The numerical simulation results in the three sections are presented based on the finite element method as below:

1. Two particles interactions in Oldroyd-B fluid under confined shear are demonstrated  showing the three behavior types “pass”, “return” and “tumbling” in functions of initial separation and Weissenberg number. The single fibre dynamics  is also presented with the slow motion showing the vorticity directional orientation in Oldroyd-B fluid and shear thinning fluid with Gisekus model.

2. The particle hydrodynamic effect on the mass transfer in the convection-diffusion problem are presented at Re=0 and Re=finitie. First, at Re=0, it is found that the disturbed streamlines on the convection enhance the mass transfer inducing the larger spectrum of the mass transfer area. Second, at Re>0, it is shown that the shear thickening phenomena by a inertial particle can promote the mass transfer on increasing effective viscosity. However, when Re_p is over critical value, it is also seen that inertial clustering particles being migrated in the region of low-vorticity by centifure-out can interrupt the mass transfer.

3. The mass transfer during the buoyant CO2 bubble absorption in a particle suspension is presented in terms of the experimental and computational studies. In both case, mass transfer enhancement (MTE) based on the mass transfer coefficient by the particle suspension is found. Especially, in numerical study, it is seen that the enhanced mass flux is highly influenced by the particle hydrodynamic interaction on the bubble surface. This can lead to declare a possible mechanism for MTE on a gas-absorption in a suspension.

In this talk, the briefly highlighted results are introduced in each section, not being included the numerical detail.