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1. A reciprocal theorem for biphasic poro-viscoelastic materials

   https://doi.org/10.1017/jfm.2024.719  

   Moradi, Moslem; Shi, Wenzheng; Nazockdast, Ehssan (October 2024, Journal of Fluid Mechanics)

   In studying the transport of inclusions in multiphase systems we are often interested in integrated quantities such as the net force and the net velocity of the inclusions. In the reciprocal theorem the known solution to the first and typically easier boundary value problem is used to compute the integrated quantities, such as the net force, in the second problem without the need to solve that problem. Here, we derive a reciprocal theorem for poro-viscoelastic (or biphasic) materials that are composed of a linear compressible solid phase, permeated by a viscous fluid. As an example, we analytically calculate the time-dependent net force on a rigid sphere in response to point forces applied to the elastic network and the Newtonian fluid phases of the biphasic material. We show that when the point force is applied to the fluid phase, the net force on the sphere evolves over time scales that are independent of the distance between the point force and the sphere; in comparison, when the point force is applied to the elastic phase, the time scale for force development increases quadratically with the distance, in line with the scaling of poroelastic relaxation time. Finally, we formulate and discuss how the reciprocal theorem can be applied to other areas, including (i) calculating the network slip on the sphere's surface, (ii) computing the leading-order effects of nonlinearities in the fluid and network forces and stresses, and (iii) calculating self-propulsion in biphasic systems. 

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2. Contact Nonlinearity in Indenter–Foam Dampers

   https://doi.org/10.1115/1.4054054  

   Liu, Lejie; Yerrapragada, Karthik; Henak, Corinne R.; Eriten, Melih (October 2022, Journal of Vibration and Acoustics)

   Abstract In this paper, the nonlinear response of indenter–foam dampers is characterized. Those dampers consist of indenters pressed on open-cell foams swollen with wetting liquids. Recently, the authors identified the dominant mechanism of damping in those dampers as poro-viscoelastic (PVE) relaxations as in articular cartilage, one of nature’s best solutions to vibration attenuation. Those previous works by the authors included dynamic mechanical analyses of the indenter–foam dampers under small vibrations, i.e., linear regime. The current study features the dynamic response of similar dampers under larger strains to investigate the nonlinear regime. In particular, the indenter–foam dampers tested in this paper consist of an open-cell polyurethane foam swollen with castor oil. Harmonic displacements are applied on the swollen and pre-compressed foam using a flat-ended cylindrical indenter. Measured forces and corresponding hysteresis (force–displacement) loops are then analyzed to quantify damping performance (via specific damping capacity) and nonlinearities (via harmonic ratio). The effects of strain and strain rates on the damping capacity and harmonic ratio are investigated experimentally. The dominant source of the nonlinearity is identified as peeling at the indenter–foam interface (and quantified via peeling index). A representative model consisting of a linear viscoelastic foam and rate-dependent adhesive interface (slider element with limiting adhesive strength) explains the observed trends in peeling and thus nonlinear dynamic response. Possible remedies to suppress those nonlinearities in future designs of indenter–foam dampers are also discussed. 

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3. Junctions at the crossroads: the impact of mechanical cues on endothelial cell-cell junction conformations and vascular permeability

   https://doi.org/10.1152/ajpcell.00605.2023  

   Brandon, Ken D; Frank, William E; Stroka, Kimberly M (October 2024, American Journal of Physiology-Cell Physiology)

