Classical Fluid Mechanics Research Articles

Combining upper bound and strain path methods for evaluating penetration resistance

The problem of penetration resistance involves a continuously moving zone of plastic distortion in the soil medium. This has been explored for cone penetration and pile installation, where additional volume is intruded into the soil, using the strain path method with the flow field derived from classical fluid mechanics. This paper focuses on a new generation of penetrometers, which have a much greater projected area than the cone shaft, and introduces a version of the strain path method based on classical upper bound solutions for the penetrometers. The new approach is used to explore the effects of high strain rates, and gradual strength degradation, on the penetration resistance of cylindrical and spherical penetrometers. Copyright © 2005 John Wiley & Sons, Ltd.

Screening of classical Casimir forces by electrolytes in semi-infinite geometries

We study the electrostatic Casimir effect and related phenomena in the equilibriumstatistical mechanics of classical (non-quantum) charged fluids. The prototype modelconsists of two identical dielectric slabs in empty space (the pure Casimir effect) or in thepresence of an electrolyte between the slabs. In the latter case, it is generally believedthat the long-ranged Casimir force due to thermal fluctuations in the slabs isscreened by the electrolyte into some residual short-ranged force. The screeningmechanism is based on a ‘separation hypothesis’: thermal fluctuations of theelectrostatic field in the slabs can be treated separately from the pure imageeffects of the ‘inert’ slabs on the electrolyte particles. In this paper, by using aphenomenological approach under certain conditions, the separation hypothesis is shownto be valid. The phenomenology is tested on a microscopic model in which theconducting slabs and the electrolyte are modelled by symmetric Coulomb gases ofpoint-like charges with different particle fugacities. The model is solved in thehigh-temperature Debye–Hückel limit (in two and three dimensions) and at the free-fermionpoint of the Thirring representation of the two-dimensional Coulomb gas. TheDebye–Hückel theory of a Coulomb gas between dielectric walls is also solved.

High-speed conveyor junction based on an air-jet floatation technique

This paper investigates how forces developed by air-jets might be used to convey or manipulate delicate planar objects at high-speed without damage. The theory of turbulent jets and classic fluid mechanics are used in combination with practical experiments to establish how air-jet velocities and forces are related to orifice size and supply pressure. The basic stability problem of how to support a planar object on a single or multiple-array of air-jets is discussed. A passive control solution is developed based on the insertion of a porous layer between the object and the air-jets. This solution is incorporated in a mechatronic conveyor junction that can selectively re-direct or lane rigid or flexible planar objects from one conveyor to another mounted at right angles. In trials the conveyor junction reliably handled fragile biscuits at more than eight per second and could re-direct objects travelling at up to 2.5 m/s.

Relativistic fluid mechanics, Kähler manifolds, and supersymmetry

We propose an alternative for the Clebsch decomposition of currents in fluid mechanics, in terms of complex potentials taking values in a Kahler manifold. We reformulate classical relativistic fluid mechanics in terms of these complex potentials and rederive the existence of an infinite set of conserved currents. We perform a canonical analysis to find the explicit form of the algebra of conserved charges. The Kahler-space formulation of the theory has a natural supersymmetric extension in 4-D space-time. It contains a conserved current, but also a number of additional fields complicating the interpretation. Nevertheless, we show that an infinite set of conserved currents emerges in the vacuum sector of the additional fields. This sector can therefore be identified with a regime of supersymmetric fluid mechanics. Explicit expressions for the current and the density are obtained.

A stream function implicit finite difference scheme for 2D incompressible flows of Newtonian fluids

AbstractThe development of a new algorithm to solve the Navier–Stokes equations by an implicit formulation for the finite difference method is presented, that can be used to solve two‐dimensional incompressible flows by formulating the problem in terms of only one variable, the stream function. Two algebraic equations with 11 unknowns are obtained from the discretized mathematical model through the ADI method. An original algorithm is developed which allows a reduction from the original 11 unknowns to five and the use of the Pentadiagonal Matrix Algorithm (PDMA) in each one of the equations. An iterative cycle of calculations is implemented to assess the accuracy and speed of convergence of the algorithm. The relaxation parameter required is analytically obtained in terms of the size of the grid and the value of the Reynolds number by imposing the diagonal dominancy condition in the resulting pentadiagonal matrixes. The algorithm developed is tested by solving two classical steady fluid mechanics problems: cavity‐driven flow with Re=100, 400 and 1000 and flow in a sudden expansion with expansion ratio H/h=2 and Re=50, 100 and 200. The results obtained for the stream function are compared with values obtained by different available numerical methods, to evaluate the accuracy and the CPU time required by the proposed algorithm. Copyright © 2002 John Wiley & Sons, Ltd.

