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Swelling induced deformation and instability of hydrogelsKang, Min Kyoo 16 November 2010 (has links)
A hydrogel consists of a crosslinked polymer network and solvent molecules, capable of large, reversible deformation in response to a variety of external stimuli. In particular, diverse instability patterns have been observed experimentally in swelling hydrogels under mechanical constraints. The present study develops a general theoretical framework based on a variational approach, which leads to a set of governing equations coupling mechanical and chemical equilibrium conditions for swelling deformation of hydrogels, along with proper boundary conditions. A specific material model is employed for analytical and numerical studies, for which the nonlinear constitutive behavior of the hydrogel is derived from a free energy function combining rubber elasticity with a polymer solution theory. A finite element method is then developed and implemented as a userdefined material (UMAT) in the commercial package, ABAQUS. By numerical simulations, the effect of constraint on inhomogeneous swelling of substrateattached hydrogel lines is elucidated. It is found that creaselike surface instability occurs when the widthtoheight aspect ratio of the hydrogel line exceeds a critical value.
Next, by considering a hydrogel layer on a rigid substrate, swellinduced surface instability is studied in details. A linear perturbation analysis is performed to predict the critical condition for onset of the surface instability. In contrast to previously suggested critical conditions, the present study predicts a range of critical swelling ratios, from about 2.5 to 3.4, depending on the material properties of the hydrogel system. A stability diagram is constructed with two distinct regions for stable and unstable hydrogels with respect to two dimensionless material parameters. Numerical simulations are presented to show the swelling process, with evolution of initial surface perturbations followed by formation of creaselike surface patterns. Furthermore, with combined swelling and mechanical compression, the stability analysis is extended to predict a general critical condition that unifies the swellinduced surface instability of hydrogels with mechanically induced surface instability of rubbers.
The effect of surface tension is found to be critical in suppressing shortwavelength modes of surface instability, while the substrate confinement suppresses longwavelength modes. With both surface tension and substrate confinement, an intermediate wavelength is selected at a critical swelling ratio for onset of surface instability. Both the critical swelling ratio and the characteristic wavelength depend on the initial thickness of the hydrogel layer as well as other material properties of the hydrogel. It is found that the hydrogel layer becomes increasingly stable as the initial layer thickness decreases. A critical thickness is predicted, below which the hydrogel layer swells homogeneously and remains stable at the equilibrium state.
Finally, threedimensional finite element models are developed to simulate swelling deformation of hydrogel lines. Depending on the aspect ratio of the cross section as well as the material properties of the hydrogel, two types of swellinduced instability patterns are envisaged, i.e., localized surface instability versus global buckling. / text

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Particle sizesegregation and rheology of geophysical granular flowsBaker, James January 2017 (has links)
Geophysical granular flows, such as snow avalanches, pyroclastic density currents, mudslides and debris flows, can be extremely hazardous to local populations, and understanding their complex behaviour remains an important challenge. This project aims to provide insight into these events by exploring different aspects in isolation, using a combination of mathematical theory, numerical simulations and smallscale experiments. Firstly, the effect of lateral confinement is examined by studying granular material moving in an inclined chute. This can have applications to natural releases flowing down confined valleys or conduits, and the relative simplicity of the geometry also provides a useful test case for new theoretical models. One such model is the recent depthaveraged μ(I)rheology, which, because of the viscous terms introduced into the depthaveraged momentum balance, may be described as an intermediate approach between full constitutive laws and classical shallowwatertype equations for dense granular flows. Here, a generalisation of the new system to two spatial dimensions is described, and the resulting viscous equations are able to capture the crossslope curvature of the downslope velocity profiles in steady uniform chute flows. This may be regarded as major progress compared to traditional hyperbolic models, which only admit constant velocity solutions. Particle sizesegregation in geophysical granular flows is then investigated, which can cause important feedback on the overall bulk properties as it can lead to the development of regions with different frictional properties. A particularly striking example is segregationinduced 'finger' formation, where large particles are segregated to the flow surface and sheared to form a resistive coarserich front, which is unstable and spontaneously breaks down into a series of lobate structures. These travel both faster and further than one might anticipate. To model such segregationmobility feedback effects, the depthaveraged μ(I)rheology is extended to bidisperse flows by coupling with a depthintegrated model for sizesegregation. The system of equations remains mathematically wellposed and is able to qualitatively capture finger formation, with the newlyintroduced viscous terms controlling the characteristics of the leveed channels that develop. A more subtle segregation effect is studied in bidisperse roll waves, which form as small irregularities merge and coarsen as they move downslope, eventually growing into destructive large amplitude pulses. Experimental measurements show lateral, as well as vertical, segregation profiles, with the coarser grains accumulating at the fastest moving wave crests. The disturbances that form in mixtures with higher proportions of large particles grow more slowly, leading to smaller amplitude waves that travel at slower speeds, and the new coupled model predicts qualitatively similar behaviour. Finally, the influence of complex topography is investigated. A smooth twodimensional bump is placed across the width of a chute, which, depending on the initial conditions, can lead to the formation of an airborne jet or granular shock at steady state. A simple depthaveraged model in a curvilinear coordinate system following the topography accurately captures both regimes, and represents a significant improvement on using an aligned Cartesian approach.

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Charakterisierung von Kavitationsblasenpopulationen / Characterization of cavitation bubble populationsThiemann, Andrea 09 June 2011 (has links)
No description available.

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