Dispersion of a solute in a Poiseuille flow of a viscoelastic fluid

Gill and Sankarasubramanian's analysis of the dispersion of Newtonian fluids in laminar flow between two parallel walls is extended to the flow of non-Newtonian viscoelastic fluids (known as Phan-Thein-Tanner (PTT)). Using a generalized dispersion model which is valid for all times after the solute injection, the diffusion coefficient K_i(t) is obtained exactly and numerically for linearized and exponential forms of the PTT fluids, respectively. The analysis leads to the novel result for K₁ and K₂(t) (which is a measure of the longitudinal dispersion coefficient of the solute). It is found that the value of K₂(t) depends on the value of Deborah number (De=a measure of the level of elasticity in the fluid) whereas the value of K₁ is constant in both cases. Finally, the effect of the Deborah number on the axial distribution of the mean concentration θ_m is investigated in detail.     

Analysis of a Premature Failure of a Hub from a Diesel Generator of a High-Speed Motor Ship

Failure analysis is carried out on a fractured hub obtained from a diesel generator of a high-speed motor ship. Macrofractography, microfractography, standard optical metallography, material characterization techniques, and numerical modeling were used to verify the findings of the current investigation. Cracking initiation is attributed to fretting fatigue caused by a modification performed in the vicinity of the fractured hub. Operational vibrations contributed to the propagation of the cracks as typical fatigue cracks until final fracture.     

Analysis of a crack at a weak interface

The problem of two elastic half-planes joined along the common part of their boundary by a cracked weak interface is considered. The central part of the joint is detached, while in the remaining part there is a continuous distribution of springs which assures continuity of stress which is proportional to the displacement gap. The adherents are homogeneous and isotropic, while the interface is allowed to be orthotropic with principal directions normal and tangential to the interface, respectively. The body is subjected to constant normal and tangential loads applied at infinity and at the crack faces. Using classical solutions for elastic half-planes as Green functions, the integral equation governing the problem is obtained and solved numerically. Attention is paid to the analysis of the solution around the crack tip, and an asymptotic estimate showing that the derivative of the solution is logarithmically unbounded is obtained analytically. Accordingly, it is shown that there may exist, at most, logarithmic stress singularities. It is further shown how, contrary to the case of perfect bonding, stress singularities are not related to the normal propagation of the crack, but possibly to the crack deviation. The crack propagation is analyzed by the energy Griffith criterion, and it is shown that some drawbacks of linear elastic fracture mechanics disappear in the case of weak interface.     

Heat Transfer of a Sphere in a Constrained Flow of a Viscous Fluid

Results of an experimental investigation of the average heat transfer of a sphere in the region of Reynolds numbers 0.1–40 are given. The increase in the Nusselt number with increase in the constraint parameter of flow is established. Based on the fractal theory, the influence of the degree of constraint on the heat transfer is physically explained and a quantitative correction is introduced.     

Resistance of a sphere in a slow flow of a viscoelastic fluid

The authors have obtained an approximate solution of the problem of the resistance of a rigid sphere in a slow flow of a Maxwell viscoelastic fluid that is in good agreement with experimental data [1] for Weissenberg numbers We ≤ 0.7. It is shown that the effect of a decrease in the coefficient of resistance of a sphere in the interval 0.1 ≤ We ≤ 0.7 established experimentally is determined in full measure by the linear viscoelastic properties of the Maxwell fluid. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 6, pp. 1138–1140, November–December, 1998.     

聚醚砜四元制膜液体系的相图计算

以Ｆｌｏｒｙ－Ｈｕｇｇｉｎｓ理论为基础，对ＰＥＳ－ＰＧ－ＮＭＰ＿Ｈ２Ｏ＿）聚醚砜丙二醇－Ｎ－甲基－２－哟咯烷酮水）四元制液体系的相图进行了计算，利用三元相图考察Ｈ２Ｏ和ＰＧ对液－液相分离的影响，在三元的理论的基础上提出了低分子量添加剂的卤元改性Ｆｌｏｒｙ－Ｈｕｇｇｉｎｓ理论，并提出了一种获得四元相图的方法，利用四元相图能较争地描述四元体系，利用改性的四元理论，能了地理解该种体系的液－液相分离行为。     

Stability of a column with a follower load and a load-dependent elastic support

Summary The influence of an elastic support on the stability of an elastic column under a follower load is investigated. The support is pinned and has a rotational spring whose stiffness is either constant or increases as the load is applied. Linear and quadratic stiffening functions are treated. An adjoint variational principle and a generalized Rayleigh-Ritz method are developed for this system. Characteristic curves are examined and the critical load, which is associated with flutter instability, is determined. The effects of the initial spring stiffness and the stiffening rate on the critical load are studied. It is found that an increase in either one of these parameters may lower the critical load, which is unexpected, and that support stiffening may have a significant influence on the vibrations and stability of a nonconservative system.     

