Reports: AC9
47610-AC9 Dynamics of Three-Dimensional Droplets Sliding on Solid Substrates
With the support of this award we have investigated computationally the dynamics of droplets and bubbles in confined solid geometries in the presence of viscous flows. During the first year of the award we investigated two projects: (a) the migration and deformation of droplets and bubbles rising in wall bounded shear flows, and (b) the droplet motion in porous media or microfluidic channels with constrictions. Our work has already resulted in a number of significant publications and conference talks. In particular, a paper describing our results from the first project has been published in the top-rated Journal of Fluid Mechanics, while our work has already resulted in four conference talks and proceedings at national and international meetings.
In the following, I highlight our major accomplishments/findings during the first year of the award.
(a) Migration and deformation of droplets and bubbles rising in wall bounded shear flows
Determining how buoyant droplets and bubbles migrate horizontally in a vertical pipe flow is of central importance to estimate the averaged characteristics of the corresponding widespread two-phase flow, including the local volume fraction of the dispersed phase, wall friction and heat exchange through the wall. This determination is made difficult by the fact that any particle moving in a wall-bounded shear flow experiences two different types of lift forces, one being due to the local shear while the other results directly from the presence of the wall. Things are even more complex with drops and bubbles which may deform in such a flow and undergo an additional deformation-induced lift force. These ingredients make it difficult to predict analytically the magnitude or even the direction of the resulting lift force.
In the present study we investigated the migration and deformation of droplets and bubbles in a wall-bounded linear shear flow via computational solutions in the Stokes-flow limit utilizing our three-dimensional fully-implicit interfacial spectral boundary element algorithm. Our numerical results were accompanied with experiments performed by Dr. Takemura at the National Institute of Advanced Industrial Science and Technology in Japan, and with the asymptotic predictions of Dr. Magnaudet from the Institut de Mécanique des Fluides de Toulouse in France.
The interfacial deformation becomes significant when the viscosity of the suspending liquid is large enough. In this regime, we determined the shape of the drops/bubbles and the deformation-induced transverse force. Our experimental and computational findings are in good agreement while the theoretical predictions are found to predict accurately the deformation but to severely underpredict the deformation-induced lift force. Combined with available theories, our present results allow us to understand how slip and shear contribute to the quasi-steady inertial and deformation-induced migration of bubbles rising parallel to a wall in a linear shear flow at low-to-moderate Reynolds number. These results, together with semi-empirical correlations we derived, may now be used to obtain closure laws for predicting the motion of small bubbles rising in more complex wall-bounded flows which may locally be regarded as linear.
(b) Droplet motion in porous media or microfluidic channels with constrictions
The study of the droplet motion through a three-dimensional constriction in a circular or rectangular channel is a problem encountered in a broad range of applications including the enhance oil recovery and microfluidic devices. Utilizing our three-dimensional spectral boundary element algorithm, we investigate the motion, deformation and critical blocking conditions of a viscous droplet in a channel at low-Reynolds-number flows.
In the work, we consider the effects of several parameters affecting the dynamics of the droplet as it is squeezed through the constriction including droplet size, size of constriction and asymmetrical constriction shapes.
