With the growth of applications of microfluidics in MEMS, studies of multi-phase fluid behavior and the dynamics of fluid-fluid interfaces in microscale systems become increasingly important. Since both surface tension and evaporation have significant influences on fluid behavior at the micrometer scale, this thesis studies the shape of interfaces under the effects of surface tension, Marangoni stress (surface tension gradient) and evaporation.

The first problem considers steady thermocapillary flows and dryout inside a wedge. Under an imposed axial temperature gradient, the Marangoni stress moves fluid toward colder regions while the capillary pressure gradient drives a back flow, leading to steady state. The capillary pressure is formulated in a complete way by including both the transverse and the axial curvature effects. Lubrication theory is applied to derive a thin film equation for the position of the contact line. Numerical solutions indicate that for sufficiently large temperature gradients, dryout results and occurs more easily for larger wedge and/or contact angles.

The second problem considers the instability driven by surface tension for a convex interface. The capillary pressure gradient due to a small disturbance at the location of the contact line moves fluid from a neck region to a bulge region, causing instabilities. A nonlinear thin film equation is derived and together with a dynamic contact-line condition, is solved numerically. The result shows that the evolution process consists of a successive formation of bulges and necks of decreasing lengths and time scales, eventually resulting in a cascade structure of primary, secondary, and tertiary, and even smaller droplets. The numerical results agree qualitatively with very recent experimental results.

The third problem involves the experimental study of vapor bubbles generated by a localized heating inside a small-sized channel. The shape of liquid/vapor interfaces are of interest, together with simultaneous measurements of heat fluxes and temperature profiles. The length of vapor bubbles is found to depend nearly linearly on the power input and the heater temperature, consistent with approximate theoretical results in the literature. In addition, it is also found that bubbles oscillate slowly due to the effect of thermal relaxation.