Hysteretic effects in droplet motions on heterogeneous substrates:
Direct numerical simulation
14: (12) 3440-3453 JUN 9 1998
A method of calculation is introduced that allows the simulation
of the time-dependent three-dimensional motion of liquid droplets
on solid substrates for systems with finite equilibrium contact
angles. The contact angle is a prescribed function of position on
the substrate. An evolution equation is given, using the lubrication
assumption, that includes viscous, capillary, and disjoining forces.
Motion to and from dry substrate regions is made possible by use of
a thin energetically stable wetting layer. We simulate motion on
heterogeneous substrates with periodic arrays of high-contact angle
patches. For a homogeneous substrate, calculated droplet spreading
rates are compared to published experimental results, revealing the
need for a time-scale correction. Two different problems are treated.
The first is spontaneous motion driven only by wetting forces. If the
contact-angle difference is sufficiently high, the droplet; can find
several different stable positions, depending on the previous history
of the motion. A second simulation treats a forced cyclical motion.
Energy dissipation per cycle for a heterogeneous substrate is found
to be larger than that for a uniform substrate with the same total
energy. Comparison is made with simple quasi-static theories.