Effects of viscoelasticity on the retraction of a sheared drop

Effects of drop and matrix viscoelasticity on the retraction of a sheared drop are numerically investigated. Retraction of an Oldroyd-B drop in a Newtonian matrix is initially faster and later slower with increasing drop Deborah number. The observed behavior is explained using an ordinary differential equation model representing the dominant balance between various forces during retraction. The initial faster relaxation of viscoelastic drops is due to viscoelastic stresses pulling the drop interface at the tips inward. The later slower retraction is due to the slowly-relaxing viscoelastic forces at the equator, where they act against the capillary force. The drop inclination decreases substantially during retraction unlike in a Newtonian case. Matrix viscoelasticity slows the relaxation of a Newtonian drop because of the increasingly slow relaxation of highly stretched polymers near the drop tip with increasing Deborah number. Increasing the ratio of polymeric to total viscosity further accentuates the viscoelastic effects in both cases. For an Oldroyd-B drop in an Oldroyd-B matrix, a competition between the dispersed and the continuous phase elasticities, represented by their ratio, determines the dynamics; larger values of the ratio leads again to initial faster and later slower retraction.