By Hyoung-Woo Oh
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The model given by equations (7) to (11) may be simplified under several hypothetical asymptotic conditions. We consider two cases: Case 1 - For τ c >> τ d , τ c 1 << τ c 2 it can be shown that equation (7) is equivalent to the turbulent diffusion force model obtained by Lopez de Bertodano et. al. (2006): M TD 2 =− 1 τb ( ρ 2 + CVM ρ1 )ν 2 ∇ α (12) where ν 2 is the turbulent diffusivity of the bubbles. This equation was used by Lopez de Bertodano (2006) to model the diffusion of small bubbles by the very large vortices generated by cap bubbles in cap-bubbly flow.
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Computational fluid dynamics by Hyoung-Woo Oh