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Journal of Colloid and Interface Science, Vol.172, No.1, 1-13, 1995
Sound-Wave Mobilities in a Nondilute Suspension of Spheres
The motion of particles due to the passage of a sound wave through a nondilute, monodisperse suspension of spheres is calculated correct to the first order in particle volume fraction using the macroscopic boundary integral technique (O’Brien, R. W., J. Fluid Mech. 91, 17 (1979)). This calculation uses functions describing the hydrodynamic interactions of pairs of spheres in a sound wave of arbitrary frequency. These functions are calculated using the multipole collocation technique (Weinbaum, S., Ganatos, P., and Yan, Z., Annu. Rev. Fluid Mech. 22, 275 (1990)). The results of the sound wave mobility calculation are compared with the high frequency limit which has previously been calculated by Sangani et al. (Sangani, A. S., Zhang, D. Z., and Prosperetti, A., Phys. Fluids A 3(12), 2955 (1991)). The agreement in the limit of infinitely high frequencies is found to be excellent for particle densities more than 0.52 times that of the suspending fluid. Discrepancies exist between the theories when the corrections to the high frequency limit given in Sangani et al. are used to calculate mobilities at finite frequencies. The results of this paper are designed to be the first step in developing a rigorous approach toward using ultrasonic techniques to determine the properties (size or density) of particles in a colloidal suspension.