Self-Similar Solution of Spherical Shock Wave Propagation in a Mixture of a Gas and Small Solid Particles with Increasing Energy under the Influence of Gravitational Field and Monochromatic Radiation

Similarity solution for a spherical shock wave with or without gravitational field in a dusty gas is studied under the action of monochromatic radiation. It is supposed that dusty gas be a mixture of perfect gas and micro solid particles. Equilibrium flow condition is supposed to be maintained and energy is varying which is continuously supplied by inner expanding surface. It is found that similarity solution exists under the constant initial density. The comparison between the solutions obtained in gravitating and non-gravitating medium is done. It is found that the shock strength increases with an increase in gravitational parameter or ratio of the density of solid particles to the initial density of the gas, whereas an increase in the radiation parameter has decaying effect on the shock waves.     

Self-similar Solution of a Cylindrical Shock Wave under the Action of Monochromatic Radiation in a Rotational Axisymmetric Dusty Gas

A self-similar flow behind a cylindrical shock wave is studied under the action of monochromatic radiation in a rotational axisymmetric dusty gas. The dusty gas is taken to be a mixture of small solid particles and perfect gas,and solid particles are continuously distributed in the mixture. The similarity solutions are obtained and the effects of the variation of the radiation parameter, the ratio of the density of solid particles to the initial density of the gas, the mass concentration of solid particles in the mixture and the index for the time dependent energy law are investigated.It is observed that an increase in the radiation parameter has decaying effect on the shock waves; whereas the shock strength increases with an increase in the ratio of the density of solid particles to the initial density of the gas or the index for the time dependent energy law. Also, it is found that an increase in the radiation parameter has effect to decrease the flow variables except the density and the azimuthal component of fluid velocity. A comparison is also made between rotating and non-rotating cases.     

Shock wave driven out by a piston in a mixture of a non-ideal gas and small solid particles under the influence of the gravitation field with monochromatic radiation

Similarity solutions for a spherical shock wave in a mixture of small solid particles of micro size and a non-ideal gas are discussed under the influence of the gravitational field with monochromatic radiation. The solid particles are uniformly distributed in the mixture, and the shock wave is assumed to be driven by a piston. It is assumed that the equilibrium flow-conditions are maintained and the moving piston continuously supplies the variable energy input. Due to the central mass ($\overline{m}$) at the origin (Roche model), the medium is considered to be under the influence of the gravitational field. In comparison to the attraction of the central mass at the origin, the gravitational effect of the mixture itself is neglected. The density of the undisturbed medium is assumed to be constant in order to obtain the self-similar solutions. The effect of the parameter of non-idealness of the gas $\overline{b}$, the mass concentration of solid particles in the mixture μ_p, the ratio of the density of solid particles to the initial density of the gas G_a and the gravitational parameter G₀ are obtained. It is shown that due to an increase in the gravitational parameter the compressibility of the medium at any point in the flow field behind the shock front decrease and the flow variables velocity, pressure, radiation flux and shock strength are increased. Also, an increase in the ratio of the density of solid particles to the initial density of the gas G_a and the gravitational parameter G₀ has the same effect on the shock strength and the reverse effect on the compressibility. The non-idealness of the gas causes a decrease in the shock strength and widens the disturbed region between the piston and the shock.     

Propagation of shock waves in a dusty gas with exponentially varying density

The variation of flow-variables with distance, in the flow-field behind a shock wave propagating in a dusty gas with exponentially varying density, are obtained at different times. The equilibrium flow conditions are assumed to be maintained, and the results are compared with those obtained for a perfect gas. It is found that the presence of small solid particles in the medium has significant effects on the variation of density and pressure. Received 20 October 1999 and Received in final form 9 March 2000     

