Thermocapillary flow and aggregation of bubbles on a solid wall

Theory suggests that thermocapillary flow about neighboring bubbles in liqu ids on hot walls pulls the bubbles together. A temperature gradient perpend icular to the wall establishes a surface tension gradient at the bubble-liq uid interface, which in turn sustains a shear stress gradient that pumps ad jacent fluid away from the wall. Neighboring bubbles are mutually entrained in this how and also respond thermophoretically to lateral temperature gra dients in the temperature near field. The theory predicts that the aggregat ion velocity scales with the temperature gradient, the radius of the bubble s, the derivative of the surface tension with respect to temperature, and t he reciprocal of the liquid's viscosity. Bubble aggregation experiments und er controlled conditions were performed to test the theory. Scaling the exp erimental bubble trajectories according to the theory substantially collaps es all of the data onto a master curve when the interbubble separation is g reater than 3 radii, which suggests that the theory is correct. Calculated velocities agree with the experimental results when hindrance of bubble mot ion due to the wall is included. Values for the parameter that describes th e hindrance effect are obtained from fitting the data to the theory, from i ndependent measurements, and from direct hydrodynamic calculation. The resu lts of the three determinations agree within 15% of the possible range of t he value of the parameter. (C) 2000 Academic Press.