Gravity Effects on Capillary Flows in Sharp Corners

We analyze the effect of gravity on capillary flows in sharp corners. We consider gravity perpendicular and parallel to the channel axis. We analyze both steady and unsteady flows. In the steady analysis the main result is a closed form expression for the flow rate as a function of the two gravity components. Good agreement with steady experiments is offered as support of the model. The unsteady analysis is restricted to “small” values of the two gravity parameters and is accomplished using a similarity formulation. The similarity coefficients of the gravity corrections are fully determined by the coefficients of the gravityless problem. The main result of the unsteady analysis is the gravity corrections to the flow rate (or rate of advance) of the liquid in the channel. In addition, we obtain corrections for the liquid height as a function of position and time. We address in detail unsteady problems with select boundary conditions that are representative of typical flow types. In Appendix A we present a new exact solution to one of the gravityless similarity cases, which is analogous to a nonlinear heat conduction equation. In Appendix B we offer dimensional formulas for all the unsteady flow results, which are valuable for systems design and analysis