Институт теоретической физики им. Л.Д. Ландау РАН
L.D. Landau Institute for Theoretical Physics RAS
Landau Days 2022
June, 27-30, 2022
Marangoni convection within ellipsoidal isotropic droplets in free standing smectic films.
Date/Time: 09:30 29-Jun-2022
We present theoretical study of the Marangoni convection within isotropic droplets spontaneously formed in free standing smectic films (FSSF) heated above the temperature of the bulk smectic-isotropic transition. The thermocapillary instability is due to vertical temperature gradient across the horizontal film. Because the isotropic droplets in FSSF are of the height of units and tens of microns, the effects of gravity on the convection can be neglected. The shape of the drops is well approximated by an oblate spheroid. The surface of isotropic droplets in overheated FSSFs is covered by smectic layers, the amount of which depends on the degree of overheating. We considered the situation when the temperature at the upper side of the drop is significantly higher than at the lower one. Due to continuous thermal nucleation and growing of the dislocation loops (holes), the smectic layering at the upper (hot) drop surface disappears and the drop interface is getting free. In contrast to this, at the lower (cold) side of the drop the additional layers (islands) are formed due to release of the smectic material from the meniscus. This introduces the effects of sticking at the border between the isotropic fluid and the smectic shell at lower drop interface. We solved analytically the system of equations of Marangoni convection in ellipsoidal droplets for above asymmetric geometry. The linearly independent stationary basic solutions for Stokes stream functions in oblate spheroid coordinates were determined. The corresponding temperature distribution in the ellipsoidal drops and the surrounding air was determined in the frame of the perturbation theory. The analytical calculations predict the axially-symmetric circulatory convection motion as a function of the droplet ellipticity ratio determined by the Marangoni effect at the upper droplet free surface, Figure 1. In such way the stream functions, velocities and temperature distribution corresponding to the stationary thermocapillary convection within the ellipsoidal drop are calculated in the main approximation. The peculiarity of the Marangoni convection in the ellipsoidal drops is that due to curvature of the drop interface there is always a temperature gradient along its free surface. Thus, the thermocapillary convection is possible for the arbitrarily small Marangoni numbers. The stability of stationary solution and crossover to the limit of the plane fluid layer are also investigated.
(no additional information)