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Using HPC To Predict Impacts of Flow Conditions
Predicting and understanding the conditions for droplet coalescence is important for many applications. For example, emulsion flows, where drops of one fluid are dispersed in another, in large vessels and process equipment are often subjected to complex turbulent flows, such as mixing. In such a flow, droplets are sheared and collide, causing breakup and coalescence.
The result of these interactions is a particular droplet size distribution, which affects macroscopic properties such as the emulsion’s effective viscosity and mass transfer rates between the fluids. Similarly, in micro-fluidic devices, droplet interactions at a T junction or the nozzle of a flow-focusing device can impact how individual droplets are formed and how they can be manipulated.
Simulating droplet coalescence is challenging, however, because small-scale (tens of nanometers) phenomena determine the behavior of much larger (micrometer- to millimeter-scale) droplets. In general, liquid droplets colliding in a liquid medium coalesce when the capillary number is less than a critical value.
University of Alberta researchers Jos Derksen and Sushanta Mitra, along with their graduate student Orest Shardt, are using WestGrid computing resources to run droplet and flow simulations that enable them to more closely analyze and better predict how flow conditions change droplet sizes.
In a paper recently published in Langmuir, Simulations of Droplet Coalescence in Simple Shear Flow, WestGrid facilities were used to create simulations of droplet collisions and coalescence in simple shear flow using the free-energy binary-liquid lattice Boltzmann method.
In previous simulations of low-speed collisions, droplets coalesced at unrealistically high capillary numbers. Simulations of noncoalescing droplets have not been reported, and therefore, the critical capillary number for simulated collisions was unknown. By simulating droplets with radii up to 100 lattice nodes, Shardt, Mitra, and Derksen were able to determine the critical capillary number for coalescence and quantify the effects of several numerical and geometric parameters.
Also, in light of coalescence occurring at higher capillary numbers with lower Pećlet numbers (higher diffusivity), the effects of the vertical offset between the droplets and the confinement of the droplets were also studied. Physically reasonable results were obtained and provide insight into the conditions for coalescence.
Simulations that match the conditions of experiments reported in the literature remain computationally impractical. However, the scale of the simulations is now sufficiently large that a comparison with experiments involving smaller droplets (≈10 μm) and lower viscosities (≈10−6 m2/s, the viscosity of water) may be possible. Experiments at these conditions are therefore needed to determine the interface thickness and Pećlet number that should be used for predictive simulations of coalescence phenomena.