One of Win’s major insights was that to understand fabric and its evolution, when the elements are grains, structure at the grain scale and the grain-scale processes must both be examined. That is, one cannot understand the processes responsible for the evolution of fabric without appeal to the information contained in the underlying structure. This may now seem obvious. However, much work in structural petrology (e.g., Sander, 1970) has been focussed on the more abstract description based on fabric alone. Vague notions of little practical utility were introduced, one being componental movements. I imagine that Win, reading about componental movements, decided to go about seeing what, in fact, the detailed motions in a deforming and recrystallizing polycrystalline rock actually were. A second major insight was that to discover what motions do take place in a deforming and recrystallizing rock, of all possible, it is necessary to directly observe them. Papers that deal with Win’s innovative work based on these two insights include Means (1977, 1980, 1989, 1994), and Means et al. (1984).

To make sense of such observations requires an understanding of kinematics, and Win has made numerous contributions to the structural geology literature in this area (Means, 1976,1990, 1993, 1994; Cobbold et al., 1984). To understand the causative elements that determine the motions, it is necessary to bring in concepts such as stress and constitutive behavior (Means, 1976, 1990).

Much structural geology follows, to a large degree, an approach advocated by Bruno Sander, the Austrian geologist. He commented (Sander, 1970, p. 12): "A clear separation between geometrical and dynamic considerations was maintained by Becker, the American geologist, at a very early date, and he referred to the English physicist Thomson (Lord Kelvin), who says very clearly:

I do not know the context of Lord Kelvin’s remark. Though much may be learned by observation of natural and experimental examples and from detailed consideration of kinematics, either through experimental observation or interpretation, the processes of rock deformation must finally be studied by means of models incorporating mechanics. This necessitates going beyond Lord Kelvin’s "first step," and the use of physical and chemical principles and constitutive postulates not derivable from observation of structure or even of the detailed motions within rocks or analog materials.

Metamorphic differentiation is one example of a process that cannot be adequately addressed purely on the basis of kinematics. Deformation could take place without differentiation, or with variable amounts of it, as seen in natural and experimentally produced examples. The amount of differentiation depends on the value of a physical parameter controlling the rate of deformation, namely, the viscosity, several that control dissolution, transport, and precipitation, and an absolute length scale (see also Bayly, 1996).

In this paper, I present models for three examples in which "pressure-solution" at the macroscopic scale of interest results in "metamorphic differentiation," the separation of one or more minerals from some region in a rock and their segregation in another.

The examples are: (i) the filling of a gap between boudins; (ii) the development of pressure shadows around a stiff inclusion; and (iii) the transfer of a soluble mineral from the limbs of a multilayer fold or crenulation to the hinges. The last is the example to which "metamorphic differentiation" is most generally applied. However, the behavior in all three examples is expressed by results that are similar in form, varying only with the geometry of the structure and the conditions of loading. In each case, dissolution, diffusive transport, and precipitation of a soluble mineral modify the deformation that goes on anyway. The degree to which "differentiation" modifies the deformation may be quantified by the ratio between a rate of deformation ascribable to it and the rate of deformation due to creeping flow. In these examples, and perhaps generally, this ratio is a product of two dimensionless numbers. One contains the physical quantities governing dissolution and precipitation, diffusion, and rock creep; the other is made up of geometric quantities and may change markedly during structural evolution.

For simplicity, the mechanical elements are treated as Newtonian viscous fluids. Dissolution, diffusion, and precipitation take place along discrete interfaces. Hence, the postulate is made that these depend upon an interfacial chemical potential of the solid components, the variation in the equilibrating value of which (Gibbs, 1906; Kamb, 1961) is dominated by a term proportional to the normal stress acting across the interface. This postulate is seemingly in contrast to the use of a continuum formulation by Fletcher (1982), but the latter formulation implicitly follows from a micromechanical model in which the former postulate is applied. The postulate used here may differ in a more fundamental way from continuum approaches of other sorts (e.g., Bayly, 1992, and this volume), although this point is not established at present.

I give results obtained from the mechanical analysis of simple models, but do not provide the details of the analysis, partly to avoid greatly lengthening the paper. As Win has noted (Means, 1990, p. 953; 1994, p. 445), students of structural geology generally do not acquire the background in mechanics required to formulate and analyze such models. Perhaps the results obtained and their potential application to interpretation of natural examples will inspire students (Means, 1991) to study this material. The methods should work well to gain insight into the behavior of natural or analog polycrystalline materials.