It has already been commented that in the extreme high-frequency limit where each patch behaves as if it were sealed to flow (), the theory of Hill (1963) applies. Hill demonstrated, among other things, that when each isotropic patch has the same shear modulus, the volumetric deformation within each patch is a spatial constant. The fluid pressure response in this limit is thus a uniform spatial constant throughout each phase except in a vanishingly small neighborhood of the interface where equilibration is attempting to take place. The small amount of fluid-pressure penetration that is occuring across can be locally modeled as a one-dimensional process normal to the interface.

Using the coordinate *x* to measure linear distance normal to the interface (and
into phase 1),
one has that equation (56) is satisfied by

(72) | ||

(73) |

(74) | ||

(75) |

(76) |

To obtain the high-frequency limit of the transport coefficient , we use the definition (53) of the internal transport (note that )

(77) |

(78) |

10/14/2003