For this case, , so . The two eigenvectors are , with no dependence on the fluid properties. However, the eigenvalues continue to be functions of the fluid properties. This seems to be a rather special case, but again considering the quasi-isotropic limit, we find that ,where is Poisson's ratio and E is Young's modulus. For this combination of the parameters to vanish for special values does not appear to violate any of the well-known constraints (such as positivity, etc.) on these parameters. For example, if ,the term depending on the fluid properties clearly makes a negative contribution, which might be large enough to cancel the contribution from the solid. But, for now, this case seems rather artificial, so we will not consider it further here.