It is well established that rapidly propagating cracks in brittle material are unstable such that they generate side branches. It is also known that cracks are attracted by free surfaces, which means that they attract each other. This information is used here to formulate a generic model of fragmentation in which the small-size part of the fragment-size distribution results from merged crack branches in the damage zones along the paths of the propagating cracks. This model is solved under rather general assumptions for the fragment-size distribution. The model leads to a generic distribution S(-gamma) exp(-S/S(0)) for fragment sizes S, where gamma = 2d-1/d with d the Euclidean dimension, and S(0) is a material dependent parameter.
Membranes at a microscopic scale are affected by thermal fluctuations and self-adhesion due to van der Waals forces. Methods to prepare membranes of even molecular scale, e.g., graphene, have recently been developed, and the question of their mechanical and thermal stability is of crucial importance. To this end we modeled microscopic membranes with an attractive interaction and applied Langevin dynamics. Their behavior was also analyzed under external loading. Even though these membranes folded during isotropic compression as a result of energy minimization, the process at high confinement was similar to crumpling of macroscopic nonadhesive sheets. The main difference appeared when the compression was released. In such cases, for membranes of sufficiently large size, folded or scrolled conformations emerged. At high temperature entropic effects made such conformations unfavorable, however.
Adsorption and desorption (together called sorption) processes in sampling tubes and filters of eddy-covariance stations cause attenuation and delay of water vapor signals, leading to an underestimation of water vapor fluxes by tens of percent. The aim of this work was (i) to quantify the effects on sorption in filters and tubes of humidity, flow rate, and dirtiness and (ii) to test a recently introduced sorption model that facilitates correction of fluxes. Laboratory measurements on the transport of water vapor pulses through tubes and filters were carried out, and eddy-covariance field measurements were also used.
In the laboratory measurements, the effects of sorption processes were evident, and filters caused a similar attenuation and delay of the signal as tubes. Filters could have a larger impact than a long tube, whereas the flow rate had a much smaller impact on the flux loss than the sorption processes (Reynolds numbers 2120–3360). The sorption model represented well the water vapor pulses in a wide range of conditions. As for the field measurements, the transfer function (TF) derived from the sorption model represented well the observations. Fitting parameters were found to depend strongly on the relative humidity and correlate with the signal delay. Having a more complex shape, TF of the sorption model represented much better the measured TFs than, for example, a Lorentzian or adjusted Gaussian TF, leading on average to a 4% unit difference in the flux corrections. Use of this more complex TF is recommended and its implementation is assisted by the codes provided in appendix B.
A model transport system is considered in which a pulse of tracer molecules is advected along a flow channel with porous walls. The advected tracer thus undergoes diffusion, matrix-diffusion, inside the walls, which affects the breakthrough curve of the tracer. Analytical solutions in the form of series expansions are derived for a number of situations which include a finite depth of the porous matrix, varying aperture of the flow channel, and longitudinal diffusion and Taylor dispersion of the tracer in the flow channel. Novel expansions for the Laplace transforms of the concentration in the channel facilitated closed-form expressions for the solutions. A rigorous result is also derived for the asymptotic form of the breakthrough curve for a finite depth of the porous matrix, which is very different from that for an infinite matrix. A specific experimental system was created for validation of matrix-diffusion modeling for a matrix of finite depth. A previously reported fracturecolumn experiment was also modeled. In both cases model solutions gave excellent fits to the measured breakthrough curves with very consistent values for the diffusion coefficients used as the fitting parameters. The matrix-diffusion modeling performed could thereby be validated.
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