Elastico-viscous Fluid Research Articles

Determination of rheological constants of an elastico-viscous fluid by kinematical analysis of oscillatory motions

This paper contains experimental and theoretical work on a rotatory oscillatory flow of an elastico-viscous fluid. Assuming a linear constitutive equation, the motion of the fluid contained in a spherical or circular cylindrical vessel is computed. In particular, the limited height of the cylinder is taken into account for the boundary conditions. The solutions yield the velocities of the fluid particles as functions of the constitutive equation parameters, everywhere in the flow field. The experimental study is essentially based upon quantitative vizualisation techniques with solid particles: the amplitude and phase of the displacements of the tracers suspended in the fluid are obtained from an analysis of the photographs. Using the above-mentioned theoretical results we deduce the measurement of characteristic coefficients and functions of the materials tested. An experimental investigation of moderately concentrated aqueous solutions of polyethylene oxide is carried out.

On pulsating flow of polymeric fluids

The flow problem of an elastico-viscous fluid in a straight circular pipe under the influence of a fluctuating pressure gradient is considered. Adopting a simple, generalized Maxwell model, it is shown that the percentage increase in the mean flow rate rises with increasing frequency of fluctuation. The value of the mean pressure gradient at which the flow rate enhancement attains its maximum value is determined entirely by inelastic calculations.

Nonlinear thermal convection in an elasticoviscous layer heated from below

The linear and nonlinear stabilities of a horizontal layer of an elasticoviscous fluid, whose stress-rate-of-strain relations are due to Oldroyd (1958), are studied. In the linear theory it is already shown that steady convection (the situation generally referred to as the exchange of stability) is preferred for all relevant values of the Prandtl number (which is the ratio of the kinematic viscosity to the thermal diffusivity). The study of nonlinear effects for slightly supercritical Rayleigh number (which measures the temperature contrast across the layer) shows that plane disturbances for the case where the exchange of stability is valid and plane or centred disturbances for the case of overstability are governed by equations similar to those derived by Hocking, Stewartson & Stuart (1972) for plane Poiseuille flow. The influence of elasticity is to give rise to a burst only when the principle of exchange of stability is valid and provided certain conditions relating to the elastic parameters of the fluid are satisfied. The effect of the adiabatic temperature gradient is also discussed. It is shown that it stabilizes the layer in the linear theory. However, in the nonlinear theory it can destabilize the layer if the ratio the mean temperature of the layer to the temperature difference across the layer is large enough. For most practical purposes it does not influence the conditions necessary for a burst to occur.

Elastico-viscous flow engendered due to an impulsively started porous plane wall

Approximate solution for the flow past an impulsively started infinite porous plane wall in an elastico-viscous fluid is obtained for the velocity and shearing stress. The roles of elasticity of the liquid and the suction on the velocity and the shearing stress have been studied.

Elasticoviscous flow between a rotating and a stationary disk with uniform suction at the stationary disk

The flow of an elasticoviscous fluid between a rotating and a stationary disk with uniform suction at the stationary disk is studied. The equations of motion are solved by a regular perturbation method for small suction Reynolds number and by the Runge-Kutta numerical integration method. The results from the two methods have been compared. The effects of the elasticity of the fluid and the suction parameter on the velocity components, torque on the disks, and the pressure coefficient have been studied.

Stress relaxation effect in elastico-viscous lubricants in gears and rollers

The stress relaxation effect in an incompressible elastico-viscous fluid is investigated for the case of the lubrication of line-contact rollers. Two extreme cases are considered: that of low pressures with rigid surfaces and constant viscosity and that of heavily loaded elasto-hydrodynamic lubrication. In order to solve this problem, a new invariant material time derivative is suggested. This derivative is referred to a co-ordinate system attached to the principal axes of the strain-rate tensor, while the former derivatives have been referred to the fluid particle. It is shown that, unlike the previous derivatives, the new one enables a separate parametric description of the stress relaxation process and the first normal-stress difference. The results show that a significant increase in the load capacity is obtained, owing to the relaxation time of the fluid. The investigation is for fluids with a relaxation time small compared with the transit time of the lubricant through the bearing.

Unsteady Flows in an Elastico-Viscous Fluid Induced by Torsional Oscillations of a Plate

A study is made of the unsteady flows in an electrically conducting elastico-viscous rotating liquid in the presence of a uniform magnetic field due to small amplitude torsional oscillations of an infinite, rigid non-conducting plate. This analysis is aimed at finding the general features of the steady as well as the unsteady velocity field, and the structure of the associated boondary layers on the plate. The significant interaction of rotation, hydromagnetic and elastic parameters involved in the problem is examined. The velocity field related to the small elastic parameter is calculated with physical significance. The Ekman suction velocity is calculated as the limit of w(z, t) when z→∞t→∞ and is shown to be non-zero. It is shown that the non-zero Ekman suction velocity represents the generation of an axial inflow toward the boundary layers, Several limiting results are shown to follow as special cases of this analysis.

