Scaling in linear bubble models of grain growth

We have numerically solved a linear bubble model of grain growth to study orientation effects in a polycrystal on power law growth of the average grain size and on the existence of a scaling form for the normalized grain size distribution function. We consider a binary linear bubble model such that the inter-bubble permeability between like bubbles (unity) is different from that (M) between unlike bubbles. We have also defined a continuous orientation linear bubble model that allows for a continuous distribution of orientations. The inter-bubble permeability in this case depends on the relative orientation of the two bubbles on either side. Our results suggest that scaling and the exponent in the power growth law, in grain growth models that assume uniform grain boundaries, are not altered by introducing anisotropic grain boundary properties provided the initial distribution of orientations is random.