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Animal tissues exist within a continuum of fluid to solid states, and transitions between states are important for embryonic development, wound healing and cancer metastasis. Fluid-to-solid transitions are governed by the ratio of adhesive energy to kinetic energy. Here, we find that presomitic mesoderm solidification is driven by an intrinsic decline in cell speed along with an increase in adhesion mediated by Cadherin 2 in parallel with fibronectin and its receptor Integrin α5. A computational model of cell–cell adhesion in the central tissue mesenchyme and cell–ECM adhesion on the tissue surface explains the observed phenotypes. Further, we identify negative feedback within the ECM as fibronectin supports the formation of a separate layer of Fibrillin 2b matrix that inhibits solidification. These data reveal a tissue fluidity code in which solidification is promoted by cadherins in parallel with Integrin α5 and fibronectin, whereas negative feedback through Fibrillin 2b promotes fluidization. 

Capillary droplets form due to surface tension when two immiscible fluids are mixed. We describe the motion of gravity-driven capillary droplets flowing through narrow constrictions and obstacle arrays in both simulations and experiments. Our new capillary deformable particle model recapitulates the shape and velocity of single oil droplets in water as they pass through narrow constrictions in microfluidic chambers. Using this experimentally validated model, we simulate the flow and clogging of single capillary droplets in narrow channels and obstacle arrays and find several important results. First, the capillary droplet speed profile is nonmonotonic as the droplet exits the narrow orifice, and we can tune the droplet properties so that the speed overshoots the terminal speed far from the constriction. Second, in obstacle arrays, we find that extremely deformable droplets can wrap around obstacles, which leads to decreased average droplet speed in the continuous flow regime and increased probability for clogging in the regime where permanent clogs form. Third, the wrapping mechanism causes the clogging probability in obstacle arrays to become nonmonotonic with surface tension Γ. At large Γ, the droplets are nearly rigid and the clogging probability is large since the droplets can not squeeze through the gaps between obstacles. With decreasing Γ, the clogging probability decreases as the droplets become more deformable. However, in the small-Γ limit, the clogging probability increases since the droplets are extremely deformable and wrap around the obstacles. The results from these studies are important for developing a predictive understanding of capillary droplet flows through complex and confined geometries. 

During epithelial wound healing, cell morphology near the healed wound and the healing rate vary strongly among different developmental stages even for a single species like Drosophila. We develop deformable particle (DP) model simulations to understand how variations in cell mechanics give rise to distinct wound closure phenotypes in the Drosophila embryonic ectoderm and larval wing disc epithelium. We find that plastic deformation of the cell membrane can generate large changes in cell shape consistent with wound closure in the embryonic ectoderm. Our results show that the embryonic ectoderm is best described by cell membranes with an elasto-plastic response, whereas the larval wing disc is best described by cell membranes with an exclusively elastic response. By varying the mechanical response of cell membranes in DP simulations, we recapitulate the wound closure behavior of both the embryonic ectoderm and the larval wing disc. 

Numerous experimental and computational studies show that continuous hopper flows of granular materials obey the Beverloo equation that relates the volume flow rate Q and the orifice width w : Q ∼ ( w / σ avg − k ) β , where σ avg is the average particle diameter, kσ avg is an offset where Q ∼ 0, the power-law scaling exponent β = d − 1/2, and d is the spatial dimension. Recent studies of hopper flows of deformable particles in different background fluids suggest that the particle stiffness and dissipation mechanism can also strongly affect the power-law scaling exponent β . We carry out computational studies of hopper flows of deformable particles with both kinetic friction and background fluid dissipation in two and three dimensions. We show that the exponent β varies continuously with the ratio of the viscous drag to the kinetic friction coefficient, λ = ζ / μ . β = d − 1/2 in the λ → 0 limit and d − 3/2 in the λ → ∞ limit, with a midpoint λ c that depends on the hopper opening angle θ w . We also characterize the spatial structure of the flows and associate changes in spatial structure of the hopper flows to changes in the exponent β . The offset k increases with particle stiffness until k ∼ k max in the hard-particle limit, where k max ∼ 3.5 is larger for λ → ∞ compared to that for λ → 0. Finally, we show that the simulations of hopper flows of deformable particles in the λ → ∞ limit recapitulate the experimental results for quasi-2D hopper flows of oil droplets in water.