Investigation of Elastico-Viscous Hydrodynamic Lubrication of Sleeve Bearing

An experimental investigation of the pressure distribution in a full film hydrodynamic sleeve bearing was carried out. The pressure profiles of nearly-Newtonian and significantly elastico-viscous fluids were compared. The results verify previous theoretical predictions of a small additional elastico-viscous component, perpendicular to the “Newtonian component.” For the case investigated viscoelasticity does not contribute significantly in steady state to the LCC, which is determined practically by the highest average rate of shear UIC (1-e) Presented as an American Society of Lubrication Engineers paper at the ASLF/ASME Lubrication Conference held in Miami Beach, Florida, October 21–23, 1975

Erratum to: On the unsteady non-Newtonian rotating flow induced by torsional oscillations of a disk

The unsteady boundary-layer flow generated in an incompressible, homogeneous elastico-viscous fluid bounded by an infinite rigid disk is investigated when the whole system is in a state of solid-body rotation with uniform angular velocity and, at some instant of time, the disk executes small-amplitude torsional oscillations with a given frequency. The analysis is carried out to determine various qualitative and quantitative information about the unsteady and steady velocity distributions, the structure of the associated multiple boundary layers, the effects of the elastic parameter and rotation on the flow and the Ekman suction velocity with its physical significance. It has been shown that the steady-state flow field consists of the two distinct boundary layers which are modified by the angular velocity of rotation, the elastic parameter and the frequency of the imposed oscillations. Several known results of physical interest are recovered as special cases.

On the unsteady non-Newtonian rotating flow induced by torsional oscillations of a disk

The unsteady boundary-layer flow generated in an incompressible, homogeneous elastico-viscous fluid bounded by an infinite rigid disk is investigated when the whole system is in a state of solid-body rotation with uniform angular velocity and, at some instant of time, the disk executes small-amplitude torsional oscillations with a given frequency. The analysis is carried out to determine various qualitative and quantitative information about the unsteady and steady velocity distributions, the structure of the associated multiple boundary layers, the effects of the elastic parameter and rotation on the flow and the Ekman suction velocity with its physical significance. It has been shown that the steady-state flow field consists of the two distinct boundary layers which are modified by the angular velocity of rotation, the elastic parameter and the frequency of the imposed oscillations. Several known results of physical interest are recovered as special cases.

Laminar boundary layer over a flexible surface in oscillatory flow

Oscillatory flow of an elastico-viscous fluid (Walters fluid B′) over a flexible surface is analysed. The study is limited to fluids with short memories. The effects of fluid elasticity on flow are brought out by comparing the results with those obtained in case of a Newtonian fluid.

Rotary Oscillations of a Torus in an Elastico Viscous Fluid

Rotary Oscillations of a Torus in an Elastico Viscous Fluid

The resistance to flow of elasticoviscous fluids through granular beds

The resistance to flow of elasticoviscous fluids through granular beds

Stokes problem for elastico-viscous fluid

An approximate solution to the flow past an impulsively started infinite plate in an elastico-viscous fluid is derived for the velocity and shearing stress. It is observed that the velocity increases with increasing the elastic parameterk and the shearing stress decreases with increasingk.

Unsteady free convective flow of an elastico-viscous fluid past an infinite plate with variable suction

An analysis of unsteady free convective flow of an elastico-viscous fluid past an infinite, porous plate is carried out under the following conditions: (1) suction velocity oscillates about a non-zero constant mean, (2) the plate temperature oscillates in magnitude about a non-zero constant mean. Approximate solutions for velocity, fluctuating parts of the velocity, amplitude and phase of the skin-friction and temperature, and rate of heat transfer are carried out. A comparative study is presented for viscous and elastico-viscous fluids during the course of discussion. Main results in the case of elastico-viscous fluids are presented in the conclusions.

Slow flow of an elastico-viscous fluid past cylinders and spheres

Drag measurements at very low Reynolds numbers are presented for three-dimensional flow past a sphere and planar flow past a circular cylinder. Newtonian and non-Newtonian liquids are considered and the results are compared with the existing theoretical predictions. For viscoelastic liquids the departure from the Newtonian drag appears as a quadratic function of velocity. This result seems to be true for both flow past a sphere and flow past a cylinder. No visible change occurs in the streamline pattern when compared to the purely viscous case.

Slow flow of an elastic- viscous fluid past an immersed body

The slow flow of an elastico-viscous fluid past an immersed body is examined analytically. A method is outlined using successive integral transform techniques which provide solutions for both steady and unsteady cases. The Oseen equations for the outer flow field are solved and the solutions are matched asymptotically with the Stokes solutions near the body. A detailed calculation is presented for the two-dimensional flow past a circular cylinder and three-dimensional flow past a sphere. The departure of the drag coefficient and the stream function from the purely viscous value is discussed. The results for the sphere agree qualitatively with previous analyses and the new results for the flow past a cylinder predict a departure from the Newtonian drag as a quadratic function of the velocity.

Rotating Flow of an Elastico‐Viscous Fluid on an Oscillating Palte

Rotating Flow of an Elastico‐Viscous Fluid on an Oscillating Palte

On unsteady flow of an elastico-viscous fluid past an infinite plate with variable suction

Approximate solutions of the Navier-Stokes equations are derived through the Laplace transform for two dimensional, incompressible, elastico-viscous flow past a flat porous plate. The flow is assumed to be independent of the distance parallel to the plate. General formulae for the velocity distribution, skin friction and displacement thickness as functions of the given free stream velocity and suction velocity are obtained.

Stability of the flow of an elastico-viscous fluid

The eigenvalues of the generalized Orr-Sommerfeld equation for an elasticoviscous fluid are found for a constant velocity profile. The result shows that the effect of elasticity is to stabilize the flow.