Issues in the statistical mechanics of steady sedimentation

A critical review is presented of recent experimental and theoretical work on the steady sedimentation of particulate suspensions in viscous fluids. The point of view is that of a practitioner of non-equilibrium statistical physics rather than classical fluid mechanics.

Issues in the statistical mechanics of steady sedimentation

A critical review is presented of recent experimental and theoretical work on the steady sedimentation of particulate suspensions in viscous fluids. The point of view is that of a practitioner of non-equilibrium statistical physics rather than classical fluid mechanics.

On the coupled heat equation of linear thermoelasticity

The presence of the coupling term in the coupled heat equation of linear thermoelasticity is quite undesirable. Beyond causing heat transfer to be coupled to the deformation, it is shown that it causes the internal energy to be singular in the isothermal limit where it does not go over continuously to its pure theory of elasticity form. This is very much unlike classical fluid mechanics in which the isothermal limit is regular in so far as the internal energy is concerned. It is shown that as long as the deformation does not contain high frequency vibrations, the coupling term can be dropped and the singularity can be removed. This is proven by a careful order of magnitude analysis of the governing equations and is a valid approximation for the overwhelming majority of phenomena. It is a desirable approximation to make that has been commonly made in the literature in the past anyhow. The full implications of these results for research in thermoelasticity are thoroughly discussed.

Boundary Layer Solutions in Elastic Solids

Circumferential shear deformation in an annular domain is studied for a large class of incompressible isotropic elastic materials. It is demonstrated that large strains are confined in a region adjacent to a boundary, in analogy to the boundary layer phenomenon in fluid mechanics. The size of this region is quantified. An approximate solution technique for the deformation of nonlinear elastic solids, proposed by Rajagopal [7], is further studied. In this solution, akin to the boundary layer approximation in classical fluid mechanics, the full nonlinear problem is solved in a relatively small region of large strain, while the linearized problem is solved in the remaining region. Error estimates for the approximate solution are obtained.

Modelling of two-dimensional laminar flow using finite element method

In this paper, a Galerkin weighted residual finite element numerical solution method, with velocity material time derivative discretisation, is applied to solve for a classical fluid mechanics system of partial differential equations modelling two-dimensional stationary incompressible Newtonian fluid flow. Classical examples of driven cavity laminar flow and laminar flow past a cylinder are presented. Numerical results are compared with data found in the literature. Copyright © 1999 John Wiley & Sons, Ltd.

Moments of probable seas: statistical dynamics of Planet Ocean

The ocean is too big. From the scale of planetary radius to scales of turbulent microstructure, the range of length scales is 10 9. Likewise for time scales. Classical geophysical fluid dynamics does not have an apparatus for dealing with such complexity, while ‘brute force’ computing on the most powerful supercomputers, extant or presently foreseen, barely scratches this complexity. Yet the everywhere-swirling-churning ocean interacts unpredictably in climate history and climate future – against which we attempt to devise planetary stewardship. Can we better take into account the unpredictability of oceans to improve upon present ocean/climate forecasting? What to do? First, recognize that our goal is to comprehend probabilities of possible oceans. Questions we would ask are posed as moments (expectations). Then the dynamical goal is clear: we seek equations of motion of moments of probable oceans. Classical fluid mechanics offers part of the answer but fails to recognize statistical dynamical aspects (missing the arrow of time as past ⇒ future). At probabilities of oceans, the missing physics emerges: moments are forced by gradients of entropy with respect to moments. Time regains its arrow, and first (simplest) approximations to entropy-gradient forces enhance the fidelity of ocean theories and practical models.

