Dynamical equations for the contact line during the evaporation or condensation of a sessile drop

The equations that govern, away from equilibrium and accounting for dissipation, the evolution of the contact line of a sessile drop on a rigid substrate are derived. Aside from the normal and tangential components of the standard (Newtonian) force balance, these include a configurational force balance. At equilibrium, the normal component of the standard force balance reduces to Gibbs' generalization of the classical Young equation. The remaining balances are purely dissipative and hence are vacuous in equilibrium. A complete description of contact-line dynamics generally involves all three equations. The theory is embedded in a thermodynamical framework that ensures consistency of all constitutive relations with the second law. In the linearly dissipative case, these involve six contact-line viscosities. When viscous coupling is neglected, only three viscosities remain. One is associated with stretching of the fluid along the contact line. The remaining two are related to dissipation that accompanies mass transfer between liquid and vapor phases during evaporation or condensation.

Speaker Bio: Eliot Fried obtained his Ph.D. in Applied Mechanics from the California Institute of Technology in 1991. He received an NSF Mathematical Sciences Postdoctoral Fellowship, a Japan Society for the Promotion of Science Postdoctoral Research Fellowship, and an NSF Research Initiation Award. Currently he is a Professor of Mechanical Engineering and the Tier 1 Canada Research Chair in Interfacial and Defect Mechanics at McGill University. He previously held positions at Carnegie Mellon University, the Pennsylvania State University, College Park, the University of Illinois at Urbana-Champaign, and Washington University in St. Louis. At Illinois, he was a Fellow of the Center of Advanced Study and was awarded a Critical Research Initiative Grant. His research focuses on the mechanics and thermodynamics of novel materials, including liquid crystals, surfactant solutions, nematic elastomers, hydrogels, and granular materials.

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