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The dynamics of a three-phase gas–liquid–liquid multiphase system is examined by direct numerical simulations. The system consists of a continuous liquid phase, buoyant gas bubbles, and smaller heavy drops that fall relative to the continuous liquid. The computational domain is fully periodic, and a force equal to the weight of the mixture is added to keep it in place. The governing parameters are selected so that the terminal Reynolds numbers of the bubbles and the drops are moderate; while the effect of bubble deformability is examined by changing its surface tension, the surface tension for the drops is sufficiently high so they do not deform. One bubble in a “unit cell” and eight freely interacting bubbles are examined. The dependency of the slip velocities, the velocity fluctuations, and the distribution of the dispersed phases on the volume fraction of each phase are examined. It is found that while the distribution of drops around a single bubble in a “unit cell” is uneven and depends on its deformability, the distribution of drops around freely interacting bubbles is relatively uniform for the parameters examined in this study. 

Abstract The collagen-rich tumor microenvironment plays a critical role in directing the migration behavior of cancer cells. 3D collagen architectures with small pores have been shown to confine cells and induce aggressive collective migration, irrespective of matrix stiffness and density. However, it remains unclear how cells sense collagen architecture and transduce this information to initiate collective migration. Here, we tune collagen architecture and analyze its effect on four core cell-ECM interactions: cytoskeletal polymerization, adhesion, contractility, and matrix degradation. From this comprehensive analysis, we deduce that matrix architecture initially modulates cancer cell adhesion strength, and that this results from architecture-induced changes to matrix degradability. That is, architectures with smaller pores are less degradable, and degradability is required for cancer cell adhesion to 3D fibrilar collagen. The biochemical consequences of this 3D low-attachment state are similar to those induced by suspension culture, including metabolic and oxidative stress. One distinction from suspension culture is the induction of collagen catabolism that occurs in 3D low-attachment conditions. Cells also upregulate Snail1 and Notch signaling in response to 3D low-attachment, which suggests a mechanism for the emergence of collective behaviors.