Fractional crystallization is an essential process proposed to explain worldwide compositional abundances of igneous rocks. It requires crystals to precipitate from the melt and segregate from its residual melt, or experience crystal fractionation. The compositional abundances of volcanic systems show a bell curve distribution suggesting that the process has variable efficiencies. We test crystal fractionation efficiency in convective flow in low to intermediate crystallinity regime. We simulate the physical segregation of crystals from their residual melt at the scale of individual crystals, using a direct numerical method. We find that at low particle Reynolds numbers, crystals sink in clusters. The relatively rapid motion of clusters strips away residual melt. Our results show cluster settling can imprint observational signatures at the crystalline scale. The collective crystal behavior results in a crystal convection that governs the efficiency of crystal fractionation, providing a possible explanation for the bell curve distribution in volcanic systems.

The presence of crystals in magmatic flows introduces spatial heterogeneity, which can build up to the degree that the flow behavior of the crystal‐bearing magma becomes substantially different from that of a pure melt. One example is the transition from flow to sliding, in which the deformation in the crystalline magma is concentrated almost entirely in a thin interfacial layer as opposed to being distributed in a typical flow profile throughout the domain. In this study, we use numerical reproductions of existing laboratory experiments of Fuji basalt in a rotational viscometer to identify when the flow‐to‐sliding transition is likely to occur in crystal‐bearing magma. We utilize a direct numerical method to resolve the interactions between the crystals and the magmatic melt at the scale of individual interfaces in 2‐D. All phase interactions and their aggregate effects on the flow emerge self‐consistently from the simulation itself. We find that the long‐range hydrodynamic interactions between crystals create nonlinear flow behavior even at low crystal fractions. By performing simulations in different geometries, we show that the formation and stability of force chains in crystal‐bearing magma depend sensitively not only on the crystal shape and size but also on the geometry of the experimental apparatuses. Our simulations are consistent with the observed discrepancies in previous laboratory measurements of shear thinning behavior, highlighting the delicacies of using point measurements in experiments to constrain the bulk rheology of crystal‐bearing magma.

We study the interfacial evolution of immiscible two-phase flow within a capillary tube in the partial wetting regime using direct numerical simulation. We investigate the flow patterns resulting from the displacement of a more viscous fluid by a less viscous one under a wide range of wettability conditions. We find that beyond a wettability dependent critical capillary number, a uniform displacement by a less viscous fluid can transition into a growing finger that eventually breaks up into discrete blobs by a series of pinch-off events for both wetting and nonwetting contact angles. This study validates previous experimental observations of pinch-off for wetting contact angles and extends those to nonwetting contact angles. We find that the blob length increases with the capillary number. We observe that the time between consecutive pinch-off events decreases with the capillary number and is greater for more wetting conditions in the displaced phase. We further show that the blob separation distance as a function of the difference between the inlet velocity and the contact line speed collapses into two monotonically decreasing curves for wetting and nonwetting contact angles. For the phase separation in the form of pinch-off, this work provides a quantitative study of the emerging length and timescales and their dependence on the wettability conditions, capillary effects, and viscous forces.