Acoustic nonlinearity of cracks partially filled with a viscous liquid: A quadratic approximation

A mechanism that accounts for the acoustic nonlinearity of cracks partially filled with a viscous liquid is proposed. The mechanism is related to the nonlinear dependences of the capillary and viscous pressures in liquid on the distance between the crack surfaces and on the rate of change of this distance. The nonlinear equation of state is obtained for this type of cracks, and the parameters of this equation are determined. It is shown that the presence of a viscous liquid can lead to a considerable increase in the acoustic nonlinearity of such cracks, as compared to the cracks filled with an ideal liquid.