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Simulations of Droplet Interactions with Lattice Boltzmann Methods Open Access


Other title
Janus droplet
phase field
Lattice Boltzmann Method
Type of item
Degree grantor
University of Alberta
Author or creator
Shardt, Orest
Supervisor and department
Mitra, Sushanta K. (Mechanical Engineering)
Derksen, Jos (Chemical and Materials Engineering)
Examining committee member and department
Lee, Taehun (Mechanical Engineering, CCNY)
Yeung, Anthony (Chemical and Materials Engineering)
Mitra, Sushanta K. (Mechanical Engineering)
Nikrityuk, Petr (Chemical and Materials Engineering)
Derksen, Jos (Chemical and Materials Engineering)
Department of Chemical and Materials Engineering
Chemical Engineering
Date accepted
Graduation date
Doctor of Philosophy
Degree level
Interactions between droplets were studied using two lattice Boltzmann methods (LBMs). The Shan-Chen LBM, in which repulsive forces between fluids maintain phase separation, was used to simulate systems with three immiscible components. The simulations demonstrated the three equilibrium configurations of two droplets in a third fluid: adhering, separated, and engulfed. Simulations of adhering droplet pairs, called Janus droplets due to their two-sided structure, in shear flow revealed the structure of the internal flow and the dependence of the rotation rate on the orientation of the droplet. A second type of interaction between droplets was simulated with the free-energy binary-liquid LBM: binary droplet collisions in confined simple shear flow. The conditions for coalescence were quantified and the effects of geometry and the parameters of this Cahn-Hilliard-type phase field model on the critical conditions were examined. Two parameters of the phase field model, the thickness of the diffuse interface and the mobility of the phase field, are important. Simulations with highly-resolved droplets, with radii spanning 200 lattice nodes, were used to determine the minimum film thickness before coalescence, its relationship to the interface thickness, and the effect of the mobility on the evolution of the minimum distance between the droplet interfaces during collisions. The critical conditions for coalescence in these simulations were compared with published experiments with polymers. Unlike the experimental polymer system, the interfaces of interacting droplets are often charged, as in the case of oil-water emulsions. To simulate such liquid systems, the free-energy binary-liquid LBM was coupled with an iterative finite difference solver for the linearized Poisson-Boltzmann equation that describes the electrostatic potential near a charged surface in an electrolyte solution. Simulations of collisions between charged droplets with constant zeta potentials in a sheared electrolyte showed the effects of surface charge on the critical conditions for coalescence.
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Citation for previous publication
Orest Shardt, J.J. Derksen, Sushanta K. Mitra, “Simulations of Janus droplets at equilibrium and in shear,” Physics of Fluids, 26:012104 (2014).Orest Shardt, J.J. Derksen, Sushanta K. Mitra, “Simulations of droplet coalescence in simple shear flow,” Langmuir, 29:6201–6212 (2013).

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