Micro Fluid Mechanics: Some Interface Dynamics Problems

Interface dynamics is of considerable importance in multiphase microfluidic devices such as microheat pipes, and in dewetting dynamics. We consider a liquid meniscus inside a wedge of included angle [pic] that wets the solid walls with a contact angle [pic]. Under an imposed axial temperature gradient, the Marangoni stress moves fluid toward colder regions while the capillary pressure gradient drives a reverse flow, leading to a steady state. The fluxes driven by these two mechanisms are found by numerical integration of the parallel flow equations. Perturbation theory is applied to derive an expression for the capillary pressure, which is typically dominated by the transverse curvature of the circular arc inside the crosssection, and corrected by a higher order axial curvature resulting from the axial variation of the interface. Lubrication theory is then used to derive a thin film equation for the shape of the interface. Numerical solutions indicate that for sufficiently large Marangoni numbers, M, the Marangoni stress creates a virtual dry region. It is found that dryout occurs more easily for larger wedge and/or contact angles. When the meniscus has a convex interface, it is susceptible to Rayleigh capillary instabilities. A dynamic contact-line condition is considered in which the contact angle varies linearly with the slipping speed of the contact line with a slope of G, with G=0 representing perfect slip and fixed contact angle. A nonlinear thin film equation is derived and numerically solved for the shape of the contact line as a function of parameters. The results show that the evolution process consists of a successive formation of bulges and necks in decreasing length and time scales, eventually resulting a cascade structure of primary, secondary and tertiary droplets. The numerical results agree qualitatively with very recent experimental results.