Deposition Patterns of Two Neighboring Droplets: Onsager Variational Principle Studies

When two droplets containing nonvolatile components are sitting close to each other, asymmetrical ring-like deposition patterns are formed on the substrate. We propose a simple theory based on the Onsager variational principle to predict the deposition patterns of two neighboring droplets. The contact line motion and the interference effect of two droplets are considered simultaneously. We demonstrate that the gradients of evaporation rate along two droplets is the main reason for forming asymmetrical deposition patterns. By tracing the relative motion between the contact line and the solute particles, we found that the velocities of solute particles have no cylindrical symmetry anymore because of the asymmetrical evaporation rate, giving the underlying mechanism of forming asymmetrical patterns. Moreover, controlling the evaporation rate combined with varying the contact line friction, fan-like and eclipse-like deposition patterns are obtained. The theoretical results of pinned contact line cases are qualitatively consistent with the pervious experimental results.