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The phenomenon of rate-dependent adhesion has long been recognized as an intricate problem, and the so-far-developed physics and mechanics-based approaches resulted in analytical relations between the implicit form between the work of adhesion and the contact front velocity which are difficult to implement in practice. To address this issue in the framework of spherical indentation, the adhesion relaxation test in a nominal point contact is introduced to estimate the rate-dependent adhesion. Based on a stretched exponent approximation for the contact radius evolution with time, a relatively simple four-parameter model is proposed for the functional relation between the work of adhesion and the contact front velocity, and its fitting performance is compared to that of the known Greenwood-Johnson and Persson-Brener models.

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Sedimentation is an important property of colloidal systems that should be considered when designing pharmaceutical formulations. In pharmaceutical applications, sedimentation is normally described using Stokes' law, which assumes laminar flow of fluid. In this work we studied swelling and hydration of spherical cross-linked amorphous starch microspheres in pure water, solutions of sodium chloride, and in pH-adjusted aqueous solutions. We demonstrated that Reynolds numbers obtained in these experiments correspond to the transition regime between the laminar flow and the turbulent flow and, hence, expressions based on the non-Stokes drag coefficient should be used for calculations of sedimentation velocity from known density or for assessment of density from observed sedimentation velocity. The density of starch microparticles hydrated in water was about 1050 kg/m3, while densities obtained from experiment with other liquids were dependent on the liquids' densities. The data indicate that the swelling of the cross-linked starch microparticles as characterized by their densities is not sensitive to pH and salt concentration in the studied range of these parameters.

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Gravimetric sedimentation is known as a relatively simple method of determining density of spherical particles. When the method is applied to water-swollen starch microparticles of about submillimeter sizes, it becomes evident that a careful selection of the experimental setup parameters is needed for producing accurate testing results. The main reason for this is that the mean particle density is very close to the density of water, and therefore, a dynamic model accounting for the so-called Bassett history force should be employed for describing the unsteady accelerating particle settling. A main novelty of this study consists in deriving a priori estimates for the settling time and distance.

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It is a common practice in the atomic force microscopy (AFM)-based studies of living cells to differentiate them by values of the elastic (Young's) modulus, which is supposed to be an effective characteristic of the mechanical properties of a cell as a heterogeneous matter. The elastic response of a cell to AFM indentation is known to be affected by a relative distance from an AFM probe to a solid support on to which the cell is cultured. Besides this so-called bottom effect, AFM measurements may carry significant information regarding the effect of molecular brushes covering living cells. Here, we develop a mathematical model for determining the intrinsic effective Young's modulus of a single brush-coated cell from the force-indentation curve with the bottom effect taken into account. The mathematical model is illustrated with the example of AFM data on testing of an eukaryotic cell taken from the literature.

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Diffusion of water through membranes presents a considerable challenge, as the diffusivity often depends on the local concentration of water. One particular example with strong biological relevance is the stratum corneum (SC) as the primary permeability barrier for the skin. A simple alternative for the constant diffusivity model is provided by the Fujita's two-parameter rational approximation, which captures the experimentally observed fact that the SC diffusion constant for water increases with increasing the water concentration. Based on Fick's law of diffusion, a one-dimensional concentration-dependent diffusion model is developed and applied for the analysis of both the steady-state transepidermal water loss (TEWL) and the non-steady-state so-called skin surface water loss (SSWL) occurred after removal of an occlusion patch from the SC surface. It is shown that some of the age-related changes in the SSWL can be qualitatively explained by the variation of the dimensionless Fujita concentration-dependence parameter.

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Equilibrium water sorption in stratum corneum (SC) is considered by treating it as a biocomposite with two main phases, namely, corneocytes and lipids. To validate the rule of mixtures for the individual phase sorption isotherms, a new flexible fitting model is introduced by accounting for characteristic features observed in the variations of the thermodynamic correction factors corresponding to the individual sorption isotherms. The comparison of the model fitting performance with that of the five-parameter Park's model shows a remarkably good ability to fit experimental data for different types of sorption isotherms. The effect of the lipids content on the variance of the composite sorption isotherm of stratum corneum is highlighted. The sensitivity analysis reveals that for the typical water content 20-30 wt%, which corresponds to the SC in a stable condition, the sensitivity of the composite sorption isotherm to the variation of the lipids content on dry basis is predominantly positive and sufficiently small. The good agreement observed between the experimental sorption isotherm for SC and the composite isotherm, which is based on the rule of mixtures for the individual phase sorption isotherms, yields a plausible conclusion (hypothesis) that the corneocytes-lipids mechanical interaction during unconstrained swelling of the SC membrane in the in vitro laboratory experiment is negligible.

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A contact problem of electroadhesion for a conductive elastic body pressed against a rigid plane surface of a dielectric coating covering a conductive substrate is formulated applying the Johnsen-Rahbek approximation for the attractive surface stresses and the Derjaguin-Muller-Toporov (DMT) hypothesis about the influence of the adhesive stresses on the deformable shape of the elastic body. An approximate solution is obtained using the Winkler-Fuss deformation model with the equivalent (contact load dependent) stiffness coefficient evaluated according to the Xydas-Kao soft finger model. The friction force under applied voltage is evaluated as the product of the coefficient of friction and the integral of the macro contact pressure over the apparent contact area. The upper and lower estimates for the friction force are discussed in the case of absence of any external normal load.

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In the present paper, we review the current state-of-the-art in asymptotic modeling of articular contact. Particular attention has been given to the knee joint contact mechanics with a special emphasis on implications drawn from the asymptotic models, including average characteristics for articular cartilage layer. By listing a number of complicating effects such as transverse anisotropy, non-homogeneity, variable thickness, nonlinear deformations, shear loading, and bone deformation, which may be accounted for by asymptotic modeling, some unsolved problems and directions for future research are also discussed.

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The pipette aspiration testing technique is considered, and the elastic half-space model, which was originally introduced in the isotropic incompressible case, is revisited and generalized for the case of transverse isotropy. Asymptotic solutions are obtained in the two limiting cases of a wide and a narrow pipette.

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The unilateral axisymmetric frictionless adhesive contact problem for a toroidal indenter and an elastic half-space is considered in the framework of the Johnson-Kendall-Roberts theory. In the case of a semi-fixed annular contact area, when one of the contact radii is fixed, while the other varies during indentation, we obtain the asymptotic solution of the adhesive contact problem based on the solution of the corresponding unilateral non-adhesive contact problem. In particular, the adhesive contact problem for Barber's concave indenter is considered in detail. In the case when both contact radii are variable, we construct the leading-order asymptotic solution for a narrow annular contact area. It is found that for a v-shaped generalized toroidal indenter, the pull-off force is independent of the elastic properties of the indented solid.