Kamrin Group Continuum modeling from solids to fluids
Gas- and Liquid-Sediment Mixture Modeling
Mixtures of particles and fluid exhibit a vast array of phenomena. The interplay of the two phases and the complex physics of the particle phase join together to produce macroscale effects that are challenging to describe and unusual to the eye. Beyond basic scientific intrigue, these materials are important and pervasive in geophysical settings and industry.
Rather than try to represent the fluid-grain combination as a single phase material, we adopt a more general two-phase approach, in which the fluid and granular phases are modeled as two separate continuous bodies that "overlap each other". The two bodies then interact with each other through specially formulated coupling forces that arise from drag and bouyancy. Our model for simple grains in fluid formulates the rheological behavior of the granular phase so that it reproduces suspension rheology (both dilute and dense) when sheared while also capturing transient behaviors that depend in subtle ways on the packing state, such as the runout dynamics of collapsing piles of submerged grains.
We have developed a numerical method that utilizes the Finite-Volume Method for the fluid phase and the Material Point Method for the granular media to implement the mixture theory even in thermally sensitive settings. This FV-MPM method allows us to treat not only liquids but also gases to allow simulations of erosion due to air or high-speed plumes.
The mixture theoretic approah can also be used to address the exotic behavior of shear-thickening suspensions. One such example that many children are familiar with is cornstarch mixed with water, also known as "oobleck". The material acts like a gooey fluid when loaded slowly; it moves like a liquid when squeezed between one's fingers. However, it rapidly transitions into a stiff solid when loaded more violently; it can easily deflect a punch. The above described mixture framework can be augmented to model this behavior. Since wet cornstarch particles repel each other slightly, the force with which grains are pressed together is key to the odd behavior exhibited; weak compression leaves a lubricated layer that makes it easy for grains to slide by each other, whereas high compression overcomes the repulsion allowing particles to touch and establish solid-like frictional contact. To represent this effect, we add a new state field to the model that represents the fraction of particle contacts that are lubricated versus frictional. This field then modifies the granular phase rheology. Our model has been shown to correctly capture the dynamic solidification fronts exhibited in these materials, while also capturing their packing-dependent shear-thickening behavior and long stress-relaxation times.
Fine particle suspensions, such as cornstarch mixed with water, behave in very odd ways. We have developed an upscaled, continuum mixture theory representation of this material that accurately matches experimental data. The model accounts for surface-chemistry-induced inter-particle repulsion effects between particles, which gives rise to the sudden fluid-to-solid transitions characteristic of this strange material. (c/o MIT News)
Continuum simulation of a rocket engine blasting into the loose granular surface of a planetary body implemented using the FV-MPM method. Color contours are the gas phase' Mach number.
