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Тезисы докладов

Численное решение дифференциальных и интегральных уравнений

Boundary-integral methods are highly effective for modeling the creeping flow in the presence of deformable interfaces and were widely used to simulate the motion of drops bubbles induces by buoyancy or by external flow. Recently the first modification of the method were developed to handle the tangential Marangoni stresses on the interfaces in the thermocapillary-induced motion. In the present work we report on boundary-integral simulations of a pairwise interaction of highly deformable drops in the presence of Marangoni effect. The classical problem of the drops' migration in externally imposed temperature gradient is considered as well as the case of spontaneous thermocapillary motion, where the tangential temperature gradients on the interfaces are induced by the interfacial heat transfer. Also, the combined effect of gravity and thermocapillarity was studied. It is demonstrated that, if the motion is induced solely by thermocapillarity, the motion of initially spherical well separated drops is in very good agreement with the predictions of non-deformable drops theory. Substantial deformations occur only when the drops are very close to each other and prevent the interfaces coming into contact. When drops move in gravity field their interaction may case large deformations and even breakup of the drops. Our simulations show that even small temperature gradient directed oppositely to the buoyancy force that almost does not effect the drops velocity may drastically change the deformation pattern and prevent the drops from breakup. When the net thermocapillary and buoyancy forces acting on the drops are almost balanced, our analysis shows that though the deformations of the drops are apparently small their influence on the motion is considerable.

Примечание. Тезисы докладов публикуются в авторской редакции

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