Nonlinear electrostatic waves in inhomogeneous dense dusty magnetoplasmas

The nonlinear electrostatic drift waves are studied using quantum hydrodynamic model in dusty quantum magnetoplasmas. The dissipative effects due to collisions between ions and dust particles have also been taken into account. The Korteweg-de Vries Burgers (KdVB) like equation is derived and analytical solution is obtained using tanh method. The limiting cases of KdV type solitary waves, Burger type monotonic shock waves and oscillatory shock solutions are also presented. It is found that both hump and dip type solitary structures are possible in quantum dusty plasmas. However, amplitude and width of the nonlinear structure depend on the dust charge polarity and its concentration in electron-ion quantum plasmas. The monotonic shock like structure is independent of the quantum parameter. It is found that shock strength is increased in the presence of positively charged particles in comparison with negatively charged dust particles. The oscillatory shock structures are also obtained and it is found that change in dust charge polarity only shifts the phase of the oscillatory shock in plasmas. The numerical results are also presented for illustration.     

Shock wave propagation in perfectly conducting rotational axisymmetric two-phase medium with increasing energy under the action of heat conduction and radiation heat flux

The distribution of divergent cylindrical shock waves, under the effect of the variable azimuthal or axial magnetic field in space, in a perfectly conducting rotational axisymmetric dusty gas is studied. The profiles of the fluid variables were determined using numerical estimation. The effects of changing the piston velocity index, rotational parameter, and Shock Cowling number are studied. The result is that pressure and density disappear in the piston, and then the vacuum is produced at the axis of symmetry, which is perfectly in conformity with the conditions for producing a shock wave in the laboratory when the azimuthal magnetic field is present.     

Acoustic emission monitoring during laser shock cleaning of silicon wafers

A laser shock cleaning is a new dry cleaning methodology for the effective removal of submicron sized particles from solid surfaces. This technique uses a plasma shock wave produced by laser-induced air breakdown, which has applied to remove nano-scale silica particles from silicon wafer surfaces in this work. In order to characterize the laser shock cleaning process, acoustic waves generated during the shock process are measured in real time by a wide-band microphone and analyzed in the change of process parameters such as laser power density and gas species. It was found that the acoustic intensity is closely correlated with the shock wave intensity. From acoustic analysis, it is seen that acoustic intensity became stronger as incident laser power density increased. In addition, Ar gas has been found to be more effective to enhance the acoustic intensity, which allows higher cleaning performance compared with air or N₂ gas.     

Acceleration Field of a Universe Modeled as a Mixture of Scalar and Matter Fields

A model of the Universe as a mixture of a scalar (inflaton or rolling tachyon from the string theory) and a matter field (classical particles) is analyzed. The particles are created at the expense of the gravitational energy through an irreversible process whereas the scalar field is supposed to interact only with itself and to be minimally coupled with the gravitational field. The irreversible processes of particle creation are related to the non-equilibrium pressure within the framework of the extended (causal or second-order) thermodynamic theory. The scalar field (inflaton or tachyon) is described by an exponential potential density added by a parameter which represents its asymptotic value and can be interpreted as the vacuum energy. This model can simulate three phases of the acceleration field of the Universe, namely, (a) an inflationary epoch with a positive acceleration followed by a decrease of the acceleration field towards zero, (b) a past decelerated period where the acceleration field decreases to a maximum negative value followed by an increase towards zero, and (c) a present accelerated epoch. For the energy densities there exist also three distinct epochs which begin with a scalar field dominated period followed by a matter field dominated epoch and coming back to a scalar field dominated phase.     

Density perturbations in a flat universe

A well-known solution, for a flat model in general relativity obeying the Robertson-Walker metric, a perfect fluid energy-tensor and a perfect gas law of state, with constant deceleration parameter, is now shown to yield growing scalar density perturbations, provided thatq > 0. This study generalizes Weinberg's results for the radiation phase, and shows that any realistic model of this kind contains gravitational instabilities     

Dust acoustic solitary and shock waves in strongly coupled dusty plasmas with nonthermal ions

The Korteweg-de Vries-Burgers (KdV-Burgers) equation and modified Korteweg-de Vries-Burgers equation are derived in strongly coupled dusty plasmas containing nonthermal ions and Boltzmann distributed electrons. It is found that solitary waves and shock waves can be produced in this medium. The effects of important parameters such as ion nonthermal parameter, temperature, density and velocity on the properties of shock waves and solitary waves are discussed.     

