Let the rigid inclusion be a chert nodule in limestone, idealized to a circular cross-section of diameter 2 cm and a much greater length. Let the limestone be deformed, for example in the hinge of a fold, so that a region around the nodule is changed from a 10-cm square to a rectangle 6.25 cm by 16 cm. We focus attention on points 5 mm out from the nodule boundary, or 1.5 cm from its centerline. If the nodule were as readily deformable as its matrix, in the direction of maximum elongation such a point would move through 9 mm to end 2.4 cm out. If the nodule is rigid and no diffusion occurs, the motion would be reduced to 1 mm; a rigid nodule powerfully inhibits deformation of its immediate surroundings. Now let diffusion run, with stresses as in Figure 8 yielding strain rates as in Figure 9: the outward motion of the point in view would increase only about 14% --- an extra motion of only a fraction of a millimeter during the total episode of deformation. This small change is of course tied directly to the particular example described in Appendix 3, and specifically to the value of the characteristic length L in that example (0.188 x the inclusion radius). If L had a larger value, the effect of diffusion would be greater; even so, part of the effect is to reduce the stress concentrations; the effect of diffusion does not appear wholly in the form of enhanced strain rates.

Need we look at actual stress magnitudes and duration of the deformation episode? No, the length L is the essential parameter. Suppose (unrealistically) that the change in dimensions of the reference square from 10 cm to 16 cm occurred at a constant strain rate of 3.10^-14 per sec for (6.7).10¹² sec, in a rock of effective viscosity 10²⁰ Pa-sec; then the driving stress difference must have been 12 MPa, and the diffusion coefficient K = 9x10^-27 m²-Pa^-1-sec^-1, (from L²/4N). Now suppose the temperature or the pore-fluid chemistry were different so that the effective viscosity was only half as much: the time for the deformation would change, but experience indicates that K would increase by a factor close to 2 --- (K and N varying inversely), --- so that L would not change and, like the total strain, the same total diffusive effect would be gained at twice the rate in half the time.