A fluid droplet may move on solid substrate either “passively”, driven by external forces or surface inhomogeneities, or “actively”, by modifying the substrate in its vicinity. In either case, the motion involves a moving contact line, which is a locus of a non-integrable singularity in the framework of classical hydrodynamics.

Nanoscale molecular interactions resolve the singularity through either formation of an ultrathin precursor layer or effective slip near the contact line. Droplet velocities can be computed then analytically by matching the bulk and precursor regions, leaving a logarithm of the ratio of the macroscopic to molecular scales appearing in the expression for effective mobility as a telltale sign of the singularity resolved on a molecular scale. The velocity computed in this way is in a very good agreement with straightforward numerical computations.

Long-time dynamics in particular systems may lead, depending on relative time scales of motion and substrate modification, to coarsening, pattern formation or persistent wandering of droplets. I consider in more detail self-propelled motion fueled by either chemical reactions or phase transitions, when modification of wetting properties of the substrate results in asymmetry of contact angles. Reversible chemically driven motion bears peculiar resemblance to pattern-forming activator-inhibitor systems, exhibiting likewise a traveling bifurcation dividing between stationary and mobile structures. Repelling interaction of droplets may lead, depending on the ratio of motion and diffusion times, to mutual scattering or pattern formation.

 

Dr. Leonid M. Pismen is a J. & B. Naiman Professor of Fluid Mechanics and Professor Emeritus, Technion – Israel Institute of Technology, and a member of American Physical Society.

 

He received his first doctor of Philosophy from Karpov Physico-Chemical Institute, Moscow, in 1963; second doctor of Science in 1969 from Institute Electrochemistry, Moscow. From 1967, he became a senior research associate of Institute of Electrochemistry of the USSR Academy of Sciences. And since 1975 he is a professor of chemical engineering Technion-Israel Institute of Technology.

 

Dr. Leonid M. Pismen is a Russian chemical engineering educator, researcher. And until now he has published two books.