N.D. Waters

The stability of two stratified non-newtonian liquids in couette flow

Abstract Consideration is given to the stability of the interface between two Oldroyd liquids with shear-dependent viscosities, flowing in distinct layers while undergoing plane Couette flow. Results are presented as regions of stability in the plane determined by the logarithms of the viscosity and depth ratios. The work of previous authors for two Newtonian, power-law and constant-viscosity Oldroyd liquids is revealingly presented in a similar fashion. It is found that the dependence of the viscosities on shear-rate can drastically affect the regions of interfacial stability in a way over and above that due to just a change in the effective viscosity ratio. It is also found that for the Oldroyd liquids this viscosity variation affects the stability when it is present in the less-viscous layer.

The stability of two stratified ”power-law“ liquids in couette flow

Abstract Consideration is given to the stability of the flow of two ”power-law“ liquids between two infinite parallel planes when one of the planes moves with constant velocity in its own plane. It is found that the ratios of the power-law parameters for each layer have a dramatic effect and can be chosen to destabilize the flow.

The effect of oscillation on the drainage of an elastico-viscous liquid

Abstract The oscillatory drainage of liquids simulated by the Oldroyd four-constant model is investigated using a numerical time-marching technique. The drainage of constant-viscosity elastic liquids is not significantly affected by the oscillatory motion whether applied parallel or orthogonal to the direction of the main flow. During the oscillatory drainage of shear-dependent elastic liquids, there is evidence of drainage enhancement and elastic recoil on applying the vibration parallel to the direction of the main flow. The recoil has the effect of thickening parts of the liquid film. On applying the vibration orthogonal to the direction of the main flow, for such liquids, enhancement is obtained for all film thicknesses.

The numerical simulation of an oldroyd liquid draining down a vertical surface

Abstract The problem of the drainage of an elastic liquid with a shear dependent viscosity from a vertical surface is solved numerically by using a time-marching finite difference procedure. Shear-thinning is found to have a damping effect on any elastic oscillations during start-up in all but very thin films, and is confirmed as the dominant non-Newtonian property at later times.

Start-up of an elastico-viscous liquid draining from a vertical surface

Abstract The free drainage of thin films of non-Newtonian liquids from vertical surfaces occurs in a variety of industrial processes. Consideration is given in this paper to the effect of liquid elasticity on the much neglected “start-up” phase of the flow. The analysis utilizes the solution derived in 1970 by Waters and King for the generation of plane Poiseuille flow, to show that the presence of elasticity has a profound effect on the initial and the subsequent drainage profile.

Draining thin films—Part 1

Abstract In this, the first of a series of papers on the drainage of a thin film of non-Newtonian liquid down a vertical surface, a parametric solution is obtained for liquids with a shear-rate dependent viscosity and a prescribed initial profile. Experimental measurement of the mass of fluid remaining on a surface as a function of drainage time agrees with the theory.

Draining thin films—Part 2 laser measurements of film thickness and velocity profile

Abstract Two different experimental techniques involving the use of a laser are used to study liquid films draining from a vertical surface. The accuracy and consistency obtained for Newtonian liquids, and some preliminary investigations, suggest that the techniques can now be used to study the drainage of non-Newtonian liquids.

Enhancement of the drainage of non-Newtonian liquid films by oscillation

Abstract The flow of thin liquid films down an oscillating vertical surface is investigated both theoretically and experimentally for Newtonian and non-Newtonian liquids. The effects of the oscillation are explored analytically for Newtonian and linear viscoelastic liquids, and numerically for a generalized Newtonian liquid. The oscillatory motion has no net effect on the drainage of Newtonian and linear viscoelastic liquids, but enhancement is predicted for shear-dependent liquids. A gravimetric experiment is developed to check the theoretical predictions. The experiment enables the mass of liquid remaining on an oscillating glass tile to be monitored as a function of time. Good quantitative agreement between theory and experiments is shown for Newtonian liquids. For shear-thinning non-Newtonian liquids the experiments confirm that the predicted enhancement in the drainage occurs, in qualitative agreement with theory.

Draining non-Newtonian films: Part 1. The numerical simulation of a generalized Newtonian liquid draining down a vertical surface

Abstract A time-marching finite difference procedure is used to solve the problem of a generalized Newtonian liquid draining from rest down a vertical surface. It is confirmed that the unsteady start-up phase of the drainage can be ignored in most practical situations. It is suggested that the numerical procedure may be applicable to other similar, but more complicated, flows.

Draining non-Newtonian films: Part 2. Measurement of the rate of change of film thickness by laser interferometry

Abstract Consideration is given to the free drainage of Newtonian and non-Newtonian liquids from a vertical cylinder. The planar theory of Keeley et al. is readily extended and gives quantitative agreement with experimental results obtained using laser interferometry.