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1. Gradient-induced droplet motion over soft solids

   https://doi.org/10.1093/imamat/hxaa015  

   Bardall, Aaron; Chen, Shih-Yuan; Daniels, Karen E; Shearer, Michael (May 2020, IMA Journal of Applied Mathematics)

   Abstract Fluid droplets can be induced to move over rigid or flexible surfaces under external or body forces. We describe the effect of variations in material properties of a flexible substrate as a mechanism for motion. In this paper, we consider a droplet placed on a substrate with either a stiffness or surface energy gradient and consider its potential for motion via coupling to elastic deformations of the substrate. In order to clarify the role of contact angles and to obtain a tractable model, we consider a 2D droplet. The gradients in substrate material properties give rise to asymmetric solid deformation and to unequal contact angles, thereby producing a force on the droplet. We then use a dynamic viscoelastic model to predict the resulting dynamics of droplets. Numerical results quantifying the effect of the gradients establish that it is more feasible to induce droplet motion with a gradient in surface energy. The results show that the magnitude of elastic modulus gradient needed to induce droplet motion exceeds experimentally feasible limits in the production of soft solids and is therefore unlikely as a passive mechanism for cell motion. In both cases, of surface energy or elastic modulus, the threshold to initiate motion is achieved at lower mean values of the material properties. 

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2. Wetting and wrapping of a floating droplet by a thin elastic filament

   https://doi.org/10.1039/D0SM01863E  

   Prasath, S Ganga; Marthelot, Joel; Menon, Narayanan; Govindarajan, Rama (February 2021, Soft Matter)

   null (Ed.)

   We study the wetting of a thin elastic filament floating on a fluid surface by a droplet of another, immiscible fluid. This quasi-2D experimental system is the lower-dimensional counterpart of the wetting and wrapping of a droplet by an elastic sheet. The simplicity of this system allows us to study the phenomenology of partial wetting and wrapping of the droplet by measuring angles of contact as a function of the elasticity of the filament, the applied tension and the curvature of the droplet. We find that a purely geometric theory gives a good description of the mechanical equilibria in the system. The estimates of applied tension and tension in the filament obey an elastic version of the Young–Laplace–Dupré relation. However, curvatures close to the contact line are not captured by the geometric theory, possibly because of 3D effects at the contact line. We also find that when a highly-bendable filament completely wraps the droplet, there is continuity of curvature at the droplet-filament interface, leading to seamless wrapping as observed in a 3D droplet. 

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3. Aggregation in viscoelastic emulsion droplet gels with capillarity-driven rearrangements

   https://doi.org/10.1039/c9sm02134e  

   Thiel, Abigail; Atherton, Timothy J.; Spicer, Patrick T.; Hartel, Richard W. (June 2020, Soft Matter)

   null (Ed.)

   Arrested, or partial, coalescence of viscoelastic emulsion droplets can occur when elastic resistance to deformation offsets droplet surface area minimization. Arrest is a critical element of food and consumer product microstructure and performance, but direct studies of structural arrest and rearrangement have been carried out using only two or three droplets at a time. The question remains whether the behavior of small numbers of droplets also occurs in larger, more realistic many-droplet systems. Here we study two-dimensional aggregation and arrested coalescence of emulsions containing ∼1000 droplets and find that the restructuring mechanisms observed for smaller systems have a large effect on local packing in multidroplet aggregates, but surprisingly do not significantly alter overall mass scaling in the aggregates. Specifically, increased regions of hexagonal packing are observed as the droplet solids level, and thus elasticity, is decreased because greater degrees of capillary force-driven restructuring are possible. Diffusion-limited droplet aggregation simulations that account for the restructuring mechanisms agree with the experimental results and suggest a basis for prediction of larger-scale network properties and bulk emulsion behavior. 

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4. Elastic bit and Berry phase: Investigating topological phenomena in a classical granular network

   https://doi.org/10.1121/10.0027701  

   Hasan, M Arif; Mahmood, Kazi Tahsin (March 2024, The Journal of the Acoustical Society of America)

   This study investigates the Berry phase, a key concept in classical and quantum physics, and its manifestation in a classical system. We achieve controlled accumulation of the Berry phase by manipulating the elastic bit (a classical analogue to a quantum bit) in an externally driven, homogeneous, spherical, nonlinear granular network. This is achieved through the classical counterpart of quantum coherent superposition of states. The elastic bit's state vectors are navigated on the Bloch sphere using external drivers' amplitude, phase, and frequency, yielding specific Berry phases. These phases distinguish between trivial and nontrivial topologies of the elastic bit, with the zero Berry phase indicating pure states of the linearized granular system and the nontrivial π phase representing equal superposed states. Other superposed states acquire different Berry phases. Crucially, these phases correlate with the structure's eigenmode vibrations: trivial phases align with distinct, in-phase, or out-of-phase eigenmodes, while nontrivial phases correspond to coupled vibrations where energy is shared among granules, alternating between oscillation and rest. Additionally, we explore Berry's phase generalizations for non-cyclic evolutions. This research paves the way for advanced quantum-inspired sensing and computation applications by utilizing and controlling the Berry phase. 

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5. Quantum Concepts in Classical Realms: Berry Phases and Elastic Bits in Granular Systems

   Mahmood, Kazi Tahsin; Hasan, M Arif (April 2024, The American Institute of Physics, publisher, Bulletin of the American Physical Society)

   The Berry phase, a concept of significant interest in quantum and classical mechanics, illuminates the dynamics of physical systems. Our current study explores this phenomenon within a classical granular network, employing an "elastic bit" that serves as a classical counterpart to the quantum bit. This approach establishes a connection between classical and quantum mechanics. By adjusting external forces, we generate an elastic bit within the granular network and map its behavior onto a Bloch sphere, akin to operating quantum logic gates. Varied manipulations of these external drivers yield a spectrum of Berry phases, from trivial (0) to nontrivial (π), unveiling the topological nature of the elastic bit. Crucially, this topological behavior is governed by external manipulations rather than the material or geometric properties of the medium. The nontrivial Berry phases, in particular, highlight energy localization within the granule vibrations, marking a significant insight into system dynamics. This research bridges the gap between the quantum and classical realms and paves the way for designing novel materials with unique properties. 

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