Pacific Institute for the Mathematical Sciences - PIMS

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.

Fluid Mechanics Seminar 2006