Model-based simulations of pulsed laser ablation using an embedded finite element method.

A model of thermal ablation with application to multi-pulsed laser lithotripsy is presented. The approach is based on a one-sided Stefan-Signorini model for thermal ablation, and relies on a level-set function to represent the moving interface between the solid phase and a fictitious gas phase (representing the ablated material). The model is discretized with an embedded finite element method, wherein the interface geometry can be arbitrarily located relative to the background mesh. Nitsche's method is adopted to impose the Signorini condition on the moving interface. A bound constraint is also imposed to deal with thermal shocks that can arise during representative simulations of pulsed ablation with high-power lasers. We report simulation results based on experiments for pulsed laser ablation of wet BegoStone samples treated in air, where Begostone has been used as a phantom material for kidney stone. The model is calibrated against experimental measurements by adjusting the percentage of incoming laser energy absorbed at the surface of the stone sample. Simulation results are then validated against experimental observations for the crater area, volume, and geometry as a function of laser pulse energy and duration. Our studies illustrate how the spreading of the laser beam from the laser fiber tip with concomitantly reduced incident laser irradiance on the damaged crater surface explains trends in both the experimental observations and the model-based simulation results.

Influence of surface tension in the surfactant-driven fracture of closely-packed particulate monolayers.

A phase-field model is used to capture the surfactant-driven formation of fracture patterns in particulate monolayers. The model is intended for the regime of closely-packed systems in which the mechanical response of the monolayer can be approximated as that of a linearly elastic solid. The model approximates the loss in tensile strength of the monolayer with increasing surfactant concentration through the evolution of a damage field. Initial-boundary value problems are constructed and spatially discretized with finite element approximations to the displacement and surfactant damage fields. A comparison between model-based simulations and existing experimental observations indicates a qualitative match in both the fracture patterns and temporal scaling of the fracture process. The importance of surface tension differences is quantified by means of a dimensionless parameter, revealing thresholds that separate different regimes of fracture. These findings are supported by newly performed experiments that validate the model and demonstrate the strong sensitivity of the fracture pattern to differences in surface tension.

Design of stiff, tough and stretchy hydrogel composites via nanoscale hybrid crosslinking and macroscale fiber reinforcement.

Hydrogels' applications are usually limited by their weak mechanical properties. Despite recent great progress in developing tough hydrogels, it is still challenging to achieve high values of , toughness and modulus all together in synthetic hydrogels. In this paper, we designed highly stretchable, tough, yet stiff hydrogel composites via a combination of nanoscale hybrid crosslinking and macroscale fiber reinforcement. The hydrogel composites were constructed by impregnating a 3D-printed thermoplastic-fiber mesh with a tough hydrogel crosslinked both covalently and ionically. The hydrogel composites can achieve a fracture energy of over 30,000 J m(-2), a modulus of over 6 MPa, and can be stretched over 2.8 times even in the presence of large structural defects. The enhancement of toughness in the new hydrogel composites relies on multiple pairs of toughening mechanisms which span over multiple length scales. A theoretical model is further developed to predict the toughness and modulus of the hydrogel composites and guide the design of future materials.

Shock waves generated by toroidal bubble collapse are imperative for kidney stone dusting during Holmium:YAG laser lithotripsy.

