## Differential and Integral Equations

Joseph Iaia

#### Abstract

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 $x=1$.

#### Article information

Source
Differential Integral Equations, Volume 29, Number 9/10 (2016), 923-938.

Dates
First available in Project Euclid: 14 June 2016

https://projecteuclid.org/euclid.die/1465912610

Mathematical Reviews number (MathSciNet)
MR3335748

Zentralblatt MATH identifier
1374.35028

Subjects
Primary: 35B07: Axially symmetric solutions 35B09: Positive solutions

#### Citation

Iaia, Joseph. Spreading charged micro-droplets. Differential Integral Equations 29 (2016), no. 9/10, 923--938. https://projecteuclid.org/euclid.die/1465912610