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Subramanian, R. Shankar

Publications and source records attributed to Subramanian, R. Shankar.

Thermocapillary migration of a drop: an exact solution with Newtonian interfacial rheology and stretching/shrinkage of interfacial area elements for small Marangoni numbers

In this paper we analyze the effects of the following phenomena associated with the thermocapillary migration of a drop. The first is the influence of Newtonian surface rheology of the interface and the second is that of the energy changes associated with stretching and shrinkage of the interfacial area elements, when the drop is in motion. The former occurs because of dissipative processes in the interfacial region, such as when surfactant molecules are adsorbed at the interface in sufficient concentration. The interface is typically modeled in this instance by ascribing to it a surface viscosity. This is a different effect from that of interfacial tension gradients arising from surfactant concentration gradients. The stretching and shrinkage of interfacial area elements leads to changes in the internal energy of these elements that affects the transport of energy in the fluids adjoining the interface. When an element on the interface is stretched, its internal energy increases because of the increase in its area. This energy is supplied by the neighboring fluids that are cooled as a consequence. Conversely, when an element on the interface shrinks, the adjoining fluids are warmed. In the case of a moving drop, elements of interfacial area are stretched in the forward half of the drop, and are shrunk in the rear half. Consequently, the temperature variation on the surface of the drop and its migration speed are modified. The analysis of the motion of a drop including these effects was first performed by LeVan in 1981, in the limit when convective transport of momentum and energy are negligible. We extend the analysis of LeVan to include the convective transport of momentum by demonstrating that an exact solution of the momentum equation is obtained for an arbitrary value of the Reynolds number. This solution is then used to calculate the slightly deformed shape of the drop from a sphere.

Rheology/methods

Thermocapillary Convection in Bubbles and Drops

When bubbles or drops are present in an immiscible liquid in reduced gravity and the temperature of the liquid is non-uniform, a thermocapillary stress is generated at the interface due to the variation of interfacial tension with temperature. The resulting flow propels the drop freely suspended in the liquid towards warmer regions, so as to minimize the interfacial energy. In this presentation, we will focus on the effect of convective transport of momentum and energy, that are characterized by the Reynolds number and the Marangoni number, respectively. The results of asymptotic analyses for the speed of the drop for low and large values of these parameters will be discussed. These predictions as well as those from numerical simulations will be compared with reduced gravity experimental results obtained from experiments performed aboard the space shuttle.

Balassubramaniam

Motion of Drops on Surfaces with Wettability Gradients

A liquid drop present on a solid surface can move because of a gradient in wettability along the surface, as manifested by a gradient in the contact angle. The contact angle at a given point on the contact line between a solid and a liquid in a gaseous medium is the angle between the tangent planes to the liquid and the solid surfaces at that point and is measured within the liquid side, by convention. The motion of the drop occurs in the direction of increasing wettability. The cause of the motion is the net force exerted on the drop by the solid surface because of the variation of the contact angle around the periphery. This force causes acceleration of an initially stationary drop, and leads to its motion in the direction of decreasing contact angle. The nature of the motion is determined by the balance between the motivating force and the resisting hydrodynamic force from the solid surface and the surrounding gaseous medium. A wettability gradient can be chemically induced as shown by Chaudhury and Whitesides who provided unambiguous experimental evidence that drops can move in such gradients. The phenomenon can be important in heat transfer applications in low gravity, such as when condensation occurs on a surface. Daniel et al have demonstrated that the velocity of a drop on a surface due to a wettability gradient in the presence of condensation can be more than two orders of magnitude larger than that observed in the absence of condensation. In the present research program, we have begun to study the motion of a drop in a wettability gradient systematically using a model system. Our initial efforts will be restricted to a system in which no condensation occurs. The experiments are performed as follows. First, a rectangular strip of approximate dimensions 10 x 20 mm is cut out of a silicon wafer. The strip is cleaned thoroughly and its surface is exposed to the vapor from an alkylchlorosilane for a period lasting between one and two minutes inside a desiccator. This is done using an approximate line source of the vapor in the form of a string soaked in the alkylchlorosilane. Ordinarily, many fluids, including water, wet the surface of silicon quite well. This means that the contact angle is small. But the silanized surface resists wetting, with contact angles that are as large as 100 degs. Therefore, a gradient of wettability is formed on the silicon surface. The region near the string is highly hydrophobic, and the contact angle decreases gradually toward a small value at the hydrophilic end away from this region. The change in wettability occurs over a distance of several mm. The strip is placed on a platform within a Plexiglas cell. Drops of a suitable liquid are introduced on top of the strip near the hydrophobic end. An optical system attached to a video camera is trained on the drop so that images of the moving drop can be captured on videotape for subsequent analysis. We have performed preliminary experiments with water as well as ethylene glycol drops. Results from these experiments will be presented in the poster. Future plans include the refinement of the experimental system so as to permit images to be recorded from the side as well as the top, and the conduct of a systematic study in which the drop size is varied over a good range. Experiments will be conducted with different fluids so as to obtain the largest possible range of suitably defined Reynolds and Capillary numbers. Also, an effort will be initiated on theoretical modeling of this motion. The challenges in the development of the theoretical description lie in the proper analysis of the region in the vicinity of the contact line, as well as in the free boundary nature of the problem. It is known that continuum models assuming the no slip condition all the way to the contact line fail by predicting that the stress on the solid surface becomes singular as the contact line is approached. One approach for dealing with this issue has been to relax the no-slip boundary condition using the Navier model. Molecular dynamics simulations of the contact line region show that for a non-polar liquid on a solid surface, the no-slip boundary condition is in fact incorrect near the contact line. Furthermore, the same simulations also show that the usual relationship between stress and the rate of deformation breaks down in the vicinity of the contact line. In developing continuum theoretical models of the system, we shall accommodate this knowledge to the extent possible.

