INVESTIGATIONS OF LIQUID SURFACE RHEOLOGY OF SURFACTANT SOLUTIONS BY DROPLET SHAPE OSCILLATIONS - THEORY

A theoretical analysis is presented for the shape oscillations of drop s suspended in air For drops of surfactant solution, the oscillation f requency is basically determined by the surface tension; the free-damp ing constant depends on the surface viscoelasticities. Different types of surfactant mass transfer at the droplet surface produce different surface theological behaviors. Analytical approximate solutions for fr ee-oscillation frequency and damping constant are derived by a perturb ation method as functions of surface compositional elasticity, surface dilatational viscosity, and surface shear viscosity. These solutions are verified with exact numerical solutions. The existence of a second oscillation mode due to surface elasticity is illustrated. The phase relationships between the external driving forces and the droplet shap es for forced oscillations are discussed. It is found that at the 90 d egrees phase shift, the driving frequency and the slope of the phase d iagram are equivalent to the free-oscillation frequency and damping co nstant. (C) 1995 American Institute of Physics.