A theory of bubble coalescence in glacier ice (Weertman, 1968) can be used to explain why small pools of magma in the upper mantle can coalesce into large pools.

Glacier ice contains entrapped gas bubbles and water bubbles. If glacier ice is sheared, it is inevitable that the plastic deformation will lead to coalescence of bubbles (Fig. 1). If the temperature is high enough so that the process that spheriodizes inclusions is rapid, the collision of two spherical bubbles leads to their coalescence into one larger spherical bubble.

The theory that was developed for coalescence of bubbles in glacier ice (Weertman, 1968) can be applied to the problem of the collection of magma in the upper mantle into large pools. I draw attention to this possible application of a theory originally developed for glacier ice.

I have shown (1968) that the concentration C of bubbles is given by the equation.  
where Co is the initial concentration of liquid-filled spheres, e is shear strain (understood to be always a positive quantity), and V is the volume fraction of liquid in a unit volume of material. For V = 0.1, large amounts of coalescence occur for a shear strain ∈ greater than 10.

It is commonly assumed that liquid phase is present in the low-strength zone of the upper mantle. I have suggested (1967) that horizontal flow can occur in this zone in a manner similar to the flow of magma within a dike. The plate tectonic picture cannot avoid having this zone sheared to large strains. Suppose this zone is of the order of 100km thick and motion of matter in it occurs over horizontal distances of the order of 5,000 km. The average shear strain of a volume element that has traveled this distance thus is of the order of 100. For V = 0.1, the ratio C/Co predicted by equation (8) is 3 × 10−6, which is an extremely strong degree of coalescence (that is, about 3 × 105 bubbles have coalesced into one gigantic bubble). Thus shear flow in the low-strength zone of the upper mantle could lead to the concentration of small pools of magma into large ones. The magma in large pools subsequently could reach the earth's crust in rising magma-filled cracks which turn into dikes (Weertman, 1971a, 1971b).

Shaw (1969) discussed magma production in a mantle that is sheared. He stated: “The puzzling question of how magma accumulates in order to rise may be answered by the conclusion that viscous failure and flow are part of the same mechanism, and that the melt fraction is virtually kneaded from the crystalline source.” This note suggests a possible mechanism for “kneading out” the melt fraction in the upper mantle, regardless of how the melt fraction is produced.

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