Differential and Integral Equations

Spreading charged micro-droplets

Joseph Iaia

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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

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

First available in Project Euclid: 14 June 2016

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

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