R.Shankar Subramanian

The slow axisymmetric motion of two bubbles in a thermal gradient

Abstract The motion of two bubbles along their line of centers in an imposed thermal gradient is considered. The governing equations are solved in the quasistatic limit using bipolar coordinates. Representative streamlines and isotherms are presented. A simple heuristic approximation is also presented, and is found to be excellent over the entire range of values of the radius ratio and the separation distance. As expected, the interaction effect between two bubbles increases as the separation distance is decreased. A small bubble moves more rapidly in the presence of a larger bubble than in its absence, whether it leads or trails the larger bubble. The velocity of the large bubble is reduced compared to the case when it is isolated, but to a lesser extent. When the bubbles are of equal diameter, they exert no influence on each others velocity for all separation distances.

Thermocapillary migration of bubbles and droplets

Abstract The migration of a droplet in a large liquid body possessing a uniform temperature gradient is analyzed in the creeping flow limit for small values of the Marangoni number (e). The method of matched asymptotic expansions is used for the solution of the field equations. The migration velocity is calculated to 0(e2) and the result reduces to that of Young, Goldstein and Block [10] in the limit of zero Marangoni number.

The thermocapillary motion of two bubbles oriented arbitrarily relative to a thermal gradient

The interaction problem of two bubbles oriented at an arbitrary angle to a thermal gradient in the absence of gravity is studied. The problem is considered in the quasi-static limit, wherein unsteady and convective transport terms are completely neglected in the momentum and energy equations. Instead of bipolar coordinates, an approximation used in a previous analysis of the interaction effects of two bubbles moving along their line of centers in a thermal gradient is applied here to predict the interaction parameter.

Thermocapillary migration of a bubble normal to a plane surface

Abstract The influence of a plane solid or fluid surface on the thermocapillary migration of a gas bubble moving normal to it in a space laboratory is investigated in the quasi-static limit. Results are presented for a suitably defined “interaction” parameter Ω as a function of the scaled distance of the bubble from the plane surface, and compared with similar predictions for buoyant migration.

On Relaxation Phenomena in Field-Flow Fractionation

Abstract The two-dimensional unsteady convective diffusion equation satisfied by the local concentration of the colloid introduced in a field-flow fractionation (FFF) column is solved by the method of finite differences. The alternating direction implicit (ADI) method proposed by Peaceman and Rachford is used. The axial convection term is approximated by a backward difference approximation to obtain a stable and convergent scheme. Numerical results are obtained for various values of the transverse Peclet number for the case of steady laminar flow and a slug input. The numerical results from the ADI method are validated by comparison with numerical solutions obtained using an explicit scheme as well as by internal consistency checks. The results of this work show that the transverse concentration profiles depend in a complex fashion on axial position along the cloud during relaxation. In the presence of a field, asymptoticity in the transverse profiles is approached first in the rear of the colloid cloud, ...

Unsteady reverse osmosis or ultrafiltration in a tube

Abstract The unsteady behavior of a tubular hyperfiltration system, with both a pulse and a continuous feed, is analyzed using a significant extension of miscible dispersion theory. The extension permits one to treat unsteady convective diffusion in systems with convection at interfacial boundaries in a relatively straightforward manner. It is shown that such convection can effect an enormous reduction in axial dispersion in such systems. A superposition integral is used to generalize the solution for the pulse input to reverse osmosis systems with continuous feeds which may be subject to arbitrary fluctuations in feed concentrations.

Thermocapillary migration of a fluid droplet inside a drop in a space laboratory

Abstract The thermocapillary migration of a fluid droplet located inside a liquid drop in a space laboratory is analyzed. The quasi-static momentum and energy equations are solved at the instant when the droplet passes the center of the drop. Results are presented for prescribed axisymmetric distributions of temperature on the drop surface.

Thermocapillary convection in a liquid bridge

Abstract Results from experiments on thermocapillary flow in a vertical liquid bridge are reported. Data on surface velocities are presented for four different silicone oils at several values of the temperature difference across the liquid bridge, and for three different average temperatures. Also, axial velocity measured as a function of radial position in the bridge is reported. A theoretical model of the velocity and temperature fields in the system is formulated and solved by finite differences. The experimental data on surface velocities are nondimensionalized, and are found to collapse on a single line when plotted against the Marangoni number. Scaled velocities are relatively insensitive to changes in the value of the Marangoni number from 20 to 290, and the Prandtl number from 1460 to 7120. The data are in reasonable accord with predictions from theory.

The slow axisymmetric thermocapillary migration of an eccentrically placed bubble inside a drop in zero gravity

Abstract The quasi-static problem of the motion of a bubble contained inside a drop in free fall due to a prescribed axisymmetric temperature field on the drop surface is treated theoretically. The linearity of the problem permits the convenience of calculating and discussing the influence of each pure Legendre mode of the surface temperature field individually. Typical streamlines and isotherms are displayed, and the behavior of the bubble migration velocity is discussed. An approximation for the bubble velocity useful for small values of the ratio of bubble radius to drop radius is presented and compared with the exact results.

Unsteady convective diffusion in capillary chromatography

Abstract An exact theory of unsteady convective diffusion in capillary chromatography is developed from first principles. Preliminary asymptotic results from the theory for large values of time provide rigorous justification for the Golay theory of capillary columns. The exchange coefficient, K0, which arises from the analysis, is a new concept in capillary chromatography. Ko represents the result of the interaction between the diffusion of solute to the wall and its removal by the retentive layer at the wall. The theory presented here allows one to predict concentration distributions directly from first principles but the results can also be used to calculate the moments of the solute distribution and other quantities of interest in chromatography.