Dispersion of a solute in pulsatile non-Newtonian fluid flow through a tube

The unsteady dispersion of a solute by an imposed pulsatile pressure gradient in a tube is studied by modeling the flowing fluid as a Casson fluid. The generalized dispersion model is applied to study the dispersion process, and according to this process, the entire dispersion process is expressed in terms of two coefficients, the convection and the dispersion coefficients. This model mainly brings out the effects of yield stress and flow pulsatility on the dispersion process. It is observed that the dispersion phenomenon in the pulsatile flow inherently differs from the steady flow, which is due to a change in the plug flow radius during a cycle of oscillation. Also, it was found that the dispersion coefficient fluctuates due to the oscillatory nature of the velocity. It is seen that the dispersion coefficient changes cyclically, and the amplitude and magnitude of the dispersion coefficient increases initially with time and reaches a non-transient state after a certain critical time. It is also seen that this critical time varies with Womersley frequency parameter and Schmidt number and is independent of yield stress and fluctuating pressure component. It is observed that the yield stress and Womersley frequency parameter inhibit the dispersion of a solute. It is also observed that the dispersion coefficient decreased approximately 4 times as the Womersley frequency parameter increases from 0.5 to 1. The study can be used in the understanding of the dispersion process in the cardiovascular system and blood oxygenators.     

Dispersion of suspended particles in a wave boundary layer over a viscoelastic bed

This is an analytical study with an aim to show the effects of a viscoelastic muddy bottom on the wave-induced convection and dispersion of a dilute suspension in the wave boundary layer above the viscoelastic bottom. It is shown that, depending on the rheology of the mud, the convection velocity and dispersion coefficient are non-monotonic functions of the thickness of the mud layer. When the elasticity dominates, appreciable resonant amplification of the mud motion can happen to a layer of certain thickness, which may lead to an order of magnitude increase in the dispersion coefficient and a negative convection velocity as well. It is, however, also possible that, away from these resonant mud depths, the convection velocity and dispersion coefficient are diminished, even to the extent to become virtually zero. All these transport phenomena are related to the oscillatory movement of the water-mud interface, in terms of phase and amplitude, relative to the movement of the near-bottom water particles.     

Dispersion in unsteady Couette–Poiseuille flows

The paper presents the longitudinal dispersion of passive contaminant released in an incompressible viscous fluid flowing between two infinite parallel flat walls, in which the flow is driven by the application of both periodic pressure gradient and the oscillation of upper plate in its own plane with a constant velocity. A finite difference implicit scheme has been adopted to solve the unsteady convection-diffusion equation for all time period based on Aris method of moments. The dispersion coefficients are obtained for three different flow situations: steady, periodic and the combined effect of steady and periodic Couette–Poiseuille flows, separately. The results show that oscillation of upper plate produces more dispersion than the pulsation of pressure gradient and their combined action leads to a further increase of dispersion. Also plate oscillation has stronger effect on velocity distribution and on dispersion coefficient than the pressure pulsation. There is a remarkable difference in the behaviour of dispersion coefficient depending on whether the ratio of two frequencies arising from the oscillations of pressure gradient and the upper plate possesses a proper fraction or not.     

Unsteady oscillatory stagnation-point flow of a viscoelastic fluid

The unsteady stagnation point flow of the Walters B^′ fluid is examined and solutions are obtained. It is assumed that the infinite plate at y=0 is oscillating and the fluid impinges obliquely on the plate.     

Instability of Poiseuille flow in a fluid overlying a glass bead packed porous layer

The instability of Poiseuille flow in a fluid overlying a glass bead packed porous layer saturated with the same fluid is studied. A three layer configuration is adopted, where a variable effective viscosity is modelled between the outer fluid and porous homogeneous regions. Previous work on the stability of this system has assumed that all regions are homogeneous. The results demonstrate that there are two modes of instability corresponding to the fluid and porous layers, respectively.     

