Vapor-Induced Motion of Liquid Droplets on an Inert Substrate

Abstract

Evaporating droplets are known to show complex motion that has conventionally been explained by the Marangoni effect (flow induced by the gradient of surface tension). Here, we show that the droplet motion can be induced even in the absence of the Marangoni effect due to the gradient of evaporation rate. We derive an equation for the velocity of a droplet subject to non-uniform evaporation rate and non-uniform surface tension placed on an inert substrate where the wettability is uniform and unchanged. The equation explains the previously observed attraction-repulsionchasing behaviors of evaporating droplets. *

Nonmonotonic contactless manipulation of binary droplets via sensing of localized vapor sources on pristine substrates

“…1B and movie S1), the droplet experiences an attractive force toward the source. This attractive behavior is consistent with a relative larger local increase in humidity at the droplet’s edge nearest to the source, which generates motion by slowing down evaporation and comparatively increasing the value of surface tension at that edge with respect to the opposite side, similar to previous observations ( 7 , 25 ). Such considerations based on differences of absolute values of surface tension would naturally lead one to expect a stable equilibrium position to appear directly beneath the source’s center ( x s = 0), as any displacement from x s = 0 would induce a restoring force.…”

“…To efficiently harness this mechanism, we have developed a simplified analytical model to better understand our counterintuitive experimental observations. This duality (attraction versus repulsion) in the interaction between droplet and source cannot be simply explained by arguments purely based on differences of absolute values of surface tension on opposing sides of the droplet or between its edge and an adjacent precursor film, for which the droplet would always move toward the vapor source ( 7 , 25 ). Instead, as can be seen in Fig.…”

“…Beyond our experimental implementation, we can expect a similar complexity to naturally emerge in the transport of droplets of any shape driven by Marangoni flows of thermal or solutal origin. In this context, the local and tunable nature of the perturbation introduced by the vapor source makes it ideal for fundamental studies of droplet motion ( 21 , 25 , 38 ). Because of its high sensitivity, our technique’s principle could be adapted to develop force (from nN to μN) and gas sensors.…”

Capillary imbibition in a square tube

“…We shall derive the time evolution equations for both the bulk and finger parts of the imbibing fluid using Onsager principle [32]. The Onsager principle presents a general framework to derive the time evolution equation for non-equilibrium system, and the method has been successfully applied to various soft matter systems [33][34][35][36][37][38][39][40]. For the present problem, this principle amounts to the least energy dissipation principle in Stokesian hydrodynamics, which states that the dynamics of system can be directly determined by the minimum of the Rayleighian defined by…”

Application of the Onsager-Machlup integral in solving dynamic equations in nonequilibrium systems

“…A way of doing this is to assume certain forms for the solutions which involve some time dependent parameters, and determine the parameters by the variational principle. We have demonstrated the utility of this method for many examples [11][12][13][14] in fluid and soft matter systems. The method was also applied to the study of solid-state dewetting [15].…”