Modeling the coalescence of sessile droplets

Abstract

This paper proposes a simple scenario to describe the coalescence of sessile droplets. This scenario predicts a power-law growth of the bridge between the droplets. The exponent of this power law depends on the driving mechanism for the spreading of each droplet. To validate this simple idea, the coalescence is simulated numerically and a basic experiment is performed. The fluid dynamics problem is formulated in the lubrication approximation framework and the governing equations are solved in the commercial finite element software COMSOL. Although a direct comparison of the numerical results with experiment is difficult because of the sensitivity of the coalescence to the initial and operating conditions, the key features of the event are qualitatively captured by the simulation and the characteristic time scale of the dynamics recovered. The experiment consists of inducing coalescence by pumping a droplet through a substrate which grows and ultimately coalesces with another droplet resting on the substrate. The coalescence was recorded using high-speed imaging and also confirmed the power-law growth of the neck.

Mixing and internal dynamics of droplets impacting and coalescing on a solid surface

“…However, the success of such chaotic advection-driven mixing or stirring relies on repeated stretching and folding of the "interface" between the two liquids being mixed. In "pure" surface-tension driven sessile droplet coalescence, i.e., where the two sessile droplets are not driven into each other by other means, there is no repeated stretching and folding, and experiments on such a system have not shown effective mixing [2]. On the other hand, in sessile droplet coalescence where one droplet is driven into the other by a wettability gradient [23], stretching and folding of the "interface" can occur, resulting in "fingers" of each liquid penetrating the other and an enhancement of the mixing.…”

“…Coalescence and mixing of droplets on a solid surface are of great interest not only to the established inkjet printing industry but also to emerging applications such as the noncontact printing of functional electronics and biological materials and in the fields of microfluidic devices, microchemistry, and fast prototyping [1][2][3][4][5]. The advantages of the inkjet printing of liquid materials over traditional delivery techniques are many and based on the technological ability of printheads to generate homogeneously sized droplets on demand at a determined speed and direction.…”

Gravity driven current during the coalescence of two sessile drops

“…Drops are allowed to spread spontaneously into one another, 7,19 one drop is deposited onto another, 13,18,20 or one drop is blown into another 17 on a surface until they meet and merge. In other cases, drops are forced to grow into one another due to an external supply of liquid 14,15 or condensing vapor. [9][10][11]16 In still other cases, drops are forced to collide due to wettability gradients on the surface, [21][22][23] where wettability gradients cause the merging drops to exhibit different contact angles just prior to coalescence even when the drops contain identical liquids.…”

“…6,[9][10][11] In the slow process, contact lines move and the drop relaxes to a circular shape over longer time scales, slowed by the dissipation at the moving contact lines and fluid flow. 9,10,12 Experimentally, the initial bridge healing of sessile drops has been probed using high speed video microscopy of fluids including mercury, 13 silicone oils, 7 water, [14][15][16][17] and organic fluids. 11,[18][19][20] Different mechanisms have been used to cause the drops to touch and coalesce.…”

“…15,24 More detailed numerical simulations have used the volume-of-fluid method 25 and lattice Boltzmann method. 18 These studies demonstrate two main features of the initial stage of coalescence.…”