Conditions for bifurcation of the longitudinal wave in a porous medium

The critical wave number for the slow longitudinal wave in porous materials has been previously determined using asymptotic methods. However, in some situations, such as porous polymeric materials, the accuracy of the asymptotic assumption behavior is questionable. This paper presents an exact solution for calculation of the critical wave number. The solution is shown to significantly alter the critical wave number for low density highly porous materials such as polymeric porous materials. The potential importance of the measurement of critical wave number is demonstrated by showing the sensitivity of the measure to permeability and the insensitivity of the measure to other input variables.