Acoustic wave speed and attenuation in suspensions

Fundamentals of Multiphase Flow

“…Another popular way of expressing equation 9.12 is to recognize that ρc 2 is the effective bulk modulus of the mixture and that the inverse of this effective bulk modulus is equal to an average of the inverse bulk moduli of the components (1/ρ A c 2 A and 1/ρ B c 2 B ) weighted according to their volume fractions. Some typical experimental and theoretical data obtained by Hampton (1967), Urick (1948) and Atkinson and Kytömaa (1992) is presented in figure 9.1. Each set is for a different ratio of the particle size (radius, R) to the wavelength of the sound (given by the inverse of the wavenumber, κ).…”

“…Note that the minimum in the acoustic velocity at intermediate volume fractions disappears at higher frequencies. Atkinson and Kytömaa (1992) (Urick 1948); the theoretical line is from Atkinson and Kytömaa (1992). modeled the dynamics at non-zero values of κR using the following set of governing equations: (a) continuity equations 1.21 for both the disperse and continuous phases with no mass exchange (I N = 0) (b) momentum equations 1.45 for both phases with no gravity terms and no deviatoric stresses σ D Cki = 0 and (c) a particle force, F k (see equation 1.55) that includes the forces on each particle due to the pressure gradient in the continuous phase, the added mass, the Stokes drag and the Basset memory terms (see section 2.3.4, equation 2.67). They included a solids fraction dependence in the added mass.…”

“…Typical results are plotted in figure 9.1 for various κR and exhibit fair agreement with the experimental measurements. Atkinson and Kytömaa (1992) also compare measured and calculated acoustic attenuation rates given non-dimensionally by ζR where the amplitude decays with distance, s, according to e −ζs . The attenuation results from viscous effects on the relative motion between the particles and the continuous fluid phase.…”

Particle pressures in fluidized beds. Final report

“…can be examined based on existing drag models such as the Ergun model and is expected to be in the range from 0 to 5 based both on-all models available and wide range of numerical testing. There is not much information on the added mass coeficient, some studies (Stkinson (pc Kytomaa, 1992) believe that adcled mass coefficient is between 0 and 0.5, but other studies such as Homsy et ai., (1980) showed wider range on the order of 10 or so. In an attempt to cover all possibilities, the added mass coefficient was assumed to lie anywhere in the range from 0 to 20.…”

Ultrasonic Particle Sizing

“…A special case of great practical interest is the monopole resonance of gas bubbles, which has been intensively investigated. The approximate frequency of resonance is calculated as [Res=~ r:: (14) which corresponds to the particle size parameter of resonance: 1 (15) For air bubbles in water at' ambient pressure, values of about rJRes = 0.014 are obtained. The monopole resonance of gas bubbles is combined with extremely high extinction efficiencies (K Res = 100-400) and with significant changes in the wave propagation velocityi-5-6-7) (Figures 5 and 6).…”