Drop spreading with random viscosity

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We examine theoretically the spreading of a viscous
liquid drop over a thin film of uniform thickness,
assuming the liquid’s viscosity is regulated by the
concentration of a solute that is carried passively
by the spreading flow. The solute is assumed to be
initially heterogeneous, having a spatial distribution
with prescribed statistical features. To examine how
this variability influences the drop’s motion, we
investigate spreading in a planar geometry using
lubrication theory, combining numerical simulations
with asymptotic analysis. We assume diffusion is
sufficient to suppress solute concentration gradients
across but not along the film. The solute field beneath
the bulk of the drop is stretched by the spreading flow,
such that the initial solute concentration immediately
behind the drop’s effective contact lines has a longlived
influence on the spreading rate. Over long
periods, solute swept up from the precursor film
accumulates in a short region behind the contact
line, allowing patches of elevated viscosity within
the precursor film to hinder spreading. A low-order
model provides explicit predictions of the variances in
spreading rate and drop location, which are validated
against simulations.

Bibliographical metadata

Original languageEnglish
Article number20160270
JournalRoyal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences
StatePublished - 12 Oct 2016