Electrostatic charges that accumulate on substrates and at liquid-air interfaces in various coating processes can drive liquid flows that lead to defects. To better understand this phenomenon, we model the leveling of thin liquid films subject to electrohydrodynamic forces. We consider cases of homogeneous and heterogeneous substrate charge distributions and contamination of the film surface by free charge. The liquid is assumed to be Newtonian, both perfect dielectric and leaky dielectric materials are considered, and lubrication theory is employed. Linear stability analysis and nonlinear simulations reveal different leveling criteria for small- and large-amplitude perturbations to the film surface. Heterogeneous charge distributions on the substrate are found to lead to steady curved interface shapes. Using asymptotic methods, we develop analytical expressions to predict these shapes, and consequently, the magnitude of coating defects. We also employ transient nonlinear simulations track the leveling of disturbances created by contamination of the film surface by free charge. The results of our study enable us to propose simple heuristics for determining the conditions under which coatings subject to electrohydrodynamic forces will level.
Bibliographical noteFunding Information:
This work was supported through the Industrial Partnership for Research in Interfacial and Materials Engineering at the University of Minnesota . S.K. acknowledges support from the Department of Energy under Award no. DE-FG02-07ER46415 . We are grateful for resources from the University of Minnesota Supercomputing Institute. We thank R. Jendrejack for helpful discussions.
- Fluid mechanics
- Interfacial tension
- Mathematical modeling
- Transport processes