Showing papers on "Streamlines, streaklines, and pathlines published in 1994"
TL;DR: In this paper, the steady and transient deformation of a drop immersed in an ambient simple shear flow is studied in the limit of Stokes flow and the flow is examined as a function of the viscosity ratio λ between the drop and the suspending fluid, and the capillary number Ca.
217 citations
TL;DR: In this article, the authors formulated the dynamical problem of a cool wind centrifugally driven from the magnetic interface of a young star and an adjoining Keplerian disk, and showed that a wind can be driven from a small X-region just outside the stellar magnetopause.
Abstract: We formulate the dynamical problem of a cool wind centrifugally driven from the magnetic interface of a young star and an adjoining Keplerian disk. We examine the situation for mildly accreting T Tauri stars that rotate slowly as well as rapidly accreting protostars that rotate near break-up. In both cases a wind can be driven from a small X-region just outside the stellar magnetopause, where the field lines assume an open geometry and are rooted to material that rotates at an angular speed equal both to the local Keplerian value and to the stellar angular speed. Assuming axial symmetry for the ideal magnetohydrodynamic flow, which requires us to postpone asking how the (lightly ionized) gas is loaded onto field lines, we can formally integrate all the governing equations analytically except for a partial equation that describes how streamlines spread in the meridional plane. Apart from the difficulty of dealing with PDEs of mixed type, finding the functional forms of the conserved quantities along streamlines - the ratio beta of magnetic field to mass flux, the specific energy H of the fluid in the rotating frame, and the total specific angular momentum J carried in the matter and the field - constitutes a standard difficulty in this kind of (Grad-Shafranov) formalism. Fortunately, because the ratio of the thermal speed of the mass-loss regions to the Keplerian speed of rotation of the interface constitutes a small parameter epsilon, we can attack the overall problem by the method of matched asymptotic expansions. This procedure leads to a natural and systematic technique for obtaining the relevant functional dependences of beta, H, and J. Moreover, we are able to solve analytically for the properties of the flow emergent from the small transsonic region driven by gas pressure without having to specify the detailed form of any of the conserved functions, beta, H, and J. This analytical solution provides inner boundary conditions for the numerical computation in a companion paper by Najita & Shu of the larger region where the main acceleration to terminal speeds occurs.
167 citations
TL;DR: In this article, the position and structure of the hydraulic jump are determined by numerically solving the resulting problem with a boundary condition at the edge of the plate that expresses the matching of the layer with the shorter region where the liquid turns around and falls under the action of gravity.
Abstract: The hydraulic jump appearing in the viscous laminar flow of a thin liquid layer over a finite horizontal plate is studied using the boundary-layer approximation for the flow in and around the jump. The position and structure of the jump are determined by numerically solving the resulting problem with a boundary condition at the edge of the plate that expresses the matching of the layer with the shorter region where the liquid turns around and falls under the action of gravity. When the Froude number of the flow ahead of the jump is very large, the jump is much shorter than the horizontal extent of the layer, though still much longer than its depth. An asymptotic description of the inner structure of such a jump is given, building upon the analysis of Bowles & Smith for the short interaction region at the leading end of the jump. This structure consists of a fast moving separated flow in the upper part of the layer that progressively slows down by ingesting new fluid across its lower boundary, until the hydrostatically generated adverse pressure gradient makes it recirculate in the lower part of the layer. The effects of the surface tension and the cross-stream pressure variation owing to the curvature of the streamlines are taken into account in the jump and in the flow approaching the edge of the plate, showing that they can lead to quantitative and also qualitative changes of the jump structure, including a local breakdown of the boundary-layer approximation.
93 citations
TL;DR: In this article, a numerical study of the combined forced and natural convective cooling of heat-dissipating electronic components, located in a rectangular enclosure, and cooled by an external through flow of air is carried out.
Abstract: A numerical study of the combined forced and natural convective cooling of heat-dissipating electronic components, located in a rectangular enclosure, and cooled by an external through flow of air is carried out. A conjugate problem is solved, describing the flow and thermal fields in air, as well as the thermal field within the walls of the enclosure and the electronic components themselves. The interaction between the components is of interest here, depending on their relative placement in the enclosure, and different configurations are considered. For Re=100 laminar, steady flow is predicted for up to Gr/Re 2 =10, but R single-frequency oscillatory behavior is observed for most of the configurations studied, at Gr/R 2 =50
81 citations
TL;DR: In this article, a finite element technique was used to solve the incompressible Navier-Stokes equatikons simultaneously with the elastic membrane equations on the flexible boundary, and the coupled fluid and elastic equations were solved by a Newton-Raphson scheme which displays quadratic convergence down to low membrane tensions and extreme states of collapse.