Subramanian, R. Shankar

Numerical Simulation of Thermocapillary Drop Motion with Internal Circulation

The thermocapillary motion of drops in zero gravity is analyzed numerically. When convective transport is important, the internal circulation in the drop has a profound effect on the temperature distribution in its vicinity and hence on its migration speed. For sufficiently large values of the Marangoni number number Ma, for steady motion of the drop, the temperature difference on the drop surface and its scaled speed increase with Ma. This is in contrast to (1) existing computational results for liquid drops whose scaled speed decreases with Ma and (2) asymptotic results for gas bubbles whose scaled speed is independent of Ma when it is large.

Ma, Xiangjiang

Thermocapillary Migration and Interactions of Bubbles and Drops

When a drop or bubble is placed in another fluid and subjected to the action of a temperature gradient, the drop will move. Such motion is a direct consequence of the variation of interfacial tension with temperature, and is termed thermocapillary migration. This paper discusses results from experiments conducted in reduced gravity on the thermocapillary motion of bubbles and drops.

Balasubramaniam, R.

Measurement of interfacial tension of immiscible liquid pairs in microgravity

A discussion is given of a containerless microgravity experiment aimed at measuring the interfacial tension of immiscible liquid pairs using a compound drop rotation method. The reasons for the failure to execute such experiments in microgravity are described. Also, the results of post-flight analyses used to confirm our arguments are presented.

Weinberg, Michael C.

The migration of a compound drop due to thermocapillarity

The quasistatic thermocapillary motion of a compound drop in an unbounded fluid possessing a uniform temperature gradient is analyzed. For completeness, gravitational effects are included in the treatment. The general model is formulated, and the equations for the concentric case are solved using spherical polar coordinates, while the eccentric case is handled using bispherical coordinates. Results are given for the velocity of the drop as well as that of the droplet with respect to the drop, along with useful approximations. Illustrative results are presented graphically for the thermocapillary migration of a compound drop in the special case when the droplet is a gas bubble. In addition to the velocities of the drop and the bubble, representative isotherms and streamlines also are presented which display interesting qualitative features.

Morton, David S.

Physical phenomena in containerless glass processing

Flight experiments are planned on drops containing bubbles. The experiments involve stimulating the drop via non-uniform heating and rotation. The resulting trajectories of the bubbles as well as the shapes of the drops and bubble will be videotaped and analyzed later frame-by-frame on the ground. Supporting ground based experiments are planned in the area of surface tension driven motion of bubbles, the behavior of compound drops settling in an immiscible liquid and the shapes and trajectories of large bubbles and drops in a rotating liquid. Theoretical efforts will be directed at thermocapillary migration of drops and bubbles, surfactant effects on such migration, and the behavior of compound drops.

Subramanian, R. Shankar

The dissolution or growth of a gas bubble inside a drop in zero gravity

The radius-time history of a gas bubble located concentrically within a spherical liquid drop in a space laboratory is analyzed within the framework of the quasi-stationary approximation. Illustrative results are calculated from the theory which demonstrate interesting qualitative features. For instance, when a pure gas bubble dissolves within a liquid drop in an environment containing the same gas and some inert species, the dissolution can be more or less rapid than that in an unbounded liquid depending on the initial relative size of the drop. Further, given a similar growth situation, indefinite growth is not possible, and the bubble will initially grow, but always dissolve in the end.

Kondos, Pericles A.

The behavior of multiphase systems in low gravity

The motion of drops and bubbles due to interfacial tension gradients is studied. It is noted that, when a drop or bubble is inserted into a fluid possessing a temperature gradient, the resulting gradient of interfacial tension will, through viscous traction on the neighboring fluid, cause it to move. In response, the drop will propel itself in the direction of the pole with the lower interfacial tension. This phenomenon, thermocapillary migration, is discussed in detail.

Subramanian, R. Shankar

The Stokes force on a droplet in an unbounded fluid medium due to capillary effects

The Stokes force on a fluid droplet is obtained when the droplet is placed in an unbounded fluid medium and motion ensues due to an arbitrary interfacial-tension gradient on the droplet surface. The force, derived here for a spherical droplet, is proportional to the integral of the interfacial-tension gradient over the droplet surface. When the interfacial-tension gradients are caused by temperature or concentration variations, the result for the force may be further specialized when convective transport effects are negligible. In this case, it is possible to express the force in terms of the gradient of the undisturbed temperature (or concentration) field evaluated at the location of the droplet center in a form analogous to Faxen's force law.

Subramanian, R. Shankar

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.

Meyyappan, M.

The dissolution or growth of a sphere

The problem of the dissolution or growth of an isolated stationary sphere in a large fluid body is analyzed. The motion of the boundary as well as the the resulting motion in the liquid are properly taken into account. The governing equations are solved using a recently developed technique (Subramanian and Weinberg, 1981) which employs an asymptotic expansion in time. Results for the radius of the sphere as a function of time are calculated. The range of utility of the present solution is established by comparison with a numerical solution of the governing equations obtained by the method of finite differences.

Shankar, N.

Of drops and bubbles - The technology of space processing

It is possible to manipulate a large, molten mass of material, such as a glass, aboard an orbital platform using acoustic fields. Attention is presently given to the problem of bubble removal from such a melt; it is desirable to make small bubbles coalesce into larger ones through floating melt rotation, to create an artificial convective field in which the bubbles will move centripetally to the axis of rotation. Computer models of bubble migration have been developed in order to define the operational conditions required aboard such experiment platforms as the Space Shuttle Orbiter.

Subramanian, R. Shankar