MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Coarsening rates for the dynamics of slipping droplets

Georgy Kitavtsev


We derive reduced ODE models starting from one dimensional lubrication equations describing coarsening dynamics of droplets in nanometric polymer film interacting on a hydrophobically coated solid substrate in the presence of large slippage at the liquid/solid interface. In the limiting case of the infinite slip length corresponding in applications to free films a collision/absorption model then arises and is solved explicitly. The exact coarsening law is derived for it analytically and confirmed numerically. Existence of a threshold for the decay of initial distributions of droplet distances at infinity at which the coarsening rates switch from algebraic to exponential ones is shown.

MSC Codes:
35B36, 35G20, 35Q35
68.15.+e, 83.50.Rp, 02.30.Jr
coarsening rates, collision and absorbtion, lubrication equations, slippage, free films

Related publications

2014 Repository Open Access
Georgy Kitavtsev

Coarsening rates for the dynamics of slipping droplets

In: European journal of applied mathematics, 25 (2014), pp. 83-115