Abstract: Fluid flow through a significantly compressed elastic tube occurs in a variety of physiological situations. Laboratory experiments investigating such flows through finite lengths of tube mounted between rigid supports have demonstrated that the system is one of great dynamical complexity, displaying a rich variety of self-excited oscillations. The physical mechanisms responsible for the onset of such oscillations are not yet fully understood, but simplified models indicate that energy loss by flow separation, variation in longitudinal wall tension and propagation of fluid elastic pressure waves may all be important. Direct numerical solution of the highly non-linear equations governing even the most simplified two-dimensional models aimed at capturing these basic features requires that both the flow field and the domain shape be determined as part of the solution, since neither is known a priori. To accomplish this, previous algorithms have decoupled the solid and fluid mechanics, solving for each separately and converging iteratively on a solution which satisfies both. This paper describes a finite element technique which solves the incompressible Navier-Stokes equatikons simultaneously with the elastic membrane equations on the flexible boundary. The elastic boundary position is parametized in terms of distances along spines in a manner similar to that which has been used successfully in studies of viscous free surface flows, but here the membrane curvature equation rather than the kinematic boundary condition of vanishing normal velocity is used to determine these diatances and the membrane tension varies with the shear stresses exerted on it by the fluid motions. Bothy the grid and the spine positions adjust in response to membrane deformation, and the coupled fluid and elastic equations are solved by a Newton-Raphson scheme which displays quadratic convergence down to low membrane tensions and extreme states of collapse. Solutions to the steady problem are discussed, along with an indication of how the time-dependent problem might be approached.
69 citations
TL;DR: The structure of the alveolar duct has an important role in gravitational sedimentation and inertial impaction in the lung acinus, and Lagrangian description of particle dynamics in an alveolated duct flow was developed.
Abstract: We studied the effects of alveolated duct structure on deposition processes for particle diameters > or = 1 micron. For such large particles, Brownian motion is insignificant but gravity and inertial forces play an important role. A Lagrangian description of particle dynamics in an alveolated duct flow was developed, and computational analysis was performed over the physiologically relevant range. At low flow rates gravity caused deposition. Gravitational cross-streamline motion depended on the coupled effects of curvature of gas streamlines and duct orientation relative to gravity. The detailed convective flow pattern was an important factor in determining deposition. At higher flow rates, inertial impaction contributed markedly to deposition. The curved nature of streamlines again played a major role on deposition, but duct orientation had little effect. In the medium range of flow rates, both gravitational and inertial forces simultaneously influenced particle motion. Particle inertia, per se, did not cause deposition but substantially suppressed gravitational deposition. The deposition mechanism was complex; contrary to what is often assumed in past analyses, the interaction between gravitational and inertial effects could not be described in a simple additive fashion. We conclude that the structure of the alveolar duct has an important role in gravitational sedimentation and inertial impaction in the lung acinus.
64 citations
TL;DR: In this paper, the authors extend the canonical formalism to three-dimensional steady flows and show how the methods of the theory of Hamiltonian systems can be successfully used to investigate the advection of a passive particle.
Abstract: It is well known that the equations of motion of a fluid particle in a two-dimensional flow can be written in the canonical form with the stream function playing the role of the Hamiltonian. Here we extend this canonical formalism to three-dimensional steady flows. We show how the methods of the theory of Hamiltonian systems can be successfully used to investigate the advection of a passive particle. As an example of the perturbed closed streamline flow we consider a rigid rotation with added small quadratic velocity field and explain the structure of streamlines by averaging the corresponding Hamiltonian. We also show how the Hamiltonian formulation can be used to find the invariants of the fluid particle motion which are then used for non-canonical averaging.
60 citations
TL;DR: In this article, the stagnation flow along the centerline behind a rigid sphere is examined experimentally by laser Doppler velocimetry and numerically by finite elements, and the experimental Weissenberg number is varied up to approximately 3.5.
Abstract: The flow of a viscoelastic liquid past a rigid sphere held on the centerline of a circular cylinder is examined experimentally by laser Doppler velocimetry and numerically by finite elements. The study deals with elastic fluids that exhibit shear-thinning behaviour, and focuses on the stagnation flow along the centerline behind the sphere. The experimental Weissenberg number is varied up to approximately 3.5. The speed of the sphere relative to the cylinder is fixed and the Weissenberg number is changed by adjusting the fluid properties. In this way a wide range of behaviour is produced, varying from the upstream shift of streamlines and velocity overshoot (‘negative wake’) seen in some previous experimental investigations to the downstream shift of streamlines characteristic of elastic fluids having shear-constant viscosity. The simulations indicate that the net response is strongly influenced by the elongational properties of the fluid, and this is used to rationalise the observed behaviour. In particular, it is shown that the Weissenberg number alone is not a sufficient basis for characterisation of the flow.
56 citations
TL;DR: The plasma-skimming mechanism that causes phase separation due to uneven distribution of red blood cells at the inlet cross section of the parent vessel is analyzed to determine the side-to-parent vessel RBC flux ratio and discharge hematocrit ratio as a function of corresponding flow ratios.
