V. Kumaran

Stability of the viscous flow of a fluid through a flexible tube

The stability of Hagen-Poiseuille flow of a Newtonian fluid of viscosity eta in a tube of radius R surrounded by a viscoelastic medium of elasticity G and viscosity eta(s) occupying the annulus R 0 and eta(r) = 0, though there is an increase in Gamma(t) in the limit k much greater than 1. When the viscosity of the surface is non-zero (eta(r) > 0), however, there is a qualitative change in the Gamma(t) vs. k curves. For eta(r) infinity. For eta(r) > 1, Gamma(t) is finite only for k(min) k(max) are stable in the limit Gamma--> infinity. As H decreases or eta(r) increases, the difference k(max)- k(min) decreases. At minimum value H = H-min, which is a function of eta(r), the difference k(max)-k(min) = 0, and for H infinity. The calculations indicate that H-min shows a strong divergence proportional to exp (0.0832 eta(r)(2)) for eta(r) much greater than 1.

Structure and rheology of the defect-gel states of pure and particle-dispersed lyotropic lamellar phases

Abstract:We present important new results from light-microscopy and rheometry on a moderately concentrated lyotropic smectic, with and without particulate additives. Shear-treatment aligns the phase rapidly, except for a striking network of oily-streak defects, which anneals out much more slowly. If spherical particles several microns in diameter are dispersed in the lamellar medium, part of the defect network persists under shear-treatment, its nodes anchored on the particles. The sample as prepared has substantial storage and loss moduli, both of which decrease steadily under shear-treatment. Adding particles enhances the moduli and retards their decay under shear. The data for the frequency-dependent storage modulus after various durations of shear-treatment can be scaled to collapse onto a single curve. The elasticity and dissipation in these samples thus arises mainly from the defect network, not directly from the smectic elasticity and hydrodynamics.

Electrohydrodynamic instability of the interface between two fluids confined in a channel

The stability of the interface between two dielectric fluids confined between parallel plates subjected to a normal electric field in the zero Reynolds number limit is studied analytically using linear and weakly nonlinear analyses, and numerically using a thin-layer approximation for long waves and the boundary element technique for waves with wavelength comparable to the fluid thickness. Both the perfect dielectric and leaky dielectric models are studied. The perfect dielectric model is applicable for nonconducting fluids, whereas the leaky dielectric fluid model is applicable to fluids where the time scale for charge relaxation,

Dense granular flow down an inclined plane: from kinetic theory to granular dynamics

\epsilon \epsilon_o/\sigma

Experimental study of the instability of the viscous flow past a flexible surface

, is small compared to the fluid time scale

Constitutive relations and linear stability of a sheared granular flow

(\mu R/\Gamma)

Stability of wall modes in fluid flow past a flexible surface

, where

Voronoi neighbor statistics of hard-disks and hard-spheres.

\epsilon_o

Kinetic theory for a vibro-fluidized bed

is the dielectric permittivity of the free space,\epsilon and \sigma are the dielectric constant and the conductivity of the fluid,\mu and \Gamma are the fluid viscosity and surface tension, and R is the characteristic length scale. The linear stability analysis shows that the interface becomes unstable when the applied potential exceeds a critical value, and the critical potential depends on the ratio of dielectric constants, electrical conductivities, thicknesses of the two fluids, and surface tension. The critical potential is found to be lower for leaky dielectrics than for perfect dielectrics. The weakly nonlinear analysis shows that the bifurcation is supercritical in a small range of ratio of dielectric constants when the wavelength is comparable to the film thickness, and subcritical for all other values of dielectric constant ratio in the long-wave limit. The thin-film and boundary integral calculations are in agreement with the weakly nonlinear analysis, and the boundary integral calculation indicates the presence of a secondary subcritical bifurcation at a potential slightly larger than the critical potential when the instability is supercritical. When a mean shear flow is applied to the fluids, the critical potential for the instability increases, and the flow tends to alter the nature of the bifurcation from subcritical to supercritical.

Stability of the flow of a fluid through a flexible tube at intermediate Reynolds number

The hydrodynamics of the dense granular flow of rough inelastic particles down an inclined plane is analysed using constitutive relations derived from kinetic theory. The basic equations are the momentum and energy conservation equations, and the granular energy conservation equation contains a term which represents the dissipation of energy due to inelastic collisions. A fundamental length scale in the flow is the ‘conduction length’