We developed a theoretical model to study the thin films involving deformable interfaces (for example drops and bubbles) which are interacting at low speeds. We assume the tangentially immobile boundary conditions holds at the fluid-fluid interface. The evolution equations for such system are of differential-algebraic nature in which the position of the boundary advances and deforms at the same time and the deformation depends on the solution. We focus on the model derivation and numerical implementation. The equations are solved using a Matlab routine and the numerical results are compared to experimental data from the literature, which were produced by researchers in different labs and using different techniques and shows the model is adequate to solve a variety of problems.
Differential algebraic system; Stokes-Reynolds equations and Young-Laplace equations; flow in thin films; coalescence; droplets and bubbles
