Abstract
The propagation of continuous-wave cylindrical ripples as observed in the laboratory is the subject of this paper. The first explicit formulation of the linearized Navier-Stokes in cylindrical coordinates for waves in the presence of a surface dilatational viscoelastic response is derived. Observations of wave slope as measured by a laboratory laser slope gauge are reported; they are described accurately by the theoretically predicted Hankel functions of the second kind. The study uses n-decane as the liquid on which the waves propagate. Three surfaces are tested: they are pure n-decane, n-decane with a surface film of polydimethylsiloxane (PDMS) and a film of a fluorinated surfactant (FC740). The observed dispersion relation is shown to be in excellent agreement with theory and indicates values of surface dilatational elasticity equal to −0.048 ± .091 mN/m, 0.477 ± 0.012 mN/m, and 1.72 ± 0.300 mN/m for the cases of pure n-decane, n-decane with PDMS, and n-decane with FC740, respectively.
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