   Cells depend on precisely regulating barrier function within the vasculature to maintain physiological stability and facilitate essential substance transport. Endothelial cells achieve this through specialized adherens and tight junction protein complexes, which govern paracellular permeability across vascular beds. Adherens junctions, anchored by vascular endothelial (VE)-cadherin and associated catenins to the actin cytoskeleton, mediate homophilic adhesion crucial for barrier integrity. In contrast, tight junctions composed of occludin, claudin, and junctional adhesion molecule A interact with Zonula Occludens proteins, reinforcing intercellular connections essential for barrier selectivity. Endothelial cell-cell junctions exhibit dynamic conformations during development, maturation, and remodeling, regulated by local biochemical and mechanical cues. These structural adaptations play pivotal roles in disease contexts such as chronic inflammation, where junctional remodeling contributes to increased vascular permeability observed in conditions from cancer to cardiovascular diseases. Conversely, the brain microvasculature’s specialized junctional arrangements pose challenges for therapeutic drug delivery due to their unique molecular compositions and tight organization. This commentary explores the molecular mechanisms underlying endothelial cell-cell junction conformations and their implications for vascular permeability. By highlighting recent advances in quantifying junctional changes and understanding mechanotransduction pathways, we elucidate how physical forces from cellular contacts and hemodynamic flow influence junctional dynamics. 

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4. Active gels, heavy tails, and the cytoskeleton

   https://doi.org/10.1039/D1SM00705J  

   Swartz, Daniel W.; Camley, Brian A. (November 2021, Soft Matter)

   The eukaryotic cell's cytoskeleton is a prototypical example of an active material: objects embedded within it are driven by molecular motors acting on the cytoskeleton, leading to anomalous diffusive behavior. Experiments tracking the behavior of cell-attached objects have observed anomalous diffusion with a distribution of displacements that is non-Gaussian, with heavy tails. This has been attributed to “cytoquakes” or other spatially extended collective effects. We show, using simulations and analytical theory, that a simple continuum active gel model driven by fluctuating force dipoles naturally creates heavy power-law tails in cytoskeletal displacements. We predict that this power law exponent should depend on the geometry and dimensionality of where force dipoles are distributed through the cell; we find qualitatively different results for force dipoles in a 3D cytoskeleton and a quasi-two-dimensional cortex. We then discuss potential applications of this model both in cells and in synthetic active gels. 

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5. Size-Dependent Diffusion and Dispersion of Particles in Mucin

   https://doi.org/10.3390/polym15153241  

   Kumar, Parveen; Tamayo, Joshua; Shiu, Ruei-Feng; Chin, Wei-Chun; Gopinath, Arvind (August 2023, Polymers)

   Mucus, composed significantly of glycosylated mucins, is a soft and rheologically complex material that lines respiratory, reproductive, and gastrointestinal tracts in mammals. Mucus may present as a gel, as a highly viscous fluid, or as a viscoelastic fluid. Mucus acts as a barrier to the transport of harmful microbes and inhaled atmospheric pollutants to underlying cellular tissue. Studies on mucin gels have provided critical insights into the chemistry of the gels, their swelling kinetics, and the diffusion and permeability of molecular constituents such as water. The transport and dispersion of micron and sub-micron particles in mucin gels and solutions, however, differs from the motion of small molecules since the much larger tracers may interact with microstructure of the mucin network. Here, using brightfield and fluorescence microscopy, high-speed particle tracking, and passive microrheology, we study the thermally driven stochastic movement of 0.5–5.0 μm tracer particles in 10% mucin solutions at neutral pH, and in 10% mucin mixed with industrially relevant dust; specifically, unmodified limestone rock dust, modified limestone, and crystalline silica. Particle trajectories are used to calculate mean square displacements and the displacement probability distributions; these are then used to assess tracer diffusion and transport. Complex moduli are concomitantly extracted using established microrheology techniques. We find that under the conditions analyzed, the reconstituted mucin behaves as a weak viscoelastic fluid rather than as a viscoelastic gel. For small- to moderately sized tracers with a diameter of lessthan 2 μm, we find that effective diffusion coefficients follow the classical Stokes–Einstein relationship. Tracer diffusivity in dust-laden mucin is surprisingly larger than in bare mucin. Probability distributions of mean squared displacements suggest that heterogeneity, transient trapping, and electrostatic interactions impact dispersion and overall transport, especially for larger tracers. Our results motivate further exploration of physiochemical and rheological mechanisms mediating particle transport in mucin solutions and gels. 

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