Mechanical interactions between phenocrysts during magma flow give rise to a grain dispersive pressure. Considerations of the balance of the dispersive pressure are utilized to deduce the velocity profile of the magma flowing through a picritic dike from the observed distribution of olivine phenocrysts. The dike, from the Isle of Skye, Scotland, has a gradual increase in phenocryst concentration from the walls to the center. The analysis of this dike yields a pluglike velocity profile in which the velocity is within 1 percent of the maximum velocity throughout the central half of the dike, with large velocity gradients near the walls.
Factors such as a viscosity increase toward the walls due to cooling and variations in the proportionality coefficient in the grain dispersive relationship are considered in the analysis. Other possible corrections required to improve the results are indicated. The velocity profile obtained in the analysis is first compared to profiles for pseudoplastic and Bingham-plastic non-Newtonian fluids. Poor agreement is found, and it is concluded that non-Newtonian fluid models are unsatisfactory. The data are then compared to a model in which the pluglike velocity profile results from the simultaneous requirement of a constant grain dispersive pressure and a balance between the pressure gradient producing the magma intrusion and the viscous dissipation of its momentum. This comparison was successful, and I concluded that such balances cause the pluglike velocity profile as well as the increase in phenocryst concentration toward the dike center.