Mechanical interactions between phenocrysts during magma flow give rise to a grain-dispersive pressure. During intrusion into a dike or sill, in the absence of forces other than those of grain interaction, the grain-dispersive pressure must be constant across the flow width. As a result, the concentration of phenocrysts must decrease toward the walls to offset the increase in the velocity gradient as the walls are approached. This mechanism has been offered as an explanation for the observed rapid but gradational increases in content from phenocryst-poor margins to a phenocryst-rich center, especially in picritic dikes and sills.
A relation for the grain dispersive pressure is solved together with the momentum equation of fluid flow, utilizing an empirical relation for the apparent viscosity of the phenocryst suspension. Solutions for steady flow between parallel walls demonstrate pluglike velocity profiles as well as phenocryst-concentration increases toward the center away from the walls. The velocity is nearly the maximum value within the central half of the flow. Therefore very strong pseudoplastic non-Newtonian behavior of the magma need not be assumed to explain the observed phenocryst concentration variations.