Contact line moving on a solid

The moving contact line problem can be summarized as follows: consider the triple line where a solid, a liquid and its vapor meet. This contact line may be the perimeter of a liquid droplet standing on a solid. Suppose now that, because of gravity for instance, the droplet and so its perimeter slides on the solid surface. The boundary conditions for viscous fluids impose that the flow velocity on an immobile solid is zero. If one assumes that the liquid/vapor surface is a material surface, i.e. that it is convected by the fluid, the contact line cannot move with respect to the solid, contrary to what is observed. Over the years many suggestions have been made to solve this problem. I show that solutions relying on the introduction of microscopic length scales are not consistent within the general framework of continuum mechanics. To get consistent solutions, one needs to introduce evaporation/condensation near the moving line, in agreement with experimental findings.     

Dynamic response of a poroelastic stratum to moving oscillating load

The dynamic response of a poroelastic stratum subjected to moving load is studied. The governing dynamic equations for poroelastic medium are solved by using Fourier transform. The general solutions for the stresses and displacements in the transformed domain are established. Based on the general solutions, with the consideration of boundary conditions, the final expressions of stresses and displacements in physical domain are put forward for the three-dimensional single-layer medium. Some numerical solutions for the stresses, displacements and pore fluid pressure are presented and reveal that the response of a poroelastic stratum varies obviously with the moving velocity.     

Flow and heat transfer of a hybrid nanofluid past a permeable moving surface

A steady flow and heat transfer of a hybrid nanofluid past a permeable moving surface is investigated. In this study, 0.1 solid volume fraction of alumina (Al₂O₃) is fixed, then consequently, various solid volume fractions of copper (Cu) are added into the mixture with water as the base fluid to form Cu-Al₂O₃/water hybrid nanofluid. The similarity equations are obtained by converting the governing equations of the hybrid nanofluid using the technique of similarity transformation. The bvp4c function available in Matlab software is used to solve the similarity equations numerically. The numerical results are obtained for selected parameters and discussed in detail. It is found that hybrid nanofluid enhances the heat transfer rate compared to the regular nanofluid. The results show that two solutions exist up to a certain value of the moving parameter and suction strengths. The critical value in which the solution is in existence decreases as nanoparticle volume fractions increase. The temporal stability analysis is conducted in determining the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.     

Interaction of a moving domain wall with surface magnetoelastic waves in yttrium orthoferrite

The amplitude-frequency characteristics of magnetoelastic surface waves excited by moving domain walls in a lamellar yttrium orthoferrite samples are discovered and measured. The results of analysis of the effect of magnetoelastic surface waves on the dynamics of domain walls in this orthoferrite are considered. The nonlinear interaction between magnetoelastic surface waves accompanying a moving domain wall is analyzed.     

Fluctuation-induced electromagnetic interaction of a moving particle with a plane surface

The most general (nonrelativistic) formulas for the force of attraction to the surface and for the drag of a nonrelativistic atom moving parallel to it, as well as for the lateral and normal forces acting on a moving dipole molecule and on a charged particle (in the case of parallel and perpendicular motion), are derived for the first time in the framework of the fluctuational electromagnetic theory. The dependences of these forces on the velocity, temperature, separation, and dielectric properties of the atom and the surface are derived. The effect of the nondissipative resonance interaction between a moving neutral atom and the field of surface plasmons, as well as the possible emergence of a positive (accelerating) force acting on the atom (nanoprobe), is substantiated theoretically. The role of dynamic fluctuational forces and their possible experimental measurement when using the quartz microbalance technique and an atomic-force microscope (in the dynamic mode), as well as during deceleration of atomic beams in open nanotubes, are considered. The correctness of the obtained results is confirmed by their agreement with most of the available theoretical relations derived by other authors.     

Application of surface and normal ultrasonic waves for measuring the parameters of technical fluids: II. Density measurements

The effect of a fluid on the surface waves moving in a waveguide along its boundary with the fluid is considered. The effect of the shear and volume viscosities of the fluid on the damping coefficient of such a surface wave is estimated. It is shown that the effect of fluids may be neglected at a measurement accuracy of about 10^?3 if their shear viscosities are lower than 0.1 Pa s. At a higher viscosity, corrections that take into account the contribution of viscous losses to the measured damping coefficient of a surface wave should be introduced. A technique for calibrating a density sensor for low-viscosity fluids is described, and the densities of NaCl and saccharose solutions in distilled water are measured. The experimental results agree qualitatively with the theoretical estimates. It is noted that this method of measuring the longitudinal impedance of a fluid can use the same apparatus design in both the principle (pulsed) and the frequency range (1?C10 MHz) for measuring the density, both viscosities, the velocity, and the sound absorption coefficient of a fluid. This design almost coincides with the apparatus used in the means of nondestructive quality control of materials and articles.     

