Bubble shapes and orientations in low Re simple shear flow

Abstract

We present measurements of shape and orientation of air bubbles in a viscous Newtonian fluid deformed by simple shear. The apparatus is a variation of the "parallel band" device developed by G. I. Taylor. Previous experimental studies on low viscosity ratio, low Reynolds number (Re << 1) bubble deformation have focussed on either small or large deformations (mostly small deformation) and have only qualitatively examined the orientation of bubbles except for small deformations. Our data set spans both the theoretical small deformation and high deformation limits. With these data we confirm theoretical relationships and assess the range of capillary numbers (Ca) over which theoretical relationships for shape and orientation of bubbles are appropriate. We also examine the geometry of deformed bubbles as they relax to a spherical shape once shear stresses are removed. Our data indicate that for extremely small Reynolds numbers and viscosity ratios, the small deformation theoretical relationship first developed by Taylor, is a good approximation for Ca<0.5. The large deformation results for both shape and bubble orientation derived by Hinch and Acrivos agree with our data for Ca>1 and Ca>0.5, respectively.