Droplet interactions in thermocapillary motion

The slow axisymmetric motion of two bubbles in 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.

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

Heat transfer in polymer reaction molding

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.

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

The general quasistatic Stokes force and settling velocity acting on a spherical droplet were formulated. The droplet is submerged in an unbounded flow field, which is Stokes'ian far from the droplet. The drag force formulated here by eq. (41) includes the law of Faxen as a special case. The settling velocity formulated here by eq. (43) includes all previous solutions with similar boundary conditions. It is demonstrated that these parameters can be computed solely from a knowledge of the solution of Hadamard-Rybczynski and the unperturbed flow field.



Es werden die an einem kugelformigen Tropfen wirkende quasistatische Stokes-Kraft und seine Sinkgeschwindigkeit formuliert. Der Tropfen ist in ein unbegrenztes Stromungsfeld eingebettet, das in groser Entfernung von Stokesscher Art ist. Die in Gl. (41) formulierte Widerstandskraft schliest das Gesetz von Faxen als Spezialfall ein; die in Gl. (43) angegebene Sinkgeschwindigkeit enthalt alle fruheren, bei ahnlichen Randbedingungen gewonnenen Losungen. Es wird gezeigt, das die beiden Parameter allein auf Grund der Kenntnis der Losung von Hadamard-Rybczynski und des ungestorten Stromungsfeldes berechnet werden konnen.

G. Hetsroni

Papers

The Hydrodynamic Resistance of a Fluid Sphere Submerged in Stokes Flows

Heat Conduction in Reactor Fuel Elements