In many interfacial processes, multiple length scales appear and affect the interfacial dynamics. Common examples constitute the drop coalescence process (which, beyond the drop size, also includes the small gap between the interfaces), droplets in close proximity to solid surfaces (as in microfluidic channels and porous media) as well as the appearance of tips and necks during large droplet deformation in strong flows.

Currently the study of multi-length interfacial dynamics in three-dimensions constitutes a computational challenge owing to the requirement of extreme numerical accuracy for the accurate determination of the dynamics between the regular (drop-size) scale and the small length scale present in these problems. Roughly speaking, the accurate determination, over at least 3 significant digits, of an interfacial system with length ratio of 4 orders of magnitude, may require a computational method which should show an overall accuracy of 7 significant digits.

To overcome this difficulty, we propose the utilization of our Jacobian-free, fully-implicit interfacial spectral boundary element algorithm. This methodology exhibits high accuracy (even with regular grids) due to its spectral nature. In addition, its fully-implicit nature makes the employed time-step independent of the space discretization and the presence of small length scales. In this talk, we will discuss the performance of our algorithm for interfaces in close contact, for interfaces in close proximity to solid walls, as well as during the appearance of tips and necks in large droplet deformation.