Analysis of electrokinetic effects on the liquid flow in rectangular microchannels

The effects of the electrical double layer near the solid/liquid interface on liquid flow through a rectangular microchannel are analyzed in this work. Based on the Debye–Hückel approximation, a linear solution of a two-dimensional Poisson–Boltzmann equation governing the electrical potential distribution in the cross-section of rectangular channels is presented to describe the electrical double-layer field near the solid/liquid interface. An additional body force originating from the presence of the electrical double layer is considered to modify the conventional Navier–Stokes equation. By using the Green's function formula, an exact solution to this modified Navier–Stokes equation in rectangular microchannels is obtained. The effects of the electrical double-layer field, channel size and the electrical static charge on the fluid velocity distribution, streaming potential, volume flow rate, friction coefficient and apparent viscosity have been discussed. The results show that, for diluted liquid, the liquid flow in rectangular microchannels is influenced significantly by the electrical double layer and hence deviates from the flow characteristics described by classical fluid mechanics.

Electrokinetic Effects on Pressure-Driven Liquid Flows in Rectangular Microchannels

The effects of the electrical double layer near the solid-liquid interface and the induced electrokinetic field on the pressure-driven liquid flow through a rectangular microchannel are analyzed in this work. A nonlinear, two-dimensional Poisson–Boltzmann equation governing the electrical double layer field in the cross section of rectangular channels is numerically solved with the use of a finite-difference scheme. A body force caused by the electrical double field and the flow-induced electrokinetic field is considered in the equation of motion. An exact solution to this equation of motion in rectangular microchannels is obtained by employing the Green function formulation. The effects of the ionic concentration of the liquid, the zeta potential of the solid surface, and the size and the shape of microchannels on the fluid velocity distribution, streaming potential, volumetric flow rate, friction coefficient, and apparent viscosity are discussed. The results clearly show that for a liquid solution of low ionic concentration and a solid surface of high zeta potential the liquid flow in rectangular microchannels is significantly influenced by the presence of the electrical double layer field and hence deviates from the flow characteristics described by classical fluid mechanics.

Plasma Processing of Advanced Materials

A plasma, commonly referred to as the “fourth state of matter,” is an ensemble of randomly moving charged particles with a sufficient particle density to remain, on average, electrically neutral. While their scientific study dates from the 19th century, plasmas are ubiquitous, comprising more than 99% of the known material universe. The term “plasma” was first coined in the 1920s by Irving Langmuir at the General Electric Company after the vague resemblance of a filamented glow discharge to a biological plasma.Plasmas are studied for many reasons. Physicists analyze the collective dynamics of ions and electron ensembles, utilizing principals of classical electromagnetics, and fluid and statistical mechanics, to better understand astrophysical, solar, and ionospheric phenomenon, and in applied problems such as thermonuclear fusion. Electrical engineers use plasmas to develop efficient lighting, and high-power electrical switchgear, and for magneto-hydrodynamic (MHD) power conversion. Aerospace engineers apply plasmas for attitude adjustment and electric propulsion of satellites. Chemists, chemical engineers, and materials scientists routinely use plasmas in reactive ion etching and sputter deposition. These methods are commonplace in microelec tronics since they allow synthesis of complex material structures with submicron feature sizes. A substantial portion of the multi-billion-dollar market for tooling used to manufacture semiconductors employs some form of plasma process. When compared with traditional wet-chemistry techniques, these dry processes result in minimal waste generation. Plasmas are also useful in bulk processing—for example as thermal sprays for melting materials.While the quest for controlled thermonuclear fusion dominated much of plasma research in the 1960s and 1970s, in the last 20 years it has been the application of plasmas to materials processing that has provided new challenges for many plasma practitioners. It is not surprising that the guest editors and several of the authors for this issue of MRS Bulletin come from a fusion plasma-physics background.

