Force Action of a Body with a Permeable Boundary on a Wall in a Fluid

The ideal fluid flow due to fluid penetration through the boundary of an infinitely long solid cylinder in contact with a solid wall is determined. A formula is derived according to which the force exerted by a finite-length part of the cylinder on the wall is directed into the wall and can thus have an arbitrarily large absolute value. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 82–84, January–February, 2006.     

On a Paradox in the Motion of a Rigid Particle along a Wall in a Fluid

The results of an experimental investigation of spherical particles with different surface roughnesses rolling under their own weight down an inclined pipe wall in a Newtonian fluid at low Reynolds numbers, both with (friction should be taken into account) and without contact with the wall, are presented. It is shown that a fixed particle moves differently in different fluids with similar viscosities and densities. This fact, as well as the possibility of particle motion without contact with the wall, cannot be explained within the framework of the usual hydrodynamic theories. An example is the dependence of the particle motion on the static pressure.     

Torsion problems for a cylinder with a rectangular hole and a rectangular cylinder with a crack

Using the method of singular integral equation and the crack-cutting technique, the rigorous solutions are obtained for a cylinder with a rectangular hole and a rectangular cylinder with a crack, which exactly satisfy the boundary conditions and the conditions at the corner points. After that the torsional rigidities and the stress intensity factors at the crack tip are determined. Next, for the doubly connected circular cylinder with a rectangular hole the expressions for the singular stresses around the concave corner points are derived and the generalized stress intensity factors are then defined. Since the crack-cutting technique is used in this paper, the solution of the matching rectangular cylinder is also obtained and its numerical results coincide with those in references. Thus the method proposed here is verified. The project supported by National Natural Science Foundation of China     

Pumping of a fluid through a microchannel by means of a bubble driven by a light beam

A new method of pumping a fluid through a microchannel device using a gas bubble-piston, set in motion by the thermocapillary force induced by a light beam, is proposed. To demonstrate the method, a model micropump has been assembled. The model consists of two reservoirs connected by two channels with a bubble-piston driven by a light beam. The pumping rate and the volume per piston stroke are evaluated experimentally. The method proposed is compared with known microfluid pumping methods. Some advantages of the new method are indicated.     

Interaction of a screw dislocation with a notch in a piezoelectric bi-material

Summary The electro-elastic interaction of a screw dislocation and a notch in a piezoelectric bi-material is analyzed. The electro-elastic fields induced by the dislocation are derived using the conformal mapping and the image-dislocation approach, where the solution for a piezoelectric bi-material without a notch is used as a base. The stress and the electric displacement intensity factors of the notch and the image force on the dislocation are given explicitly. We find that intensity factors are expressed in terms of the effective material constants, while the radial component of the image force is independent of the notch angle and the angular position of the dislocation in the polar coordinate system. Numerical results for the image force are provided for the use when one of the two media is purely elastic. They illustrate the behavior of the dislocation in the neighborhood of the notch.     

Transformation of a breaking wave at a drop of a channel bottom

This paper gives results of an experimental study of incident and reflected waves of the bore type in the neighborhood of a sharp change in the channel bed level. It is shown that under conditions typical of accidents at ship locks, the wave height can reach 8 m.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 115–121, March–April, 2005.     

Repair of a Plate with a Circular Hole by Applying a Patch

The stressed state of a thin elastic infinite plate with a circular hole covered by a circular patch of a greater radius is considered. The center of the hole coincides with the center of the patch. The patch is attached to the plate along its entire boundary. Stresses are prescribed at infinity on the plate and at the hole boundary. Complex Muskhelishvili potentials are found by the method of power series, and the behavior of stresses on the patch–plate interface and at the hole boundary is studied.     

Simulation by a source of a thin jet from a body

An exact analytic solution is found to the following plane hydrodynamic problem. An unbounded flow of an ideal incompressible fluid flows around a plate BB' placed at right angles to the velocity vector of the flow at infinity. The pressure on the free boundary P is equal to the pressure in the flow. From an opening in the center of the plate, a jet with flow rate Q from a cavity with pressure P₀ encounters the flow head-on. As a result of the solution, it is found that for fixed width of the opening the values of Q allowed by the scheme are limited. In the limiting case Q = 0 Chaplygin's flow is obtained with stagnation region at the front [1], and in the limiting case Q = Q_max a jet out of a cavity with pressure P₀ into a cavity with pressure P. As Q varies in this interval, the total drag, regarded as the drag of the plate and the chamber from which the jet emerges, takes a minimal value at a certain point. If the width of the opening tends to the length of the slab, the problem of the collision of two jets is obtained; if the width of the opening tends to zero (Q o), the problem of jet flow past a slab with a source is obtained. It is shown that the replacement of the jet by the source gives a good approximation in both the sense of the force characteristics and in the sense of the behavior of the free streamlines.Translated from Izvestiya Akademii Nauk SSSR, Hekhanika Shidkosti i Gaza, No. 5, pp. 47–54, September–October, 1979.We thank L. I. Sedov for his interest in the work and G. Yu. Stepanov for proposing the method of solution and for a helpful discussion.     

