On the impact of thunder on droplets

<p>In the lightning channel pressures can be of the order of 100 atm and hence in the produced thunder, sound pressure levels (SPL) can be very high. Additionally, the thunder frequency spectra have peaks for peal and claps at around 100 Hz and around 50 Hz for rumble sounds, with intracloud lightning having peaks at even fewer Hz. These low frequencies are ideal for acoustically induced orthokinetic agglomeration of droplets. Thunder occurs in cloud environments where not only large numbers of droplets are present, but additionally the shockwave front expands at supersonic velocities in excess of 60 km/s and hence could cause also modulations of droplet size distributions through e.g. vibrational breakup. We present calculations for the two mechanisms above (orthokinetic agglomeration and vibrational breakup) for typical cloud droplet sizes and concentrations. In thunderstorm conditions, it is found that acoustic orthokinetic agglomeration of droplets can be very effective and can produce very rapidly changes in the mean cloud droplet diameter. Also, it is found that the critical Weber number, over which breakup occurs, is easily exceeded in thunderstorm environments and may lead to droplet and ice nuclei breakup. We note that these processes need further study to assess how they could interfere with the lightning generation process itself, through charge redistribution in the modified droplet size distribution spectra. </p>

Singularities in Euler Flows: Multivalued Solutions, Shockwaves, and Phase Transitions

In this paper, we analyze various types of critical phenomena in one-dimensional gas flows described by Euler equations. We give a geometrical interpretation of thermodynamics with a special emphasis on phase transitions. We use ideas from the geometrical theory of partial differential equations (PDEs), in particular symmetries and differential constraints, to find solutions to the Euler system. Solutions obtained are multivalued and have singularities of projection to the plane of independent variables. We analyze the propagation of the shockwave front along with phase transitions.

EVALUATING CONTACT STRESSES IN AN IMPACTOR PENETRATING A HARD SOIL

Finite formulas have been derived for evaluating contact stresses in a rigid impactor penetrating a soil, taking into account the friction in the framework of the local interaction model. In analyzing dynamic deformation of the soil, its volumetric compressibility, shear resistance and initial strength are accounted for. The obtained evaluations of resistance to penetration of an impactor into the soil are based on a quadratic relation between the stress normal to the impactor surface and impact velocity. The authors have pioneered in deriving finite expressions for coefficients of a trinomial approximation as a function of experimentally determined physical-mechanical parameters of the soil - a dynamic compressibility diagram (a shock adiabat) and a yield strength - pressure diagram. Impact compressibility of soils is described based on Hugoniot's adiabat - a linear relation between shock wave velocity and mass velocity of the medium particles behind the shockwave front. Plastic deformation obeys the Mohr - Coulomb yield criterion with a constraint on the limiting value of maximal tangential stresses according to Tresca's criterion - the Mohr - Coulomb - Tresca plasticity condition. An earlier obtained analytical solution of a one-dimensional problem of a spherical cavity expanding at a constant velocity from a point in a half-space occupied by a plastic soil medium is used. A formula for determining critical pressure (a minimal pressure required for the formation of a cavity, accounting for internal pressure in the framework of Mohr - Coulomb's yield criterion) is also used, which generalizes a known solution for an elastic ideally plastic medium with Tresca's criterion. The derived formulas have been verified by comparing their results with the available data from experiments on the penetration of a steel conical impactor into a frozen sandy soil. It is shown that the disagreement between the numerical and experimental results is within 10%.

