Session P16: Deformable Particles in Soft Materials

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The mobility of cells in tissues and of soft particles in emulsions, foams, and other soft matter is determined by a complex interplay between particle shape and deformability. To understand and predict the mobility of non-spherical, deformable particles, we compare the mobility of rigid versus deformable, non-spherical particles driven by active forces and thermal fluctuations, which allows us to disentangle the roles of shape and deformability in determining particle transport. Are non-spherical particles more mobile? Or do particles with larger mobilities typically deform more from a spherical shape? Using discrete element method simulations, we will compare the long-time diffusion coefficient and the mobility in response to a small external force in dense liquids of soft particles with rigid shapes, including spheres, ellipses, and asymmetric dimers, to the same measurements for systems of particles with similar shapes, but explicit deformability. We show the results for the diffusion coefficient and mobility as a function of the packing fraction, temperature, and activity.   

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We study how cell-cell adhesion controls the behavior of tissues under mechanical constraint. To this end, we use biomimetic emulsions that were shown to reproduce the minimal mechanical and adhesive properties of cells in biological tissues. The adhesion between the droplets can be introduced in two different ways: nonspecific depletion attraction is induced by tuning the concentration of SDS micelles in the continuous phase; while specific adhesion is introduced by grafting the surface of the droplets with binding molecules. To study the behavior of such emulsions under an applied mechanical perturbation, we flow them through microfluidic constrictions with controlled geometries. Image analysis allows us to characterize the elasto-plastic response of the emulsions under such perturbations. Thus, we measure the level of deformation of the droplets in the channel (elastic response) and monitor irreversible droplet rearrangements (plastic response). We find that while adhesion slows down the dynamics of individual rearrangements, it does not significantly modify the large scale topology of neighbor exchanges within the packing. However, adhesion induces large scale droplet deformations, suggesting that this could be a mechanism for cell polarization in biological tissues.   

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Computational studies of the soft particle model, where interparticle overlaps give rise to purely repulsive forces, have shown interesting behavior of the vibrational modes as a function of the packing fraction and particle shape. However, this model does not accurately describe particle deformability, which is significant in packings of foams and emulsions, as well as confluent cell monolayers. In this work, we numerically study the vibrational modes in packings of deformable particles in two dimensions, as a function of the shape parameter A = p²/(4πa), where p is the perimeter and a is the area of the particle. We find that packings of deformable particles possess low-frequency quartic modes, where the energy increases quartically with the perturbation amplitude when the system is perturbed along these modes. We show that the number of quartic modes equals the number of missing interparticle contacts required to constrain the total number of degrees of freedom in the system. We then decompose each mode into the contributions from particle translations, rotations, and shape changes. We find that nearly all of the vibrational modes contain large contributions from particle shape changes and these contributions couple strongly to particle translations and rotations. In fact, we find that there are large contributions to the vibrational modes from the shape degrees of freedom even when packings are compressed to confluence, underscoring the importance of deformability in soft particulate systems. We further show that as the particle bending rigidity is increased, the quartic modes disappear, and all of the nontrivial vibrational modes become quadratic in the perturbation amplitude. For systems with finite particle bending rigidity, we find that the shear modulus scales as a power-law in pressure with a smaller exponent compared to the shear modulus exponent for packings of particles without bending rigidity.   

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Self-assembly of close-packed deformable grains into ordered structures is of basic interest in developmental biology as well as in tissue engineering. A significant challenge associated with manipulation of soft-granular materials is their inherent metastability associated with deformability of the grains which leads to complex energy landscapes. Here, we demonstrate that the control over rearrangements can be established via precisely balancing the internal elastic stresses with external viscous forces. We use microfluidics to generate monodisperse droplet structures and superstructures such as linear chains, multi-chains or chains with recurring folds adapting to the external flow. We stabilize the generated structures via adding a small volume fraction of a third immiscible phase to the system (besides the droplet and external phases) which engulfs the droplets and leads to their capillary arrest. We not only study the stability of the structures (against uncontrolled rearrangements) but also demonstrate that they can be ‘printed’ at a substrate which opens a range of applications, not only in tissue engineering but also (upon miniaturization) in photonics and/or microelectronics.   