Rheological flow from a die and painting on a moving solid wall

1IntroductionThemanufacturesoffluidfilmandpolymerrequireanunderstandingofthehydrodynamicprocess[1,2].Theenlargedcross-sectionofthefluidjetwasobservedinthepolymerprocessing,wherethedieswellisanimportantphenomenon.TheSwellorDieSwelleffectisexplainedusuallybyrheologicalpropertiesoftheliquidmedium.TannersuggestedatheoryofDie-Swell,andassumedthatthevelocityvectorhasonlyonecomponentalongthejet[3].Becauseofthenon-uniformityofthecross-section,theflowfieldintheDie-Swelltheoryshouldbeatleasttwo-dime…     

On the stability of the flow and heat transfer over a moving thin needle with prescribed surface heat flux

The steady flow and heat transfer over a moving thin needle with prescribed surface heat flux is studied. The similarity equations are obtained by using similarity transformation technique. The problem is solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The plots of the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are presented and their behaviors are discussed for different values of the needle size and the velocity ratio parameter. Results show that the decreasing of the needle size enhance the skin friction coefficient and the local Nusselt number on the needle surface. It is found that dual solutions exist (upper and lower branches) for a certain range of the velocity ratio parameter. A stability analysis of the solutions are performed and it shows that the upper branch solution is stable, while the lower branch solution is unstable.     

Numerical investigation of a coupled moving boundary model of radial flow in low-permeable stress-sensitive reservoir with threshold pressure gradient

The threshold pressure gradient and formation stress-sensitive effect as the two prominent physical phenomena in the development of a low-permeable reservoir are both considered here for building a new coupled moving boundary model of radial flow in porous medium. Moreover, the wellbore storage and skin effect are both incorporated into the inner boundary conditions in the model. It is known that the new coupled moving boundary model has strong nonlinearity. A coordinate transformation based fully implicit finite difference method is adopted to obtain its numerical solutions. The involved coordinate transformation can equivalently transform the dynamic flow region for the moving boundary model into a fixed region as a unit circle, which is very convenient for the model computation by the finite difference method on fixed spatial grids. By comparing the numerical solution obtained from other different numerical method in the existing literature, its validity can be verified. Eventually, the effects of permeability modulus, threshold pressure gradient, wellbore storage coefficient, and skin factor on the transient wellbore pressure, the derivative, and the formation pressure distribution are analyzed respectively.     

电磁波在运动介质中及表面处的传播特性

论述了运动介质对电磁波频率、速度和传播方向的影响及在运动介质表面的反射定律和折射定律。     

Effect of metallic surface microroughness on the probability and spectrum of plasmon excitation by a fast charged particle moving parallel to the surface

The Green’s function of the electric field of plasmons is determined in a semi-infinite medium with an abrupt plasma boundary where nonequilibrium conduction electrons either undergo elastic reflection from the boundary or “stick” to it and give rise to a stationary surface charge. The angular reflection of elastically scattered electrons can be either specular or diffuse. The Green’s function is used to find the singleevent spectrum of energy loss by a fast electron moving parallel to the boundary. The effect of electronboundary scattering parameters on the structure of bulk and surface plasmon resonances is analyzed. The probability of transition radiation of bulk plasmon by an electron moving in vacuum is examined. A new type of surface resonance is found under conditions of perfectly elastic scattering of conduction electrons from the plasma boundary, similar in structure to a tangential surface plasmon.     

Generation of surface plasmons in a conductor by moving charges

The surface polarization fields generated by a charge moving near a sphere or cylinder have been considered. This problem is related to the phenomena arising in an arc discharge in a gas near a solid surface during the formation of conducting cylindrical or spherical nanostructures, in particular, carbon nanotubes or fullerenes. The polarization fields, forces, energy losses, and other characteristics have been calculated.     

On acoustic radiation by a rigid object in a fluid flow

A problem of sound radiation by an absolutely rigid object, moving with respect to the surrounding fluid, is considered on the basis of the Lighthill's equation for aerodynamic sound. An integral representation of the radiated acoustic field is utilized, where the field is characterized as the sum of three fields, generated by a volume distribution of monopoles and by distributions of monopoles and dipoles on the surface of the rigid object. It is shown that, due to a discontinuity of Lighthill's stress tensor on the rigid boundary, a layer of surface divergence of hydrodynamic stresses on the boundary must be taken into account when evaluating the volume integral over Lighthill's quadrupole sources. When the contribution of the surface divergence is included in the solution of Lighthill's equation, amplitudes of the monopole and dipole sound radiated by the rigid object are shown to depend on the potential components of the normal velocity and the pressure on the rigid surface. The obtained solution is compared with Curle's solution for this problem, which establishes that the sound radiation by a rigid object is determined by the force exerted by the object upon the fluid. Both solutions are applied to two known problems of sound scattering and radiation by a rigid sphere in variable pressure and velocity fields. It is shown that predictions based on the obtained solution are equivalent to the results known from literature, whereas Curle's solution gives predictions contradicting the known results. It is also shown that the Ffowcs Williams and Hawkings equation, which coincides with Curle's equation for an immoveable rigid object, does not lead to the correct predictions as well.     