Slow viscoelastic fluid flow past a rotating sphere

The problem of axially symmetric flow of a particular type of non-Newtonian fluid past a rotating sphere due to a uniform stream at infinity is investigated. The presence of a region of reversed flow is found under certain conditions depending on the angular velocity of the sphere, the speed of the uniform stream and radius of the sphere. This region which is attached to the rear portion of the sphere is found to depend strongly on the viscoelasticity of the fluid. The vortex is seen to move towards the sphere as the viscoelastic parameter increases while the other parameters are kept fixed. As this viscoelastic parameter approaches a critical value, the vortex is found to disappear.     

MHD flow of a viscoelastic fluid past a stretching surface

Summary The flow of a viscoelastic fluid past a stretching sheet in the presence of a transverse magnetic field is considered. An exact analytical solution of the governing non-linear boundary layer equation is obtained, showing that an external magnetic field has the same effect on the flow as the viscoelasticity.     

Hydromagnetic stability of plane Poiseuille flow of an Oldroyd fluid

Summary The linear stability of plane Poiseuille flow of a conducting Oldroyd liquid in the presence of a transverse magnetic field is studied. The fourth-order Orr-Sommerfeld equation governing the stability analysis in this case is solved numerically by a spectral method.     

Resistance of a sphere in a slow flow of a viscoelastic fluid

The authors have obtained an approximate solution of the problem of the resistance of a rigid sphere in a slow flow of a Maxwell viscoelastic fluid that is in good agreement with experimental data [1] for Weissenberg numbers We ≤ 0.7. It is shown that the effect of a decrease in the coefficient of resistance of a sphere in the interval 0.1 ≤ We ≤ 0.7 established experimentally is determined in full measure by the linear viscoelastic properties of the Maxwell fluid. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 6, pp. 1138–1140, November–December, 1998.     

The flow of a viscoelastic fluid past a porous plate

Summary The flow of a second order viscoelastic fluid past a porous plate is considered. It is characterized by a boundary value problem in which the order of the differential equation exceeds the number of available boundary conditions. The boundary value problem is solved by making a plausible assumption, namely that the variation of the normal derivative of the velocity at the plate withk is sufficiently smooth, wherek is the viscoelastic fluid parameter. Under this assumption it is shown that dual solutions exist for values ofk less than a critical value. Beyond this value, no solution exists.     

On heat transfer to pulsatile flow of a viscoelastic fluid

Summary A study is made of a problem of heat transfer to pulsatile flow of a viscoelastic fluid between two parallel plates of which the upper one is at a temperature higher than the lower one. The solutions for the steady and the fluctuating temperature distributions are obtained. The rate of heat transfer at the plates is also calculated. Numerical solutions are discussed with graphical representations. It is shown that the elasticity of the fluid significantly increases the temperature in the boundary layers near the plates. The magnitude of heat transfer at the plates is also greatly affected by the elasticity of the fluid and the Eckert number.     

Film flow of a nonlinear viscoelastic fluid along a conical rotor

Film flow of a nonlinear viscoelastic fluid, whose deformed behavior is described by using kinematic matrices, is considered along the surface of a rotating conical rotor.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 31, No. 2, pp. 231–236, August, 1976.     

Heat transfer in the flow of a viscoelastic fluid over a stretching sheet

Summary The problem of heat transfer in the viscoelastic fluid flow over a stretching sheet is examined. The important physical quantities such as the skin-friction coefficient and the heat transfer coefficient, are determined. It is found that the heat transfer coefficient decreases with the non-Newtonian parameter.     

MHD flow of a viscoelastic fluid past a stretching sheet with suction

Summary The laminar flow of a viscoelastic fluid past a stretching sheet in the presence of a magnetic field, when the fluid is extracted from the sheet at a uniform rate, is considered. An exact analytical solution exists for the problem. It is shown that when there is a suction of the fluid, the solutions are possible only upto a critical value of the viscoelastic parameter. Also, for values less than this critical value, dual solutions exist.     

Entrance effects in viscoelastic fluid flow in cylindrical nozzles

The pressure losses prior to entry into a nozzle are determined in the flow of a viscoelastic medium in broad ranges of the viscosity and the discharge. A generalized dependence of the entrance pressure losses on the rate of shear is obtained in dimensionless form. An empirical equation is proposed for the computation of entrance pressure losses.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 1, pp. 83–89, January, 1977.     

