Capillary breakup of Discontinuously Rate Thickening Suspensions

Abstract

In this study, we investigated the behavior of Discontinuously Rate Thickening Suspensions (DRTS) in capillary breakup, where a thin suspension filament breaks up under the action of surface tension forces. We performed experiments with 55% by weight suspension of cornstarch in glycerol. To minimize the effect of gravity on the experiments, we developed a new experimental method, where the filament is supported in a horizontal position at the surface of an immiscible oil bath by the interfacial tension of the oil-air interface. It was found that after a brief transition period, the radius of the filament decreases at an exponentially decaying rate, which is half the deformation rate at which the apparent viscosity of DRTS appreciably increases beyond it's low-deformation rate value. Late in the filament's evolution, a bead forms in its center, leading to formation of morphologically complex, high aspect ratio structures. It was found that the formation of these structures is caused by the viscous drag exerted on the filament by the oil bath. The behavior of DRTS filaments in capillary breakup was modeled with 1- dimensional approximations to momentum and mass balance equations, which are valid in the limit of slender geometry of the filament. The rheology of the suspension was modeled with a simple function diverging at the deformation rate at which the increase in viscosity becomes appreciable. The governing nonlinear coupled partial differential equations were solved numerically with a finite volume scheme using the Newton's method. It was found that this simple model reproduces the observed behavior well. It was found that in contrast to Newtonian filaments, the viscous stress in the DRTS filaments reaches a plateau and does not increase indefinitely. This is a result of a coupling between the nonlinear rheology of the suspension and the nonlinearity associated with evolving shape of the filament. It was found that the evolution of DRTS filaments with no external viscous drag depends on the value of a single parameter, [epsilon]Wi, which is a function of the Weissenberg number Wi associated with the flow, and the aspect ratio of the filament . When [epsilon]Wi < 1/3, the viscous stress at the center of the filament scales as [epsilon]-1 and when [epsilon]Wi > 1/3, the viscous stress scales as Wi- 1. These findings are supported by analytical arguments based on the governing equations in the regime where [epsilon]Wi < 1/3. The formation of the beaded structures was investigated, focusing on the appearance of the first bead at the center of the filament. It was found that the viscous drag from the environment plays a central role in formation of the beads. Numerical