Douglas P. Holmes

Mechanics of surface area regulation in cells examined with confined lipid membranes

Cells are wrapped in inelastic membranes, yet they can sustain large mechanical strains by regulating their area. The area regulation in cells is achieved either by membrane folding or by membrane exo- and endocytosis. These processes involve complex morphological transformations of the cell membrane, i.e., invagination, vesicle fusion, and fission, whose precise mechanisms are still under debate. Here we provide mechanistic insights into the area regulation of cell membranes, based on the previously neglected role of membrane confinement, as well as on the strain-induced membrane tension. Commonly, the membranes of mammalian and plant cells are not isolated, but rather they are adhered to an extracellular matrix, the cytoskeleton, and to other cell membranes. Using a lipid bilayer, coupled to an elastic sheet, we are able to demonstrate that, upon straining, the confined membrane is able to regulate passively its area. In particular, by stretching the elastic support, the bilayer laterally expands without rupture by fusing adhered lipid vesicles; upon compression, lipid tubes grow out of the membrane plane, thus reducing its area. These transformations are reversible, as we show using cycles of expansion and compression, and closely reproduce membrane processes found in cells during area regulation. Moreover, we demonstrate a new mechanism for the formation of lipid tubes in cells, which is driven by the membrane lateral compression and may therefore explain the various membrane tubules observed in shrinking cells.

Bending and twisting of soft materials by non-homogenous swelling

Soft materials such as biological tissues and gels undergo morphological changes, motion, and instabilities when subjected to external stimuli. We examine how thin elastic plates undergo rapid bending and buckling instabilities after non-homogenous exposure to a favorable solvent that swells the network. An unconstrained beam bends along its length, while a circular disc bends and buckles with multiple curvatures. In the case of a disc, a large-amplitude transverse travelling wave rotates azimuthally around the disc. We provide theoretical interpretations inspired by the complementary thermal expansion problem of transient shape changes triggered by non-homogenous time-dependent heating, which allows collapse of time-dependent swelling data onto universal curves. Control of dynamical, swelling-induced shape changes provides new directions for the utilization of soft materials.

Morphing of geometric composites via residual swelling

Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel, adaptive ways such as fabricating smart actuators or mimicking living tissues. Here, we present the controlled growth-like morphing of 2D sheets into 3D shapes by preparing geometric composite structures that deform by residual swelling. The morphing of these geometric composites is dictated by both swelling and geometry, with diffusion controlling the swelling-induced actuation, and geometric confinement dictating the structures deformed shape. Building on a simple mechanical analog, we present an analytical model that quantitatively describes how the Gaussian and mean curvatures of a thin disk are affected by the interplay among geometry, mechanics, and swelling. This model is in excellent agreement with our experiments and numerics. We show that the dynamics of residual swelling is dictated by a competition between two characteristic diffusive length scales governed by geometry. Our results provide the first 2D analog of Timoshenkos classical formula for the thermal bending of bimetallic beams - our generalization explains how the Gaussian curvature of a 2D geometric composite is affected by geometry and elasticity. The understanding conferred by these results suggests that the controlled shaping of geometric composites may provide a simple complement to traditional manufacturing techniques.

Control and manipulation of microfluidic flow via elastic deformations

We utilize elastic deformations via mechanical actuation to control and direct fluid flow within a flexible microfluidic device. The device consists of a microchannel with a flexible arch prepared by the buckling of a thin elastic film. The deflection of the arch can be predicted and controlled using the classical theory of Euler buckling. The fluid flow rate is then controlled by coupling the elastic deformation of the arch to the gap within the microchannel, and the results compared well with analytical predictions from a perturbation calculation and numerical simulations. We demonstrate that placement of these flexible valves in series enables directed flow towards regions of externally applied mechanical stress. The simplicity of the experimental approach provides a general design for advanced functionality in portable microfluidics, self-healing devices, and in situ diagnostics.

