Oscillations of a soft viscoelastic drop

A soft viscoelastic drop has dynamics governed by the balance between surface tension, viscosity, and elasticity, with the material rheology often being frequency dependent, which are utilized in bioprinting technologies for tissue engineering and drop-deposition processes for splash suppression. We study the free and forced oscillations of a soft viscoelastic drop deriving (1) the dispersion relationship for free oscillations, and (2) the frequency response for forced oscillations, of a soft material with arbitrary rheology. We then restrict our analysis to the classical cases of a Kelvin-Voigt and Maxwell model, which are relevant to soft gels and polymer fluids, respectively. We compute the complex frequencies, which are characterized by an oscillation frequency and decay rate, as they depend upon the dimensionless elastocapillary and Deborah numbers and map the boundary between regions of underdamped and overdamped motions. We conclude by illustrating how our theoretical predictions for the frequency-response diagram could be used in conjunction with drop-oscillation experiments as a drop vibration rheometer, suggesting future experiments using either ultrasonic levitation or a microgravity environment.

Automated summary

The dynamics of a soft viscoelastic drop are governed by the balance between surface tension, viscosity, and elasticity, with rheology often being frequency dependent. The study focuses on the free and forced oscillations of a soft material with arbitrary rheology, particularly analyzing the cases of a Kelvin-Voigt and Maxwell model relevant to soft gels and polymer fluids. The complex frequencies, characterized by oscillation frequency and decay rate, depend on dimensionless elastocapillary and Deborah numbers, and map the boundary between regions of underdamped and overdamped motions.