Diffusive shrinkage of a void within a grian of a stressed polycrystal

A method to predict the shrinkage rate of a void centered at an equiaxial grain under hydrostatic pressure is developed. The rate process is controlled by lattice diffusion under the combined influence of void surface energy, grain boundary interface energy and elastic energy stored in the solid. A dimensionless loading parameter that controls the void evolving is introduced. Below a certain value of this parameter the void will be rounded and is stable. Then the shrinkage behavior of the voids is described by the parameters controlling the lattice diffusion. It is found that only gas-free voids could be totally eliminated through lattice diffusion; for a gas-filled void, the internal pressure produced by the gas firstly retards the rate of the shrinkage and eventually stops the shrinkage process as it becomes high enough.     

Growth of a new phase in a substance in a metastable state

A model of kinetics of phase transitions in a substance in a metastable state is proposed, where the probability of extensive nucleation owing to homogeneous mechanisms is rather large; the model is an alternative to Kolmogorov’s model. The use of this model is demonstrated to offer analytical solutions that describe both the crystallization processes with similar densities of the liquid and solid phases and, for instance, the kinetics of nucleation and growth of bubbles in surface boiling. Solutions obtained by Kolmogorov’s model and by the present model coincide at the initial stage of the process where the volume fraction of the new phase is small. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 75–80, March–April, 2007.     

Dynamics of a vapor shell around a heated particle in a liquid

The dynamics and heat and mass exchange of a vapor bubble containing a heated particle is studied in relation to the problem of vapor explosions. It is shown that the process involves two stages: dynamic stage and thermal stage. The dynamic stage is characterized by pressure fluctuations and a rapid increase in the thickness of the vapor layer. It is shown that the simplifying assumptions of the constancy of assumptions of constant heat conductivity of the vapor and linear temperature profile in the vapor layer lead to qualitatively incorrect results. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 69–78, July–August, 2007     

Unsteady-state filtration of a liquid in a fractured-porous stratum to a well with a hemispherical end-face

A study is made of the motion of a liquid toward a well with a hemispherical end-face with unsteady-state spherical-radial filtration in a fractured-porous stratum consisting of hemispherical regions with different values of the permeability of the system of cracks, superposed one on another. A Laplace transform is used to find exact solutions to the problem of the lowering of the stratum pressure as a function of time and distance as well as of the output of a well working with a constant end-face pressure. The article discusses partial cases corresponding to the exploitation of closed and bounded open fractured-porous strata by a central well with a hemispherical end-face. On the basis of numerical calculations, the effect of the parameters of fractured-porous strata on the change in the indices of the process of their exploitation is established. It is established that, with the exploitation of fractured-porous strata, the process of the lowering of the end-face pressure of the well and its output become stabilized with sufficiently large values of the time.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 115–123, November–December, 1973.     

Interaction of a cylinder with a free surface and a jet

The problem of the asymmetric flow around a cylinder of a nonviscous jet is considered and, in particular, of flow with one free boundary. The problem of the choice of circulation is posed, based on a generalization of the Zhukovskii-Chaplygin postulate. Several possibilities are considered and the principle of the minimum of the maximum velocity on a contour is proposed, which qualitatively and quantitatively truly reflects certain aspects of the interaction of the cylinder with the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 50–58, September–October, 1977.     

Squeezing a viscoelastic fluid from a cone

The paper reports an exact kinematics for the squeezing flow from a cone of a general viscoelastic fluid. To obtain numerical values for the stresses, a network model that allows stress overshoot and shear-thinning in the start-up of a shear flow is adopted. Both these features are important in this flow. For the special case of an Oldroyd-B fluid it is shown that there is a limiting Weissenberg number above which at least one component of the stresses increases unboundedly with time.     

Interaction of a rigid punch and a circular plate with a fixed side and a stress-free face

The axisymmetric contact problem of a rigid punch indentation into an elastic circular plate with a fixed side and a stress-free face is considered. The problem is solved by a method developed for finite bodies which is based on the properties of a biorthogonal system of vector functions. The problem is reduced to a Volterra integral equation (IE) of the first kind for the contract pressure function and to a system of two Volterra IE of the first kind for functions describing the derivative of the displacement of the plate upper surface outside the punch and the normal (or tangential) stress on the plate lower fixed surface. The last two functions are sought as the sum of a trigonometric series and a power-law function with a root singularity. The obtained ill-conditioned systems of linear algebraic equations are regularized by introducing small parameters and have a stable solution. A method for solving the Volterra IE is given. The contact pressure functions, the normal and tangential stresses on the plate fixed surface, and the dimensionless indentation force are found. Several examples of a plane punch computation are given.