Modeling of the influence of matrix elasticity on coalescence probability of colliding droplets in shear flow

Abstract

The theory of shear-flow-induced coalescence of monodisperse Newtonian droplets in Newtonian and viscoelastic (described by the Maxwell model) matrices has been derived. Changes in flattening of droplets during coalescence are considered. Calculated dependences on the system parameters of probability, Pc, that the droplet collision is followed by their fusion for Newtonian systems agree qualitatively with the Rother–Davis theory [Phys. Fluids 13, 1178–1190, (2001)]. Values of Pc for a certain set of parameters are substantially affected by the model used to describe mobility of the interface. It has been found that increasing elasticity (relaxation time) of the matrix leads to decreasing Pc irrespective of mobility of the interface. This decrease is small for short relaxation times but pronounced for long relaxation times. The shapes of the dependences of Pc on the droplet radii and the shear rate are similar for systems with a Newtonian matrix but differ qualitatively for systems with a viscoelastic matrix. Results of the theory show that Pc for viscous and viscoelastic matrices can be semiquantitatively approximated by a product of probability for spherical droplets and probability for highly flattened droplets, calculated from Janssen’s theory [“Dynamics of liquid–liquid mixing,” Ph.D. thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 1993] for a viscous system.