| The shear flow dynamics of a viscous liquid drop placed in another fluid medium is analyzed in the Stokes-flow regime. This study is motivated by investigations on protein crystal growth for which it is known that shear flow in the protein solution affects the nucleation rate. It is of interest to be able to generate and control shear flow in the sessile-drop geometry which is commonly used for crystal growth and protein aggregation studies. While drops for such experiments are usually of the spherical-cap shape, the enormous analytical complexity has led us to first deal with a two-dimensional drop with linear shear in the external medium, i.e., the cylindrical equivalent of the cap. With the bipolar coordinate system, the circular interface can be exactly identified by constant value of one of the coordinates, and lends itself to satisfying the relevant continuity conditions at the gas-liquid and the solid-liquid interfaces of the system. The second case of a three-dimensional axisymmetric sessile drop with extensional flow shear is analyzed under toroidal coordinate system with the same advantage of fitting gas-liquid interface as bipolar coordinate system. While these two cases rely on the mechanical shear, a third case of electrostatically driven flow applied to a hemispherical drop on a solid surface is also considered. The exact solutions within the framework of Stokes flow of three cases are developed, and the flow field and shear stress distribution are rendered in this study. Some major effects of fluid properties, such as viscosity ratio, and dielectric constant ratio, to shear stress distributions are discussed. It is expected that the quantitive evaluation of the parameters governing shear will provide useful information for controlling shear rate in a sessile drop. The analysis would be helpful in the design of experiments where direct measurement of shear is generally intrusive and possibly disruptive to other sensitive physicochemical processes such as protein nucleation. |
