Zhiyan Wei

Villification: How the Gut Gets Its Villi

Intestinal Villus Formation The intestinal villi are essential elaborations of the lining of the gut that increase the epithelial surface area for nutrient absorption. Shyer et al. (p. 212, published online 29 August; see the Perspective by Simons) show that in both the developing human and chick gut, the villi are formed in a step-wise progression, involving the sequential folding of the endoderm into longitudinal ridges, via a zigzag pattern, to finally form individual villi. These changes are established through the differentiation of the smooth muscle layers of the gut, restricting the expansion of the adjacent proliferating and growing endoderm and mesenchyme, generating compressive stresses that lead to the buckling and folding of the tissue. Muscular control over proliferating mesenchyme and epithelium yields intestinal villi. [Also see Perspective by Simons] The villi of the human and chick gut are formed in similar stepwise progressions, wherein the mesenchyme and attached epithelium first fold into longitudinal ridges, then a zigzag pattern, and lastly individual villi. We find that these steps of villification depend on the sequential differentiation of the distinct smooth muscle layers of the gut, which restrict the expansion of the growing endoderm and mesenchyme, generating compressive stresses that lead to their buckling and folding. A quantitative computational model, incorporating measured properties of the developing gut, recapitulates the morphological patterns seen during villification in a variety of species. These results provide a mechanistic understanding of the formation of these elaborations of the lining of the gut, essential for providing sufficient surface area for nutrient absorption.

Digital instability of a confined elastic meniscus

Thin soft elastic layers serving as joints between relatively rigid bodies may function as sealants, thermal, electrical, or mechanical insulators, bearings, or adhesives. When such a joint is stressed, even though perfect adhesion is maintained, the exposed free meniscus in the thin elastic layer becomes unstable, leading to the formation of spatially periodic digits of air that invade the elastic layer, reminiscent of viscous fingering in a thin fluid layer. However, the elastic instability is reversible and rate-independent, disappearing when the joint is unstressed. We use theory, experiments, and numerical simulations to show that the transition to the digital state is sudden (first-order), the wavelength and amplitude of the fingers are proportional to the thickness of the elastic layer, and the required separation to trigger the instability is inversely proportional to the in-plane dimension of the layer. Our study reveals the energetic origin of this instability and has implications for the strength of polymeric adhesives; it also suggests a method for patterning thin films reversibly with any arrangement of localized fingers in a digital elastic memory, which we confirm experimentally.

Elastocapillary coalescence of plates and pillars

When a fluid-immersed array of supported plates or pillars is dried, evaporation leads to the formation of menisci on the tips of the plates or pillars that bring them together to form complex patterns. Building on prior experimental observations, we use a combination of theory and computation to understand the nature of this instability and its evolution in both the two- and three-dimensional setting of the problem. For the case of plates, we explicitly derive the interaction torques based on the relevant physical parameters associated with pillar deformation, contact-line pinning/depinning and fluid volume changes. A Bloch-wave analysis for our periodic mechanical system captures the window of volumes where the two-plate eigenvalue characterizes the onset of the coalescence instability. We then study the evolution of these binary clusters and their eventual elastic arrest using numerical simulations that account for evaporative dynamics coupled to capillary coalescence. This explains both the formation of hierarchical clusters and the sensitive dependence of the final structures on initial perturbations, as seen in our experiments. We then generalize our analysis to treat the problem of pillar collapse in three dimensions, where the fluid domain is completely connected and the interface is a minimal surface with the uniform mean curvature. Our theory and simulations capture the salient features of experimental observations in a range of different situations and may thus be useful in controlling the ensuing patterns.

Continuum dynamics of elastocapillary coalescence and arrest

The surface-tension–driven coalescence of wet hair, nano-pillars and supported lamellae immersed in an evaporating liquid is eventually arrested elastically. To characterize this at a continuum level, we start from a discrete microscopic model of the process and derive a mesoscopic theory that couples the inhomogeneous dynamics of drying to the capillary forcing and elastic bending of the lamellae. Numerical simulations of the resulting partial differential equation capture the primary unstable mode seen in experiments, and the dynamic coalescence of the lamellae into dimers and quadrimers. Our theory also predicts the elastic arrest of the pattern or the separation of lamellar bundles into their constituents as a function of the amount of liquid left at the end of the process.

The branch with the furthest reach

How should a given amount of material be moulded into a cantilevered beam clamped at one end, so that it will have the furthest horizontal reach? Here, we formulate and solve this variational problem for the optimal variation of the cross-section area of a heavy cantilevered beam with a given volume V, Youngs modulus E, and density ρ, subject to gravity g. We find that the cross-sectional area should vary according a universal profile that is independent of material parameters, with both the length and maximum reach-out distance of the branch that scale as (EV/ρg)1/4, with a universal self-similar shape at the tip with the area of cross-section a~s3, s being the distance from the tip, consistent with earlier observations of tree branches, but with a different local interpretation than given before. A simple experimental realization of our optimal beam shows that our result compares favorably with that of our observations. Our results for the optimal design of slender structures with the longest reach are valid for cross-sections of arbitrary shape that can be solid or hollow and thus relevant for a range of natural and engineered systems.

Fluid-driven fingering instability of a confined elastic meniscus

When a fluid is pumped into a cavity in a confined elastic layer, at a critical pressure, destabilizing fingers of fluid invade the elastic solid along its meniscus (Saintyves B. et al., Phys. Rev. Lett., 111 (2013) 047801). These fingers occur without fracture or loss of adhesion and are reversible, disappearing when the pressure is decreased. We develop an asymptotic theory of pressurized highly elastic layers trapped between rigid bodies in both rectilinear and circular geometries, with predictions for the critical fluid pressure for fingering, and the finger wavelength. Our results are in good agreement with recent experimental observations of this elastic inter- facial instability in a radial geometry. Our theory also shows that, perhaps surprisingly, this lateral-pressure-driven instability is analogous to a transverse-displacement-driven instability of the elastic layer. We verify these predictions by using non-linear finite-element simulations on the two systems which show that in both cases the fingering transition is first order (sudden) and hence has a region of bistability. Copyright c EPLA, 2015

Wrinkling instability of an inhomogeneously stretched viscous sheet

Motivated by the redrawing of hot glass into thin sheets, we investigate the shape and stability of a thin viscous sheet that is inhomogeneously stretched in an imposed non-uniform temperature field. We first determine the associated base flow by solving the long-timescale stretching flow of a flat sheet as a function of two dimensionless parameters: the normalized stretching velocity

Exactly isochoric deformations of soft solids

\alpha

A geometric model for the periodic undulation of a confined adhesive crack

, and a dimensionless width of the heating zone

2D and Axisymmetric Incompressible Elastic Green's Functions

\beta