Surface tension driven oscillations of a bubble in a viscoelastic liquid

Small amplitude surface tension driven oscillations of a spherical bubble in a dilute polymer solution are considered. The rheological properties of the liquid are modelled by using a 3-constant constitutive equation of the Oldroyd type. The Laplace transform of the solution of the initial value problem is inverted numerically. As in the Newtonian fluid case, both a discrete and a continuous spectrum occurs. In addition to the non-dimensional parameters in the corresponding problem for a Newtonian fluid, the results depend on two other parameters: the ratio of the relaxation time of the polymer solution and the time scale of the flow (the Deborah number) and the product of the polymer concentration and the intrinsic viscosity. For small bubbles in an aqueous solution having a small relaxation time, significant additional damping is found even for dilute solutions.