NUMERICAL-SIMULATION OF THE DYNAMICS OF ACOUSTICALLY LEVITATED DROPS

Numerical simulation of the dynamics of acoustically levitated drops i s accomplished by solving the Helmholtz equation governing the acousti c scattering problem and the Laplace equation governing the motion of an inviscid and incompressible drop. The boundary element method with quadratic elements is used to solve the surface integral forms of both the Hehmholtz equation and the Laplace equation simultaneously. Bound ary conditions on the drop surface render a system of first-order diff erential equations which is integrated with respect to time by the use of fourth-order Runge-Kutta integration to study the drop translation al frequency, shape oscillation frequency, and the static equilibrium shape. A spherical shape approximation method is used to obtain an ana lytic estimate of the minimum trapping pressure (MTP) and the translat ional frequency of the drop. In particular, the translational frequenc y is shown to agree with the analytic result obtained from the spheric al shape approximation for a small acoustic number or a small wave num ber. The shape oscillation frequencies are found to increase initially with the increasing acoustic number, D [D = (a(0)P(2)rms)/(rho(o)c(2) sigma), P-rms is the root-mean-squared sound intensity, a(0) is the e quivalent radius of drop, rho(o) is the density of host medium, c is t he sound speed in host medium, sigma is the surface tension of the dro p liquid] up to a critical value and then decreases with the increasin g acoustic number due to the nonlinear nature of the acoustic radiatio n pressure. The equilibrium shape of the drop is computed by incorpora ting the normal viscous stress terms into the dynamical system intenti onally to get rid of the transients. The equilibrium shapes are found to agree with the existing result for small acoustic numbers but diffe r for large acoustic numbers. (C) 1996 Acoustical Society of America.