Abstract
A combined analytical—numerical study is presented for the axisymmetric thermocapillary motion of a finite chain of spherical droplets along their line of centers. The droplets may be formed from different fluids and have arbitrary radii, and they are allowed to be unequally spaced. Using a boundary-collocation method, the appropriate equations of conservation of energy and momentum are solved in the quasisteady limit and the droplet interaction effects are calculated for various cases. The numerical solutions can be obtained to the satisfactory degree of accuracy by the increase of the collocation points on each droplet interface. For the thermocapillary motion of two-droplet systems, our results for the droplet velocities agree very well with the exact calculations using spherical bipolar coordinates. For the cases of two or three droplets touching one another, the numerical calculations for the particle interaction parameters compare quite favorably with the formulas derived analytically. All of our data for the special case of multiple gas bubbles demonstrate the fact that the thermocapillary migration velocity of each bubble is unaffected by the presence of the others if all the bubbles have identical radii.
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