Urick equation

An elaborated version of the Urick equation derived from scattering theory and called the modified Urick equation (Pinfield and Povey, 1997) is ... 

The magnitude of the fluctuations in volume (dilatation) and density (condensation) associated with US wave is controlled by the properties of the medium and the applied forces. The velocity of sound in mixtures and suspensions will therefore be controlled by the mean density and mean compressibility as expressed by the Urick equation (see Eq.9.7-9.10). The equation can be formulated in terms of partial molar volumes by forming an identity between the volume fraction of the solute, its partial volume Vm2), the mean molar volume of the solution Vm) and the mole fraction Cm) as follows ... 

Equations (1.10)-(1.12) together form what is known as the Urick equation, in which the quantities p and are the average emulsion density and adiabatic compressibility, and the subscripts 1 and 0 refer to the dispersed and continuous... 

Urick (71) has shown that the sonic velocity through a mixture of solid particles in a fluid is dependent upon the volume fraction, / , density, q2 and compressibility, K2 of the particles and upon the density, et, and compressibility, Kt, of the fluid. His equation is... 

The method is used for measuring the compressibility of silica particles by ultrasoimd velocity and density measurements on their suspensions. Prior studies with kaolin particles have shown the acceptability of Urick s theory of the dependence of soimd velocity on the volume fraction of the suspensions. So to calculate the particle compressibility from this equation, we had to know both the volume fractions and the densities of the particles. Therefore the possibilities of the determination of these quantities were investigated for gel-like Stoeber silica in water by measuring the sedimentation coefficients of the particles and the densities of their suspensions. Large differences have been foimd between the dried and wetted densities of silica, on the one hand, and between those of their volume fractions, on the other. These differences can be interpreted by looking at the 64% water content of the particles. Thus an effective density approach is... 

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