Spinning of a liquid film from a rotating disc in the presence of a magnetic field — a numerical solution

Summary A numerical solution is obtained for the development of a conducting fluid film on the surface of a spinning disc, in the presence of a magnetic field applied perpendicular to the disc. A finite-difference method is employed to obtain the solution of Navier-Stokes equations modified to include magnetic forces due to MHD interactions. The combined effects of film inertia, acceleration of the disc and magnetic forces are analysed. The numerical results reveal that the rate of thinning of the fluid film is strongly influenced by the inertial and magnetic forces when the Reynolds number is large and that the existing asymptotic theory by Ray and Dandapat [24] is inadequate for predicting transient film thickness. When the disc has a finite acceleration at the start-up, the magnetic and inertia effects are important even at low Reynolds numbers and the thinning rate is reduced. It is observed that for both low and high Reynolds number flows, the film thickness increases with Hartmann numberM for a fixed time and the rate of depletion is less for largeM than for smallM.     

Motion of a rigid sphere in a shear field in a micropolar fluid

The motion of a rigid sphere, suspended in a micropolar fluid which is undergoing a shearing motion, is discussed. The expressions for the pressure, velocity and spin in the fluid and those for the force and torque on the sphere are obtained. A compromise boundary condition, relating the spin of the particle with the vorticity vector at the boundary, is employed. The results are compared with the classical values and apart from other interesting observations, it is noted that the torque on the sphere depends upon the various parameters in a complicated manner. By extending the definitions of the effective viscosity for the viscous fluids, an expression for the viscosity of the suspension in the micropolar fluid is derived.     

Longitudinal vibrations of a rod with a coating

A solution is obtained to the problem of the longitudinal vibration of a rod with a coating. The solution is obtained in a refined formulation. The same theoretical model is also used to find the solution for the case of static tension. An analysis is made of the way in which the properties of a deformable rod are affected by the stiffness of the shear constraints, which is regarded as a physicomechanical characteristic of the coating-substrate system. A method is proposed for experimental determination of stiffness for both static and cyclic loading conditions. All of the relations needed to analyze the stress-strain state are presented, including those required for fatigue tests in tension-compression.Translated from Problemy Prochnosti, No. 10, pp. 68–75, October, 1994.     

Complex gyrator circuit of a three-port circulator using a planar resonator composed of a gyromagnetic disk, a triplet of UEs and a triplet of single radial magnetic walls

A classic planar gyromagnetic resonator, encountered in the construction of three-port circulators, is one with top and bottom electric walls and a magnetic sidewall symmetrically loaded with a triplet of single magnetic walls. The main purpose is to experimentally characterise the complex gyrator circuit of a three-port junction using a resonator made up of a circular region, a triplet of single magnetic walls and a triplet of short 58 long UEs. It is compatible with the design of degree-2 circulators with commercial specifications and one experimental example is included for completeness sake. The effect of the UE embodied in the resonator under consideration is to decouple the coupling angle of the resonator terminals from any external microwave circuits, thereby facilitating the practical design of degree-2 circulators. A similar magnetised resonator loaded with a triplet of triple magnetic walls instead of single ones is also dealt with. It has the effect of reducing the spacing between the first three cut-off numbers of the isotropic geometry.     

Micromechanics of a Double Continuum in a Model of a Medium with Variable Periodic Structure

A new model of a double continuum with variable local topology is used to develop an essentially nonlinear theory of a medium with a cardinally rearranged periodic structure. This theory is based on a continualization of the periodic structure of a complex crystalline lattice consisting of two sublattices. In the long-wave approximation, the standard linear theory of acoustic and optic oscillations of the complex lattice is generalized. In this generalization, an internal translational symmetry of relative shear of the sublattices is taken into account. As a result, the interaction between the sublattices is expressed in terms of a nonlinear periodic force described, in particular, as a sine of the relative shear of two atoms belonging to an elementary cell. The corresponding equations describe elastic and inelastic catastrophic deformations due to the structural instability which accompanies phase transitions, twinning, defect formation, etc. Some static and dynamic problems are analyzed     

Reminiscence of a teacher and a researcher

Abstract

The names of previous after-dinner speakers at this conference read like a Who is Who of Quantum Optics and Photonics research. When the organizers of this conference asked me to present an after-dinner talk I felt honored by the invitation, but also humbled by joining such a distinguished company. This fact gives me a “Leitmotiv” for my present talk, because being humbled by, and feeling inferior to, all the brilliant minds one encounters in one's career is a necessary occurrence, which most of the younger listeners in this audience have either experienced or will experience. I have witnessed these feelings as advisor to students at MIT. Many of them fear that everything worth doing has already been done. There is a simple answer to this. Do not get discouraged, work harder and you will also make a respectable contribution to science or engineering.     

Stress analysis of a strip with a step and a crack

Stress analysis for a strip of which widths are different at the right and left handsides is carried out for before and after occurrence of a crack at a corner of a step. The strip is analyzed as a thin plate bending problem subject to transverse bending and torsion, and as a plane eleastic problem subject to bending in the plane and uniaxial tension. The rational mapping function of a sum of fractional expressions and complex variable method are used. Stress distribution and stress intensity factors are obtained.     