ANALYZING THE SPHERICAL CAVITY EXPANSION PROBLEM IN A MEDIUM WITH MOHR − COULOMB − TRESCA'S PLASTICITY CONDITION

An analytical solution of the one-dimensional problem of a spherical cavity expanding at a constant velocity from a point in a space occupied by a plastic medium has been obtained. Impact compressibility of the medium is described using linear Hugoniot's adiabat. Plastic deformation obeys the Mohr - Coulomb yield criterion with constraints on the value of maximum tangential stresses according to Tresca's criterion. In the assumption of rigid-plastic deformation (the elastic precursor being neglected), incompressibility behind the shockwave front and the equality of the propagation velocities of the fronts of the plastic wave and the plane shockwave defined by linear Hugoniot's adiabat, a boundary-value problem for a system of two first-order ordinary differential equations for the dimensionless velocity and stress depending on the self-similar variable is formulated. A closed-form solution of this problem has been obtained in the form of a stationary running wave - a plastic shockwave propagating in an unperturbed half-space. This solution is a generalization of the earlier obtained analytical solution for a medium with the Mohr - Coulomb plasticity condition. The effect of constraining the limiting value of maximal tangential stresses on the distribution of dimensionless stresses behind the shockwave front has been examined. Formulas for determining the range of cavity expansion velocities, within which a simple solution for a medium with Tresca's plasticity condition is applicable, have been derived. The obtained solution can be used for evaluating resistance to high-velocity penetration of rigid strikers into low-strength soil media.

Effects of nanobubble collapse on cell membrane integrity

Recent studies have shown that ultrasound is used to open drug-carrying liposomes to release their payloads; however, a shockwave energetic enough to rupture lipid membranes can cause collateral damage to surrounding cells. Similarly, a destructive shockwave, which may be used to rupture a cell membrane in order to lyse the cell (e.g., as in cancer treatments) may also impair or destroy nearby healthy tissue. To address this problem, we use dissipative particle dynamic (DPD) simulation to investigate the addition of a cavitation bubble between the shockwave and the model cell membrane to alter the shockwave front, allowing low-velocity shockwaves to specifically damage an intended target. We focus specifically on a spherical lipid bilayer model, and note the effect of shockwave velocity, bubble size, and orientation on the damage to the model cell. We show that a cavitation bubble greatly decreases the necessary shockwave velocity required to damage the lipid bilayer and rupture the model cell. The cavitation bubble focuses the kinetic energy of the shockwave front into a smaller area, inducing penetration at the edge of the model cell. With this work, we provide a comprehensive approach to the intricacies of model cell destruction via shockwave impact, and hope to offer a guideline for initiating targeted cellular destruction using induced cavitation bubbles and low-velocity shockwaves.

The shockwave dispersion/attenuation potential of a protective structure made of a chemically reactive mixture

Purpose In the recent work, a new blast-wave impact-mitigation concept involving the use of a protective structure consisting of bimolecular reactants (polyvinyl pyridine+cyclohexyl chloride), capable of undergoing a chemical reaction (to form polyvinyl pyridinium ionic salt) under shockwave loading conditions, was investigated using all-atom reactive equilibrium and non-equilibrium molecular-dynamics analyses. The purpose of this paper is to reveal the beneficial shockwave dispersion/attenuation effects offered by the chemical reaction, direct simulations of a fully supported single planar shockwave propagating through the reactive mixture were carried out, and the structure of the shock front examined as a function of the extent of the chemical reaction (i.e. as a function of the strength of the incident shockwave). The results obtained clearly revealed that chemical reactions give rise to considerable broadening of the shockwave front. In the present work, the effect of chemical reactions and the structure of the shockwaves are investigated at the continuum level. Design/methodology/approach Specifically, the problem of the (conserved) linear-momentum accompanying the interaction of an incident shockwave with the protective-structure/protected-structure material interface has been investigated, within the steady-wave/structured-shock computational framework, in order to demonstrate and quantify an increase in the time period over which the momentum is transferred and a reduction in the peak loading experienced by the protected structure, both brought about by the occurrence of the chemical reaction (within the protective structure). Findings The results obtained clearly revealed the beneficial shock-mitigation effects offered by a protective structure capable of undergoing a chemical reaction under shock-loading conditions. Originality/value To the authors’ knowledge, the present manuscript is the first report dealing with a continuum-level analysis of the blast-mitigation potential of chemical reactions.