Thermocapillary Deposition of a Fluid Droplet Normal to a Planar Surface

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• 作者：Shih H. Chen
• 刊名：Langmuir
• 出版年：1999
• 出版时间：April 13, 1999
• 年：1999
• 卷：15
• 期：8
• 页码：2674 - 2683
• 全文大小：122K
• 年卷期：v.15,no.8(April 13, 1999)
• ISSN：1520-5827

文摘

An analytical study is presented for the thermocapillary migration of a fluid sphere in a constant appliedtemperature gradient perpendicular to a planar surface. The Peclet and Reynolds numbers are assumedto be small, so that the appropriate energy and momentum equations of the fluids inside and outside thedroplet are governed by the Laplace and Stokes equations, respectively. The asymptotic formulas for thetemperature and velocity fields in the quasisteady situation are obtained by using a method of reflections.The plane surface may be a solid wall or a free surface. When the droplet is migrating normal to a solidplane, the boundary effect of the planar surface retards the droplet motion, reducing the thermocapillaryvelocity of the droplet. In the situation of droplet migration toward a free surface due to thermocapillarity,the droplet velocity can be either greater or smaller than that which would exist in the absence of the planesurface. In general, the boundary effect on the thermocapillary migration is found to be weaker than thaton the motion driven by a gravitational force. However, the interaction between the plane and the dropletcan be very strong when the gap thickness approaches zero. Considering thermocapillary mobility, thedeposition time for a droplet translating across the thermocapillary boundary layer is integrated. Also,it is predicted that the deposition time will be postponed if the fluid sphere is migrating normal to a solidwall. However, the deposition time for a droplet moving normal to a free surface may be shorter thanpredicted if there is no boundary influence. Generally speaking, a free surface exerts less influence on thedroplet movement than does a solid surface.