Interlayer material transport during layer-normal shortening. Part I. The model

Abstract

To analyse mass-transfer during deformation, the case is considered of a multilayer experiencing a layer-normal shortening that is volume constant on the scale of many layers. Strain rate is homogeneously distributed on the layer-scale if diffusion is absent; when transport of matter between the layers occurs, strain rate and dilatation rate are found to vary with distance from the contacts between layers. An instantaneous model for differentiation is developed on the assumption that the sole driving force for diffusion is the difference in the hydrostatic component of stress caused by flow of Theologically contrasting layers. Physical properties incorporated in the model are: viscosity, η, mobility of the migrating component, M, and a factor ƒ for (an)isotropy in removal or addition of material. Each is found to influence flow behaviour and diffusion to a degree depending on scale. The magnitude of the characteristic diffusion length, B = √2υ0ηMƒ where υ0 is the specific volume of the diffusing component, is essential in this respect. Mass-removal and mass-addition contribute significantly to deformation of relatively thin layers. In thick layers, beyond about six times the characteristic diffusion length away from a contact, deformation proceeds as in the absence of diffusion. The theory further predicts a dynamically maintained stable layer-thickness to which thicker and thinner layers converge during prolonged deformation. The question how (periodically) layered gneiss may develop by deformation of directionless igneous rock is discussed in the light of this conclusion.