Spreading charged micro-droplets. (English) Zbl 1374.35028

Iaia, Joseph

Differ. Integral Equ. 29, No. 9-10, 923-938 (2016).

Summary: This paper considers the analysis of the BF model of the spreading of a charged microdroplet on a flat dielectric surface whose spreading is driven by surface tension and electrostatic repulsion. This model assumes the droplets are circular and spread according to a power law. This leads to a third order nonlinear ordinary differential equation on \([0,1]\) that gives the evolution of the height profile. We prove that there is only one such solution that is smooth on all of \([0,1]\). There are other solutions that are continuous on \([0,1]\), but not differentiable at \(x=1\). For these we describe the precise behavior of the solutions at \(x=1\).

MSC:

35B07	Axially symmetric solutions to PDEs
35B09	Positive solutions to PDEs

Keywords:

height profile; differentiable solution; uniqueness