Cohesive solutions of intersonic moving dislocations

A class of cohesive solutions of moving glide dislocations with intersonic speeds has been derived on the basis of the fundamental equation of a moving dislocation introduced by Weertman in conjunction with a proposed generalized Bilby–Cottrell–Swinden–Dugdale model. In this model we assume a straight weak path within an infinite elastic plate. Two length scales, namely the width (thickness) of the weak path and the material intrinsic length, which scales strain-gradient-induced hardening and energy dissipation, are taken into account by applying the traction–separation law for the decohesion of the weak path. Dislocations propagate along this weak path with a speed higher than the shear wave speed. The accumulation of these moving dislocations forms a macroscale crack growth with a cohesive zone ahead of the crack tip. Similar to the Bilby–Cottrell–Swinden–Dugdale model, the remote enforced stress and/or stress-rate boundary conditions are represented as an equivalent crack surface traction associated with the dislocation distribution. The involved Cauchy integral and corresponding eigenvalue problem are solved using the algorithms introduced by Muskhelishvili and by Weertman. The problems associated with three types of decohesion law are constant traction, traction linearly dependent on separation, and separation- and separation-rate-dependent traction. These problems are solved using three different solution strategies: the direct-integration method, the iteration method and the Jacobi polynomial expansion respectively. The derived solutions provide explicit relations between the remote load propagation speed, the material intrinsic length, the weak path thickness and the strain-rate-hardening parameter. The solutions demonstrate that the intersonic speed region can be divided into two subdomains; steady-state propagation occurs within the subdomain where the propagation speeds are equal to or greater than the Eshelby speed (c _s × 2^1/2, where c _s is the shear wave speed). For a weak path with a finite width and the corresponding decohesion law scaled by material intrinsic length, an intersonic crack propagation will not take place if only a constant remote stress is imposed. A ‘steady-state’ crack surface load and/or remote stress-rate boundary condition, which can be considered as a point force or a distributed force with a constant distance to the moving crack tip, is required to maintain steady-state intersonic crack propagation.     

Fluctuation-electromagnetic interaction of a moving neutral particle with a condensed-medium surface: relativistic approach

A relativistic theory of the fluctuation-electromagnetic interaction of a moving small particle with a flat boundary of a homogeneous isotropic polarizable medium is presented for the first time with a maximum degree of completeness. The theory is based on the dipole approximation of fluctuation-electromagnetic theory. Fundamental relativistic expressions are derived for conservative and dissipative forces and heating power of a particle. These expressions reduce to earlier nonrelativistic results in particular cases. The results obtained in other approaches and experimental studies of fluctuation-electromagnetic interactions are critically analyzed.     

Two methods to solve a fractional single phase moving boundary problem

A moving boundary problem of a melting problem is considered in this study. A mathematical model using the Caputo fractional derivative heat equation is proposed in the paper. Since moving boundary problems are difficult to solve for the exact solution, two methods are presented to approximate the evolution of the temperature. To simplify the computation, a similarity variable is adopted in order to reduce the partial differential equations to ordinary ones.     

Metal surface temperature induced by moving laser beams

Whenever a metal is irradiated with a laser beam, electromagnetic energy is transformed into heat in a thin surface layer. The maximum surface temperature is the most important quantity which determines the processing result. Expressions for this maximum temperature are provided by the literature for stationary cases. In practice, however, moving beams are of more importance.Based on a fast numerical algorithm which allows calculation of the induced temperature profile, the maximum surface temperature for stationary and moving laser beams is calculated. Next, two types of approximating functions are presented relating the scanning speed to the maximum surface temperature. Using dimensionless numbers, the results can be applied to different materials.     

The nuclear surface as a collective variable

In heavy nuclei where the thickness of the diffused edge is relatively small, a certain sharp effective surface can be defined which characterizes the shape of the nucleus, and it can be considered as a collective dynamic variable. It is shown that the problem of fluid dynamics can be simplified by reducing it to simple linearized equations for the dynamics in the nuclear interior and boundary conditions set at the effective dynamic sharp surface of the density distribution. These conditions are derived from the fluid dynamical equations. Transitional densities obtained from this simple model are compared with the numerical solution of fluid dynamical equations.     

MHD mixed convection flow near the stagnation-point on a vertical permeable surface

The steady magnetohydrodynamic (MHD) mixed convection boundary layer flow of a viscous and electrically conducting fluid near the stagnation-point on a vertical permeable surface is investigated in this study. The velocity of the external flow and the temperature of the plate surface are assumed to vary linearly with the distance from the stagnation-point. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions exist for both cases, and the range of the mixed convection parameter for which the solution exists increases with suction.