Crumpled surface structures

We present a scalable patterning method based on surface plate buckling, or crumpling, to generate a variety of topographies that can dynamically change shape and aspect ratio in response to stimuli.

Voltage-induced buckling of dielectric films using fluid electrodes

Accurate and integrable control of different flows within microfluidic channels is crucial to further development of lab-on-a-chip and fully integrated adaptable structures. Here we introduce a flexible microactuator that buckles at a high deformation rate and alters the downstream fluid flow. The microactuator consists of a confined, thin, dielectric film that buckles into the microfluidic channel when exposed to voltage supplied through conductive fluid electrodes. We estimate the critical buckling voltage, and characterize the buckled shape of the actuator. Finally, we investigate the effects of frequency, flow rate, and the pressure differences on the behavior of the buckling structure and the resulting fluid flow. These results demonstrate that the voltage--induced buckling of embedded microstructures using fluid electrodes provides a means for high speed attenuation of microfluidic flow.

Curvature-driven morphing of non-Euclidean shells

We investigate how thin structures change their shape in response to non-mechanical stimuli that can be interpreted as variations in the structure’s natural curvature. Starting from the theory of non-Euclidean plates and shells, we derive an effective model that reduces a three-dimensional stimulus to the natural fundamental forms of the mid-surface of the structure, incorporating expansion, or growth, in the thickness. Then, we apply the model to a variety of thin bodies, from flat plates to spherical shells, obtaining excellent agreement between theory and numerics. We show how cylinders and cones can either bend more or unroll, and eventually snap and rotate. We also study the nearly isometric deformations of a spherical shell and describe how this shape change is ruled by the geometry of a spindle. As the derived results stem from a purely geometrical model, they are general and scalable.

Equilibria and instabilities of a Slinky: Discrete model

Abstract The Slinky is a well-known example of a highly flexible helical spring, exhibiting large, geometrically non-linear deformations from minimal applied forces. By considering it as a system of coils that act to resist axial, shearing, and rotational deformations, we develop a two-dimensional discretized model to predict the equilibrium configurations of a Slinky via the minimization of its potential energy. Careful consideration of the contact between coils enables this procedure to accurately describe the shape and stability of the Slinky under different modes of deformation. In addition, we provide simple geometric and material relations that describe a scaling of the general behavior of flexible, helical springs.

Extended lubrication theory: improved estimates of flow in channels with variable geometry

Lubrication theory is broadly applicable to the flow characterization of thin fluid films and the motion of particles near surfaces. We offer an extension to lubrication theory by starting with Stokes equations and considering higher-order terms in a systematic perturbation expansion to describe the fluid flow in a channel with features of a modest aspect ratio. Experimental results qualitatively confirm the higher-order analytical solutions, while numerical results are in very good agreement with the higher-order analytical results. We show that the extended lubrication theory is a robust tool for an accurate estimate of pressure drop in channels with shape changes on the order of the channel height, accounting for both smooth and sharp changes in geometry.

Static bistability of spherical caps

Depending on its geometry, a spherical shell may exist in one of two stable states without the application of any external force: there are two ‘self-equilibrated’ states, one natural and the other inside out (or ‘everted’). Though this is familiar from everyday life—an umbrella is remarkably stable, yet a contact lens can be easily turned inside out—the precise shell geometries for which bistability is possible are not known. Here, we use experiments and finite-element simulations to determine the threshold between bistability and monostability for shells of different solid angle. We compare these results with the prediction from shallow shell theory, showing that, when appropriately modified, this offers a very good account of bistability even for relatively deep shells. We then investigate the robustness of this bistability against pointwise indentation. We find that indentation provides a continuous route for transition between the two states for shells whose geometry makes them close to the threshold. However, for thinner shells, indentation leads to asymmetrical buckling before snap-through, while also making these shells more ‘robust’ to snap-through. Our work sheds new light on the robustness of the ‘mirror buckling’ symmetry of spherical shell caps.