Stagnation point flow and heat transfer for a viscoelastic fluid impinging on a quiescent fluid

A theoretical study is made in the region near the stagnation point when a lighter incompressible viscoelastic fluids impinges orthogonally on the surface of another quiescent heavier incompressible viscous fluid. Similarity solutions of the momentum balance equations for both fluids are equalized at the interface. It is noted that an exact boundary layer solution is obtained for the lower lighter fluid. The velocity of the lower fluid is independent of lateral interface velocity but the velocity of the upper viscoelastic fluid increases with increasing lateral interface velocity. It is observed that lateral interface velocity increases with increasing viscoelastic parameter for fixed values of density and viscosity ratio of the two fluids. The convective heat transfer is investigated base on the similarity solutions for the temperature distribution of the two fluids. The interface temperature increases with increasing viscoelastic parameter of the upper viscoelastic fluid.     

Dispersion of solute by electrokinetic flow through post arrays and wavy-walled channels

In this work, we simulate electrokinetically driven transport of unretained solute bands in a variety of two-dimensional spatially periodic geometries (post arrays as well as sinuous/varicose channels), in the thin Debye layer limit. Potential flow fields are calculated using either an inverse method or a Schwarz-Christoffel transform, and transport is modeled using a Monte Carlo method in the transformed plane. In this way, spurious "numerical diffusion" transverse to streamlines is completely eliminated, and streamwise numerical diffusion is reduced to arbitrary precision. Late-time longitudinal dispersion coefficients are calculated for Peclet numbers from 0.1 to 3162. In most geometries, a Taylor-Aris-like scaling law for the dispersion coefficient D(L)/D(L0) = 1 + Pe2/alpha underpredicts dispersion when Pe approximately O(alpha1/2) (here D(L0) is the effective axial diffusion coefficient in the periodic geometry). A two-parameter correlation widely used in the porous media literature, D(L)/D(L0) = 1 + Pe(n)/alpha, agrees slightly better, but much better agreement can be obtained using a new quadratic form: D(L)/D(L0) = 1 + Pe/alpha1 + Pe2/alpha2. A quasi-universal relationship for stream-wise dispersion is offered that predicts 96% of the simulation data to within a factor of 2 in all geometries studied. Comparison with previous work shows that in circular post arrays, the dispersion coefficient for electrokinetic flow is a factor of 3-10 less (depending on Pe and relative post size) than for pressure-driven flow.     

A finite volume technique to simulate the flow of a viscoelastic fluid

Hydrodynamically developing flow of Oldroyd B fluid in the planar die entrance region has been investigated numerically using SIMPLER algorithm in a non-uniform staggered grid system. It has been shown that for constant values of the Reynolds number, the entrance length increases as the Weissenberg number increases. For small Reynolds number flows the center line velocity distribution exhibit overshoot near the inlet, which seems to be related to the occurrence of numerical breakdown at small values of the limiting Weissenberg number than those for large Reynolds number flows. The distributions of the first normal stress difference display clearly the development of the flow characteristics from extensional flow to shear flow.List of symbols D rate of strain tensor - L slit halfheight - P pressure, indeterminate part of the Cauchy stress tensor - R the Reynolds number - t time - U average velocity in the slit - u velocity vector - u,v velocity components - W the Weissenberg number based on the difference between stress relaxation time and retardation time - W ₁ the Weissenberg number based on stress relaxation time - x,y rectangular Cartesian coordinates - ratio of retardation time to stress relaxation time - zero-shear-rate viscosity, ₁ + ₂ - ₁ non-Newtonian contribution to - ₂ Newtonian contribution to - ₁ stress relaxation time - ₂ retardation time - density - (, , ) xx, yy and xy components of ₁, respectively - determinate part of the Cauchy stress tensor - ₁ non-Newtonian contribution to - ₂ Newtonian contribution to      

Poiseuille flow of a smectic A liquid crystal

This article considers the dynamics of smectic A liquid crystals subjected to Poiseuille flow. Linearised governing equations are constructed using a recent dynamic theory for Smectic A [36]. These equations are solved analytically and the consequent solutions are then calculated for some typical experimental data in order to determine the explicit flow behaviour. Stability of flow and layer structure solutions are proved. Results show how the response time for small perturbations to the smectic layers depends upon the permeation constant and the layer compression modulus.