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We study the flow of binary mixtures of particles in a two-dimensional hopper, mixing rigid plastic spheres with elastic, deformable ones. We explore the transition between jamming and flow based on parameters including the aspect ratio of particle size to hopper channel width, α, the mixing ratio of soft to hard spheres, and the softness of the deformable particles. Previous studies have shown that particles of uniform softness can flow through narrower hoppers, with larger α, than can rigid spheres.¹ In our studies, we measure both the probability of clogging and the components of the arch that forms in a clog. Our results suggest that adding soft particles to rigid ones facilitates flow. We measure the critical ratio of soft particles required to facilitate flow as a function of soft particle size and deformability. We further observe that the arch rarely contains more than one deformable particle.

1. X Hong, M Kohne, M Morrell, H Wang, ER Weeks. “Clogging of soft particles in two-dimensional hoppers,” Phys. Rev. E 96, 062605 (2017).   

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The development of complex plant tissues requires careful coordination of cell positions and interactions. In the spongy mesophyll tissue in leaves and flowers, cells form complex networks that maximize air conductance in leaves and minimize resource usage in flower petals. While these developmental processes are vital for plant fitness, little is known about the self-assembly process that generates such intricate structures. We investigate this process using explicitly deformable, sticky particles that self-assemble into porous yet rigid networks from initially dense packings. We investigate the effect of cell deformability and cell-cell adhesion on how maximally porous a system can become before losing rigidity. We compare our results to 3D X-ray microcomputed tomography scans of living leaf and plant tissue as well as continuum models of viscoelastic phase separation. Our studies indicate that the formation of optimally porous networks hinge upon a balance between cell-cell adhesion, cell wall bending energy and slow aging of the cell perimeter.   

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We experimentally study the flow of soft particles through quasi-two-dimensional hoppers. We examine the clogging probability for particles flowing out as a function of the hopper exit width. We find that particle softness plays a critical role in clogging, using different types of particles with varying softness. Clogging is harder for softer particles. The clogging process is caused by the arch formation at the hopper exit. We investigate how the gravitational force, exit width, and particle softness affect the arch size and the number of particles remaining in the hopper when a clog occurs. The experimental results for soft, low-friction, hydrogel particles agree well with previously published simulation data. However, experiments with harder and/or more frictional particles reveal interesting differences.   

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The rheological properties of biological tissue play an important role in developmental biology and cancer metastasis. Most previous theoretical work has employed particle-based or vertex/Voronoi models to demonstrate that tissue can transition between liquid-like and solid-like states. More recently, multi-phase field models of cells as motile and deformable particles have been proposed as versatile tools that can describe both confluent and non-confluent tissue, while independently varying cell density, cell motility and the nature of cell-cell interactions. We have used a multi-phase field model to study the phase behavior and rheology of a tissue monolayer. A new ingredient implemented in our work is the intercellular friction among cell edges that can build-up anisotropic local stresses and have profound effects on tissue rheology. We find that the interplay between motility and cellular adhesion at a fixed density (below confluence) can drive transition between a solid state, when the adhesion is strong compared to motility, to a liquid as motility overcomes adhesion. Using this model, we have performed both shear relaxation and microrheology simulations to examine the behavior of the tissue yield stress as a function of intercellular friction.   

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Motility induced phase separation (MIPS), the phenomenon in which purely repulsive motile particles phase separate into high and low density phases, is a landmark of active matter physics. As such, this transition has been widely studied, with extensions covering different types of interactions, particle shapes, confinements and biologically inspired features such as division, which breaks number conservation. Nevertheless, the literature generally considers rigid particles of fixed shape. In this work, we employ a multi-phase field model to study MIPS in assemblies of deformable particles in two dimensions and quantify how deformability alters the phase diagram. We find that highly deformable particles are less propense to phase separate, as dense clusters tend to fluidize with increasing deformability. We also examine the structural and dynamical properties of the clusters. We expect that generalizing the study of MIPS to systems of deformable particles will increase our understanding of its relevance to biological settings, such as cellular tissues.   

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Deformable soft particles, such as diblock copolymer micelles and polymer-grafted nanoparticles (PGNPs), can self-assemble into various crystalline superlattices with different geometries. The stability of such crystals cannot be understood from a simple packing model of hard spheres because the construction units are no longer isotropic spheres. We apply molecular dynamics simulation to compute the free energy cost of compressing isolated spherical PGNPs into Wigner-Seitz polyhedrons that can tile three-dimensional space. In combination with surface energy calculations, we analyze the stability of simple cubic, body-centered cubic, and face-centered cubic superlattices formed by PGNPs.