We present numerical results for the breakup of a pair of colloidal particles enveloped by a droplet under shear flow. The smoothed profile method is used to accurately account for the hydrodynamic interactions between particles due to the host fluid
. We observe that the critical capillary number, $Ca_{rm B}$, at which droplets breakup depends on a velocity ratio, $E$, defined as the ratio of the boundary shift velocity (that restores the droplet shape to a sphere) to the diffusive flux velocity in units of the particle radius $a$. For $E < 10$, $Ca_{B}$ is independent of $E$, as is consistent with the regime studied by Taylor. When $E > 10$, $Ca_{B}$ behaves as $Ca_{rm B} = 2E^{-1}$, which confirms Karam and Bellingers hypothesis. As a consequence, droplet break up will occur when the time scale of droplet deformation $dot{gamma}^{-1}$ is smaller than the diffusive time scale $t_{D} equiv a^{2}/Ltau$ in units of $a$, where $L$ is the diffusion constant and $tau$ is the 2nd order coefficient of the Ginzburg-Landau type free energy of the binary mixture. We emphasize that the breakup of droplet dispersed particles is not only governed by a balance of forces. We find that velocity competition is one of the important contributing factor.
The intrinsic viscosity of a dilute dispersion of rigid rods is studied using a recently developed direct numerical simulation (DNS) method for particle dispersions. A reentrant transition from shear-thinning to the 2nd Newtonian regime is successful
ly reproduced in the present DNS results around a Peclet number ${rm Pe}=150$, which is in good agreement with our theoretical prediction of ${rm Pe}=143$, at which the dynamical crossover from Brownian to non-Brownian behavior takes place in the rotational motion of the rotating rod. The viscosity undershoot is observed in our simulations before reaching the 2nd Newtonian regime. The physical mechanisms behind these behaviors are analyzed in detail.
A general methodology is presented to perform direct numerical simulations of particle dispersions in a shear flow with Lees-Edwards periodic boundary conditions. The Navier-Stokes equation is solved in oblique coordinates to resolve the incompatibil
ity of the fluid motions with the sheared geometry, and the force coupling between colloidal particles and the host fluid is imposed by using a smoothed profile method. The validity of the method is carefully examined by comparing the present numerical results with experimental viscosity data for particle dispersions in a wide range of volume fractions and shear rates including nonlinear shear-thinning regimes.
We present numerical results for the dynamics of a single chain in steady shear flow. The chain is represented by a bead-spring model, and the smoothed profile method is used to accurately account for the effects of thermal fluctuations and hydrodyna
mic interactions acting on beads due to host fluids. It is observed that the chain undergoes tumbling motions and that its dimensionless frequency F depends only on the Peclet number Pe with a power law. The exponent of Pe clearly changes from 2/3 to 1 around the critical Peclet number, indicating that the crossover reflects the competition of thermal fluctuation and shear flow. The presented numerical results agree well with our theoretical analysis based on Jefferys work.
