonian fluids are delineated as particular cases from the present study.

Entropy generation of magnetohydrodynamic electroosmotic flow in two-layer systems with a layer of non-conducting viscoelastic fluid

The entropy generation analysis is investigated in two-fluid dragging systems. The bottom layer fluid is considered as electrolyte solution affected by the applied magnetic field and the upper layer fluid is viewed as non-conducting viscoelastic Phan-Thien-Tanner (PTT) fluid. Under the combined influences of electric and magnetic fields, the upper layer non-conducting PTT fluid can be dragged by the bottom layer fluid due to the interfacial shear stress. Firstly, we obtain the analytical velocity expressions for both bottom layer and upper layer fluids under the unidirectional flow assumption. The bottom layer fluid velocity distribution shows a classical M-type velocity profile. The upper layer fluid flow can be viewed as the plate Couette flow or Couette-Poiseuille flow. Subsequently, the thermal transport characteristic and entropy generation analysis are discussed in the present two-fluid dragging system. The results show that magnetic field can enhance the local entropy generation rate, but viscoelastic physical parameter can restrain the local entropy generation rate. The present theoretical research can be used in the design of thermofluidic device. By manipulating the electric and magnetic fields strength and the ratio of fluid rheological properties, the fluid motion and heat transfer characteristics can be manoeuvred efficiently.