Effect of impact breakup of solid and liquid particles on two-phase supersonic flow about solids

Experimental modeling of processes occurring when a supersonic gaseous suspension containing solid or liquid particles flows about a freely flying body is carried out. Considered is the situation when the particles reach the surface of the body intact and are not entrained by the flow. It is found that, after the particles break into pieces and disperse, exchange between the phases intensifies, causing a change in the position of the bow shock wave and the formation of a layer with an increased concentration of the particles. Collisions of solid and liquid particles with the solid surface are modeled. The observation of the particle dispersion pattern after impact breakup and measurement of the particle velocity shed light upon a mechanism behind the formation and movement of a finely dispersed particle cloud that arises when initial particles experience impact breakup. It is found that the postcollision dispersion of the particles generates two shock waves originating from the interaction zone.     

Effect of solid dust particles on the propagation of shock wave in planar and non-planar gasdynamics

The aim of the present study is to analyze the propagation of shock wave along the characteristic path in planar and non-planar unsteady compressible ideal gas flow in presence of small solid dust particles. The analytical solution of the governing quasilinear hyperbolic system is computed in the characteristic plane and it is found that this analytical linear solution in this plane can exhibit non-linear phenomenon in the physical plane. The effect of the dust particles on the evolutionary behavior of the propagating shock wave in ideal gas flow is discussed. The transport equations leading to the evolution of shock wave is determined which introduces the conditions of shock formation. The growth and decay of compressive waves and expansive waves, respectively, in planar and non-planar ideal gas dynamics influenced by the presence of small solid dust particles, is discussed.     

Jeans stability of dusty space plasmas

The Jeans stability of dusty plasmas is re-considered. In contrast to a gas, a dusty plasma can support a plethora of wave modes each potentially able to impart to the dust particles the randomising energy necessary to avoid Jeans collapse on some length scale. Consequently, the analysis of the stability to Jeans collapse is many-fold more complex in a dusty plasma than it is for a charge-neutral gas. After recalling some of the fundamental ideas related to the ordinary Jeans instability in neutral gases, we extend the discussion to plasmas containing charged dust grains. Besides the usual Jeans criterion based upon thermal agitation, we consider two other ways of countering the gravitational collapse: (i) via the excitation of dust-acoustic modes and (ii) via a novel Alfvén-Jeans instability, where perturbations of the dust mass-loaded magnetic field counter the effects of self-gravitation. These two mechanisms yield different minimum threshold length scales for the onset of instability/condensation. It is pointed out that for the study of the Jeans instability produced by density enhancements induced in the plasma by the presence of normal wave modes, even more prohibitive plasma size constraints must necessarily be satisfied.     

Dynamics of Macroparticles in a Quasi-Two-Dimensional Dust–Plasma System under Directed External Action: Simulation Results

The action of the light pressure force on a bounded region of a 2D system of dust macroparticles is simulated using the molecular dynamics method. The dynamics of dust macroparticles in the quasi-2D structure (trajectories of particles, their mean square displacement, and kinetic energy) is analyzed for various values of the nonideality parameter and laser radiation power. It is shown that by varying the radiation power, it is possible to influence the self-diffusion processes and the value of chaotic velocity of particles. Analysis is performed for different initial values of the nonideality parameter of the unperturbed dust subsystem. It is found that the interparticle interaction results in an increase in the kinetic energy of particles in the region of action, as well as beyond it.     

Effect of viscosity on dust–ion acoustic shock wave in dusty plasma with negative ions

The properties of dust–ion acoustic (DIA) shock wave in a dusty plasma containing positive and negative ions is investigated. The reductive perturbation method has been used to derive the Korteweg–de Vries–Burgers equation for dust acoustic shock waves in a homogeneous, unmagnetized and collisionless plasma whose constituents are Boltzmann distributed electrons, singly charged positive ions, singly charged negative ions and cold static dust particles. The KdV–Burgers equation is derived and its stationary analytical solution is numerically analyzed where the effect of viscosity on the DIA shock wave propagation is taken into account. It is found that the viscosity in the dusty plasma plays as a key role in dissipation for the propagation of DIA shock.     