Interaction of a crack with a field of microcracks

Crack propagation in brittle materials is of ten accompanied by intensive microcracking; being a major energy sink,this phenomenon can strongly affect the fracture process. A two-dimensional problem of elastic interaction of a macrocrack with a field of microcracks is considered in the article. Consideration is based on the self-consistent method, generalized with the account of strong non — uniformity of the stress field in the vicinity of the macrocrack. The technique of double layer potentials is used. A closed form solution for the effective stress field is constructed.     

Interaction of a characteristic shock with a weak discontinuity in a relaxing gas

The evolution of a characteristic shock in a relaxing gas is investigated and its interaction with a weak discontinuity is studied. A particular solution to the governing system, which exhibits space–time dependence, is used to study the evolutionary behaviour of the characteristic shock; the properties of incident, reflected and transmitted waves, influenced by the relaxation mechanism, together with the geometry of the fluid flow and the background state at the rear of the shock, are studied.     

Free convection about a vertical frustum of a cone in a micropolar fluid

The paper studies the problem of free convection about a vertical frustum of a cone in a micropolar fluid. It is assumed that the flow is steady, and the surface temperature of the frustum of the cone is constant. Another assumption is that the angles of the frustum of the cone are large enough so that the transverse curvature effects are negligible. Under these assumptions, the governing boundary layer equations subjected to appropriate boundary conditions are first written in a non-dimensional form. These equations are then transformed into a set of non-similar partial differential equations of parabolic type, which is amenable to a direct numerical solution, using a very efficient method known as Keller-box method. Numerical solutions are obtained for a range values of the micropolar parameter Δ varying between Δ = 0 (Newtonian fluid) to Δ = 2 and Prandtl number Pr is varied from 0.1 to 10. Flow and heat transfer characteristics are determined and are given in tables and also shown on graphs. The obtained results are also compared with those known from the open literature and it is found that they are in excellent agreement.     

Flow of a Casson fluid in a narrow tube with a side branch

Development of a mathematical model suitable for studying the mass-flux and hematocrit reduction due to plasma skimming in a capillary emerging from an artery making an angle with the parent artery is of primary concern in the paper. The flow is considered to have three phases – the peripheral plasma layer, the cell depleted middle layer and the core region where the concentration of erythrocytes is highest. Both steady and pulsatile flow situation are studied. The analysis for pulsatile flow has been carried out by considering the pressure gradient as a periodic function of time and the inertial effects as negligibly small. A perturbation technique is employed to solve the resulting quasi-steady non-linear system of equations that are considered to govern the flow. Basing upon relevant experimental data available for coronary arteries as well as very small vessels of the circulatory system, the study has been performed by considering Womeresely parameter to be small (less than unity). The theoretical estimates computed under the purview of the present mathematical analysis reveal that hematocrit in the branch capillary decreases with an increase in the yield stress of blood, both in steady and pulsatile flows for any branching angle. Further, erythrocytes entrainment from the parent artery to the branch capillary is least when the branch is perpendicular to the parent artery.     

Failure of a Porous Solid from a Deep Notch

A finite strain finite element method is used to examine the stress state near the tip of a deep notch in an elastic-plastic porous solid. The notch is loaded in mode I plane strain tension and small scale yielding is assumed. Two rate independent strain hardening material models are used: a version of the Gurson model (1977) and the more recent FKM model developed by Fleck, Kuhn and McMeeking (1992). Under increasing K _I, void growth is initially stable and independent of mesh dimension. Localization of plastic flow sets in at a finite value K _i, and the deformation field is mesh-size dependent thereafter. The initiation of crack growth at the notch root is assumed to occur when a critical level of porosity is attained. The results show that the shape of the plastic zone for both the Gurson and the FKM material is highly dependent on the initial porosity. In the case of low initial porosity, the plastic zone shape is similar to that of a fully dense material; at higher initial porosities the plastic zone is concentrated ahead of the notch tip. The effect of the initial void volume fraction on the porosity field and the critical stress intensity factor is studied, and the mesh-size dependence of the results is discussed. The analysis is useful for prediction of the notched strength of porous metals. This revised version was published online in August 2006 with corrections to the Cover Date.     

Measurement of a cross-sectional profile of a thread gauge using a sinusoidally vibrating interference pattern

A sinusoidally vibrating interference pattern (SVIP) is used as an exact spatial scale in order to measure a cross-sectional profile of a thread gauge. The SVIP is projected on the thread gauge surface, and lights diffracted and reflected from the end points of the thread gauge surface are extracted by spatial frequency filtering in an imaging system to make an image of the end points whose positions are decided by the peak positions of amplitude distributions in the image. The coordinates of the end points or the cross-sectional profile of the thread gauge is obtained from the phases measured at the positions of the end points, phase distribution of the SVIP on a CCD image sensor, and the pixel positions of the CCD image sensor.