(258a) High Resolution Simulations of Droplet Collisions and Coalescence in Shear

Shardt, O., University of Alberta
Mitra, S. K., University of Alberta
Derksen, J., University of Alberta

The outcomes of collisions between droplets determine the droplet size distribution and rheology of emulsions in shear and turbulence, the flow patterns of emulsions in porous media, and the behaviour of microfluidic devices that manipulate droplets. Due to the large separation of length scales between typical droplet radii (1-100 µm) and the minimum thickness of the film that can separate drops (~10 nm), simulations that predict the outcome of a collision are challenging because both length scales must be resolved. We recently reported [Shardt et al. Langmuir (2013) DOI: 10.1021/la304919p] large-scale three-dimensional simulations of droplet collisions in simple shear flow using a diffuse interface model. In these simulations, the film between the colliding droplets was resolved and the critical capillary number for coalescence was determined as a function of several geometric and diffuse interface model parameters. For example, if the interface thickness is kept constant, the critical capillary number decreases as the droplet size increases.

While the previous results were obtained with a large initial vertical (see figures below) separation between the droplets, we now present simulations with half the previous vertical offset. By simulating droplets with double the previous size in a domain that is also twice as large (eight times the volume), the critical capillary number for this geometry is sufficiently low that it can be reached in the simulations. Due to the larger size of the droplets, we study coalescence at a nondimensional vertical offset of 0.2 (vertical distance between centres divided by droplet diameter), near the value in the experimental work of Chen et al. (Langmuir 2009, 25, 12885-12893). We analyze the results of the simulations to determine the critical capillary number for coalescence, the numerical critical film thickness, and the droplet trajectories. These results can be used to provide insight into the conditions for coalescence and eventually perform predictive simulations of coalescence phenomena.

Two sample collisions between droplets are shown below. At a capillary number Ca of 0.1 (upper sequence), the droplets coalesce. At Ca=0.2 (lower sequence), they first coalesce with an internal droplet being formed and then break apart. In these simulations, the radius of the droplet is 200 lattice nodes, and the simulation domain is 2048×512×512 lattice nodes. Due to the use of symmetry boundary conditions, this represents a domain of 2048×1024×1024. These are the largest simulations of coalescence performed so far, and they were made possible by the use of 66 Tesla M2070 GPUs, which reached typical processing speeds above 800 million lattice updates per second.

Collision at Ca = 0.1.

Collision at Ca = 0.2.