含尘气体Rayleigh-Taylor不稳定性诱导混合的多相浮阻力模型研究

文章首先采用单相浮阻力模型对不同加速度下Rayleigh-Taylor不稳定性诱发的物质渗透边界的演化过程进行了计算, 揭示了该混合在常加速度和变加速度情况下不同的发展规律, 并通过与实验结果的比较分析, 验证了该模型的适用性.在此基础上, 发展了多相浮阻力模型, 采用该模型对常加速度情况下含尘气体中的Rayleigh-Taylor不稳定性诱导混合进行了研究, 发现混合区宽度随着颗粒数密度和颗粒尺寸的增大而减小, 揭示了气体中所含杂质抑制混合发展的规律.      

Dust ion-acoustic shock waves due to dust charge fluctuation in a superthermal dusty plasma

The nonlinear propagation of dust ion-acoustic (DIA) shock waves is studied in a charge varying dusty plasma with electrons having kappa velocity distribution. We use hot ions with equilibrium streaming speed and a fast superthermal electron charging current derived from orbit limited motion (OLM) theory. It is found that the presence of superthermal electrons does not only significantly modify the basic properties of shock waves, but also causes the existence of shock profile with only positive potential in such plasma with parameter ranges corresponding to Saturn?s rings. It is also shown that the strength and steepness of the shock waves decrease with increase of the size of dust grains and ion temperature.     

Effects of double spectral electron distribution and polarization force on dust acoustic waves in a negative dusty plasma

The nonlinear features of dust acoustic waves (DAWs) propagating in a multicomponent dusty plasma with negative dust grains, Maxwellian ions, and double spectral electron distribution (DSED) are investigated. A Korteweg de Vries Burgers equation (KdVB) is derived in the presence of the polarization force using the reductive perturbation technique (RPT). In the absence of the dissipation effect, the bifurcation analysis is introduced and various types of solutions are obtained. One of these solutions is the rarefactive solitary wave solution. Additionally, in the presence of the dissipation effects, the tanh method is employed to find out the solution of KdVB equation. Both of the monotonic and the oscillatory shock structures are numerically investigated. It is found that the correlation between dissipation and dispersion terms participates strongly in creating the dust acoustic shock wave. The limit of the DSED to the Maxwell distribution is examined. The distortional effects in the profile of the shock wave that result by increasing the values of the flatness parameter, r, and the tail parameter, q, are investigated. In addition, it has been shown that the proportional increase in the value of the polarization parameter R enhances in both of the strength of the monotonic shock wave and the amplitude of the oscillatory shock wave. The effectiveness of non-Maxwellian distributions, like DSED, in several of plasma situations is discussed as well.     

Plane symmetric self-gravitating fluids with pressure equal to energy density

Solutions of the Cauchy problem associated with the Einstein field equations which satisfy general initial conditions are obtained under the assumptions that (1) the source of the gravitational field is a perfect fluid with pressure,p, equal to energy density,w, and (2) the space-time admits the three parameter group of motions of the Euclidean plane, that is, the space-time is plane symmetric. The results apply to the situation where the source of the gravitational field is a massless scalar field since such a source has the same stress-energy tensor as an irrotational fluid withp=w. The relation between characteristic coordinates and comoving ones is discussed and used to interpret a number of special solutions. A solution involving a shock wave is discussed.     

Free convection effects and radiative heat transfer in MHD Stokes problem for the flow of dusty conducting fluid through porous medium

The present note deals with the effects of radiative heat transfer and free convection in MHD for a flow of an electrically conducting, incompressible, dusty viscous fluid past an impulsively started vertical non-conducting plate, under the influence of transversely applied magnetic field. The heat due to viscous dissipation and induced magnetic field is assumed to be negligible. The governing linear partial differential equations are solved by finite difference technique. The effects of various parameters (like radiation parameter N, Prandtl number Pr, porosity parameter K) entering into the MHD Stokes problem for flow of dusty conducting fluid have been examined on the temperature field and velocity profile for both the dusty fluid and dust particles.