ALBERT

Description: In this paper, we present detailed and systematic experimental results on the sedimentation of solid particles in aqueous solutions of polyox and polyacrylamide, and in solutions of polyox in glycerin and water. The tilt angles of long cylinders and flat plates falling in these viscoelastic liquids were measured. The effects of particle length, particle weight, particle shape, liquid properties and liquid temperature were determined. In some experiments, the cylinders fall under gravity in a bed with closely spaced walls. No matter how or where a cylinder is released the axis of the cylinder centres itself between the close walls and falls steadily at a fixed angle of tilt with the horizontal. A discussion of tilt angle may be framed in terms of competition between viscous effects, viscoelastic effects and inertia. When inertia is small, viscoelasticity dominates and the particles settle with their broadside parallel or nearly parallel to the direction of fall. Normal stresses acting at the corners of rectangular plates and squared-off cylinders with flat ends cause shape tilting from the vertical. Cylinders with round ends and cone ends tilt much less in the regime of slow flow. Shape tilting is smaller and is caused by a different mechanism to tilting due to inertia. When inertia is large the particles settle with their broadside perpendicular to the direction of fall. The tilt angle varies continuously from 90° when viscoelasticity dominates to 0° when inertia dominates. The balance between inertia and viscoelasticity was controlled by systematic variation of the weight of the particles and the composition and temperature of the solution. Particles will turn broadside-on when the inertia forces are larger than viscous and viscoelastic forces. This orientation occurred when the Reynolds number Re was greater than some number not much greater than one in any case, and less than 0.1 in Newtonian liquids and very dilute solutions. In principle, a long particle will eventually turn its broadside perpendicular to the stream in a Newtonian liquid for any Re 〉 0, but in a viscoelastic liquid this turning cannot occur unless Re 〉 1. Another condition for inertial tilting is that the elastic length XU should be longer than the viscous length v/U where U is the terminal velocity, v is the kinematic viscosity and A = v/c2is a relaxation time where c is the shear wave speed measured with the shear wave speed meter (Joseph 1990). The condition M=U/c 〉 1 is provisionally interpreted as a hyperbolic transition of solutions of the vorticity equation analogous to transonic flow. Strong departure of the tilt angle from 6 = 90° begins at about M = 1 and ends with 6 = 0° when 1 〈 M 〈 4. © 1993, Cambridge University Press. All rights reserved.

Description: We do a direct two-dimensional finite-elment simulation of the Navier-Stokes equations and compute the forces which turn an ellipse settling in a vertical channel of viscous fluid in a regime in which the ellipse oscillates under the action of vortex shedding. Turning this way and that is induced by large and unequal values of negative pressure at the rear separation points which are here identified with the two points on the back face where the shear stress vanishes. The main restoring mechanism which turns the broadside of the ellipse perpendicular to the fall is the high pressure at the ‘stagnation point’ on the front face, as in potential flow, which is here identified with the one point on the front face where the shear stress vanishes. © 1994, Cambridge University Press

Description: Nonlinear stability of core-annular flow near points of the neutral curves at which perfect core-annular flow loses stability is studied using Ginzburg-Landau equations. Most of the core-annular flows are always unstable. Therefore the set of core-annular flows having critical Reynolds numbers is small, so that the set of flows for which our analysis applies is small. An efficient and accurate algorithm for computing all the coefficients of the Ginzburg-Landau equation is implemented. The nonlinear flows seen in the experiments do not appear to be modulations of monochromatic waves, and we see no evidence for soliton-like structures. We explore the bifurcation structure of finite-amplitude monochromatic waves at criticality. The bifurcation theory is consistent with observations in some of the flow cases to which it applies and is not inconsistent in the other cases. © 1991, Cambridge University Press. All rights reserved.

Description: Two-dimensional cusped interfaces are line singularities of curvature. We create such cusps by rotating a cylinder half immersed in liquid. A liquid film is dragged out of the reservoir on one side and is plunged in at the other, where it forms a cusp at finite speeds, if the conditions are right. Both Newtonian and non-Newtonian fluids form cusps, but the transition from a rounded interface to a cusp is gradual in Newtonian liquids and sudden in non-Newtonian liquids. We present an asymptotic analysis near the cusp tip for the case of zero surface tension, and we make some remarks about the effects of a small surface tension. We also present the results of numerical simulations showing the development of a cusp. In those simulations, the fluid is filling an initially rectangular domain with a free surface on top. The fluid enters from both sides and is sucked out through a hole in the bottom. © 1991, Cambridge University Press. All rights reserved.

Description: We study the stability of a motionless liquid below its vapour between heated horizontal plates. The temperature of the bottom plate is held below the vaporization temperature and the top plate is hotter than the vaporization temperature. A water film is on the cold plate and a vapour film on the hot plate. We find a basic solution depending only on the variable y normal to the plates, with steady distributions of temperature, a null velocity and no phase change. The linear stability of this basic state is studied in the frame of incompressible fluid dynamics, without convection, but allowing for phase change. An ambiguity in the choice of the conditions to be required of the temperature at the phase-change boundary is identified and discussed. It is shown that the basic state of equilibrium is overstable under conditions of large temperature gradient, when the other parameters have suitable values. An analysis of the energy of the most dangerous disturbance shows that the source of the instability is associated with change of phase. © 1992, Cambridge University Press. All rights reserved.