Holmium:yttrium-aluminum-garnet (Ho:YAG) laser lithotripsy (LL) has been the treatment of choice for kidney stone disease for more than two decades, yet the mechanisms of action are not completely clear. Besides photothermal ablation, recent evidence suggests that cavitation bubble collapse is pivotal in kidney stone dusting when the Ho:YAG laser operates at low pulse energy (Ep) and high frequency (F). In this work, we perform a comprehensive series of experiments and model-based simulations to dissect the complex physical processes in LL. Under clinically relevant dusting settings (Ep = 0.2 J, F = 20 Hz), our results suggest that majority of the irradiated laser energy (>90 %) is dissipated by heat generation in the fluid surrounding the fiber tip and the irradiated stone surface, while only about 1 % may be consumed for photothermal ablation, and less than 0.7 % is converted into the potential energy at the maximum bubble expansion. We reveal that photothermal ablation is confined locally to the laser irradiation spot, whereas cavitation erosion is most pronounced at a fiber tip-stone surface distance about 0.5 mm where multi foci ring-like damage outside the thermal ablation zone is observed. The cavitation erosion is caused by the progressively intensified collapse of jet-induced toroidal bubble near the stone surface (<100 µm), as a result of Raleigh-Taylor and Richtmyer-Meshkov instabilities. The ensuing shock wave-stone interaction and resultant leaky Rayleigh waves on the stone surface may lead to dynamic fatigue and superficial material removal under repeated bombardments of toroidal bubble collapses during dusting procedures in LL.

Impact of the inherent separation of scales in the Navier-Stokes- alphabeta equations.

We study the effect of the length scales alpha and beta in the Navier-Stokes- alphabeta equations on the energy spectrum and the alignment between the vorticity and the eigenvectors of the stretching tensor in three-dimensional homogeneous and isotropic turbulent flows in a periodic cubic domain, including the limiting cases of the Navier-Stokes- alpha and Navier-Stokes equations. A significant increase in the accuracy of the energy spectrum at large wave numbers arises for beta

Microdomain evolution on giant unilamellar vesicles.

A chemo-mechanical model is used to capture the formation and evolution of microdomains on the deforming surface of giant unilamellar vesicles. The model is intended for the regime of vesicle dynamics characterized by a distinct difference in time scales between shape change and species transport. This is achieved by ensuring that shape equilibrium holds away from chemical equilibrium. Conventional descriptions are used to define the curvature and chemical contributions to the vesicle energetics. Both contributions are consistently non-dimensionalized. The phase-field framework is used to cast the coupled model in a diffuse-interface form. The resulting fourth-order nonlinear system of equations is discretized using the finite- element method with a uniform cubic spline basis, which satisfies global higher-order continuity. Two-dimensional and axisymmetric numerical examples of domain evolution coupled to vesicle shape deformation are presented. Curvature-dependent domain sorting and shape deformation dominated by line tension are also considered.

Phase separation in biological membranes: integration of theory and experiment.

Lipid bilayer model membranes that contain a single lipid species can undergo transitions between ordered and disordered phases, and membranes that contain a mixture of lipid species can undergo phase separations. Studies of these transformations are of interest for what they can tell us about the interaction energies of lipid molecules of different species and conformations. Nanoscopic phases (<200 nm) can provide a model for membrane rafts, specialized membrane domains enriched in cholesterol and sphingomyelin, which are believed to have essential biological functions in cell membranes. Crucial questions are whether lipid nanodomains can exist in stable equilibrium in membranes and what is the distribution of their sizes and lifetimes in membranes of different composition. Theoretical methods have supplied much information on these questions, but better experimental methods are needed to detect and characterize nanodomains under normal membrane conditions. This review summarizes linkages between theoretical and experimental studies of phase separation in lipid bilayer model membranes.

Switchable friction of stimulus-responsive hydrogels.

Poly(N-isopropylacrylamide) (pNIPAAm) gels are stimulus-responsive hydrogels that exhibit large reversible changes in their volume and surface physicochemical properties near the lower critical solution temperature (LCST) in response to external stimuli, such as a change in temperature or solvent composition. Here we report how different phase states, induced isothermally by changes in the solvent composition, affect the tribological properties of pNIPAAm hydrogels. Our measurements indicate that gels in a collapsed conformation (above the LCST) exhibit significantly more friction than swollen gels (below the LCST) at low shear rates. These differences arise from changes in the surface roughness, adhesive interactions, and chain entanglements of the gel surfaces associated with the phase transition. Importantly, we show that the changes in friction, triggered by an external stimulus, are reversible. These reversible and possibly tunable changes in friction may have a significant impact on the design of coatings for biosensors and for actuation devices based on stimulus-responsive hydrogels.