Viscoelastic fluid mechanics: Interaction between prediction and experiment

The extent to which elastic effects in the flow of viscoelastic fluids can be predicted is reviewed. For this purpose, constant-viscosity elastic liquids (Boger fluids) are used for observation where shear-rate-dependent viscosity effects and inertial effects can be eliminated. By comparing observations with predictions in squeeze film flows, jet flows, isothermal spinning, and for instabilities observed in various torsion flows, it is tempting to conclude that elastic effects in complex flows of viscoelastic fluids can be predicted with a relatively simple constitutive equation like the Oldroyd B model. However, this conclusion is not valid for flows for which the elongational rates are high or for regions of high stress concentration like tubular entry flows and creeping flow around a sphere. The importance of the elongational viscosity and its variation with strain rate in such, strong flows is clearly illustrated. Elongational viscosity is often a foreign concept in classical fluid mechanics, and hence its importance in viscoelastic fluid mechanics is stressed.

Ripplon interactions on superfluid helium

The interaction of ripplons with ripplons and phonons is usually formulated, in quantum hydrodynamics, in terms of creation and anihilation operators. This formulation corresponds, in classical fluid mechanics, to the description of resonant nonlinear interaction of waves in terms of wave amplitudes. This correspondence proves to be valuable for calculation and insight in ripplon physics. It is shown how the existing literature on wave interactions gives us, e.g., the three-ripplon Hamiltonian. Calculations of the lifetime of ripplons on liquid helium at finite temperature are presented. Both ripplon-ripplon and ripplon-phonon processes are discussed. The connection between ripplon-phonon interactions and geophysics is pointed out.

Intermediate asymptotics, scaling laws and renormalization group in continuum mechanics

Scaling laws and self-similar solutions are very popular concepts in modern continuum mechanics. In the present paper these concepts are analyzed both from the viewpoint of intermediate asymptotics, known in classical mathematical physics and fluid mechanics, and from the viewpoint of the renormalization group technique, known in modern theoretical physics. The definition of the renormalization group is proposed, related to the intermediate asymptotics with incomplete similarity. The general presentation is illustrated by examples of essentially non-linear problems where all analytical properties of the solutions and their asymptotics are rigorously proved, as well by an example from turbulence, where the rigorous problem statement is missing.

The character of two-phase gas/particulate flow equations

In classical (single-phase) fluid mechanics, it is a matter of experience that, away from flow boundaries, inviscid models often give excellent results. For time-dependent two-phase flows, an attractive possibility is to likewise ignore viscosity in the “mainstream” flow. However, such equations are generally not hyperbolic, and possess complex eigenvalues. This creates severe technical difficulties as the initial value problem is then ill-posed, and serious numerical problems that may render accurate computation impossible. This ill-posedness has been the subject of heated controversy, but the conclusion is clear: Doubt remains over the correct equations even for simple two-phase flows. Complex characteristics arise as a result of multiphase flow averaging, and the consequent omission of important physical terms. With care, however, these effects may be reintroduced into the equations. Using such an approach, the specific case of gas/particulate two-phase flow is considered. The aim is not to propose a definitive, demonstrably “correct” system of equations for unsteady two-phase gas/ particulate flow; the assumptions made are too general and specific cases must be treated on their individual merits. Rather a methodology of analysis is illustrated and qualitative results concerning the nature of added terms in the equations are obtained. The effect of each term and also of combinations of terms is studied, and general conclusions are drawn concerning the hyperbolicity of the equations.

Classical vortices and quantum anyons: An analogy.

The striking resemblance between the velocity vector field of classical fluid mechanics and the statistical vector potential in anyonic quantum mechanics is utilized to obtain many of the equations of anyon physics by analogy. In particular, the energy-density functional leading to the Liouville equation is derived.

INTEGRATING COMPUTERS INTO ORTHOPEDIC RESEARCH

The role of computers in orthopedic research and education is expanding rapidly. Its potential to manipulate large amounts of data and execute multiple complex assignments with great speed and accuracy indeed make the computer an awe-inspiring device. An important instrument in research is the computerized database, a collection of related data arranged so that useful information may be retrieved. Computer models derived from classical physics and fluid mechanics have been used to study motion of both extremities and spinal articulations. Computers also have found usefulness in clinical orthopedic research. The orthopedist of the future will use the computer directly in clinics and private practice for patient evaluation, computer-assisted preoperative planning, and financial recordkeeping.