Abstract: Owing in part to a plasma-skimming mechanism, the distribution of red blood cells (RBCs) into branches of microvascular bifurcations typically differs from the distribution of the bulk blood flow This paper analyzes the plasma-skimming mechanism that causes phase separation due to uneven distribution of red blood cells at the inlet cross section of the parent vessel In a previous study, the shape of the surface that divides the flow into the branches was found by numerical simulation of three-dimensional flow of a homogeneous Newtonian fluid in T-type bifurcations Those findings are used in this study to determine, as a first approximation, the side-to-parent vessel RBC flux ratio and discharge hematocrit ratio as a function of corresponding flow ratios Calculations are based on the assumption that RBCs move along streamlines of a homogeneous Newtonian fluid and are uniformly distributed within a concentric core at the inlet cross section of the parent vessel The results of our calculations agree well for a wide range of flow parameters with experimental data from in vivo and in vitro studies
54 citations
TL;DR: In this article, the authors used a separable Rivlin-Sawyers integral constitutive equation with a spectrum of nine relaxation times to model the fluid and found that the majority of the contribution to the entrance pressure loss comes close to the die entry.
Abstract: The flow of a LDPE melt in an abrupt 10:1 axisymmetric contraction is simulated using a finite element program, and comparisons are made with experimental results reported by another researcher. The researcher performed his die entry experiment at a temperature of 150 °C, and he used Laser Doppler Anemometry to measure the velocity field at several flow rates. He thus obtained detailed information about the flow field. In our numerical simulation of this experiment, we use a separable Rivlin‐Sawyers integral constitutive equation with a spectrum of nine relaxation times to model the fluid. We assume that the ratio of second normal stress difference to first normal stress difference is a nonzero constant. The material is well‐characterized with both shear and simple elongational data from which we determine the parameters in the constitutive equation. The general performance of our model is determined by comparing the vortex growth and entrance pressure loss for various flow rates with the experimental results reported by the experimentalist. We then repeat the experimentalist’s detailed analysis of the flow field at a single flow rate using particle tracking. Specifically, particles are tracked along several streamlines and we compute the shear and elongational rates, as well as the relative shear strain and stretch ratios close to the die entry. The detailed experimental data used for comparison were obtained from the measuredvelocity field. Comparisons of experimental and numerical results show good qualitative and, in some cases, quantitative agreement. From our numerical particle tracking, we also compute the shear stress, the normal stress differences, and the invariants along streamlines. Finally, the shear and elongational contributions to the energy dissipation and the entrance pressure loss is determined throughout the entire domain and in various regions. We find that the majority of the contribution to the entrance pressure loss comes from regions close to the die entry. In addition, in regions in front of the die entry, elongational effects dominate, although shear effects are not negligible, even at high flow rates.
53 citations
TL;DR: In this paper, the flow in a trapezoidal cavity (including the rectangular and triangular cavities) with one moving wall is studied numerically by finite differences with special treatment in the corners.
TL;DR: In this article, a mathematical model is proposed for the steady two-dimensional flow of a viscous incompressible fluid past a cylinder which incorporates the details of the structure of the vorticity in this case where its behaviour is known.
TL;DR: In this paper, an experimental and theoretical study of natural convection flow and heat transfer within a rectangular enclosure partially filled with an anisotropic porous medium is conducted as a step to understand the effects of the mushy region flow characteristics on the interacting flows of the melt pool and a mushy zone of solidifying alloys.
TL;DR: In this paper, the authors showed that at a critical Reynolds number (based on channel width and cross-sectional mean velocity) of approximately 100 the flow became asymmetric and unsteady, and this transition led to an eddy shedding regime, with eddies formed and shed successively from each baffle.
Abstract: Incompressible Newtonian flow in a two-dimensional channel with periodically placed sharp edged baffles has been studied both by numerical simulation and by experimental flow visualization. The flow was observed to be steady and symmetric at low Reynolds numbers, with recirculating eddies downstream of each baffle. At a critical Reynolds number (based on channel width and cross-sectional mean velocity) of approximately 100 the flow became asymmetric and unsteady. This transition to unsteadiness led to an eddy shedding regime, with eddies formed and shed successively from each baffle. A stability study suggested that the mechanism for transition to unsteady flow is a Kelvin–Helmholtz instability associated with the shear layer formed downstream of the sharp edged baffles. The frequency of the unsteadiness is, however, dependent on the full flow field, and not only the shear layer characteristics. Experimental observations show that the instability is followed by a secondary transition to three-dimensional disordered flow. Experimentally observed flows in the two-dimensional regime were found to be in close agreement with the numerical simulation for both the steady and unsteady flows.
31 Dec 1994
TL;DR: In this paper, the authors developed physically realistic models that predict the behavior of pollutants released in the vicinity of buildings, and an understanding of the flow field is essential to predict the behaviour of pollutants.
Abstract: In order to develop physically realistic models that predict the behavior of pollutants released in the vicinity of buildings, an understanding of the flow field is essential. The main features of such flow fields around isolated block-shaped buildings are reasonably well understood. Separation of the flow generally occurs at the leading edges of the roofs and sides of the buildings and these separated layers move into the surrounding fluid. If the building is sufficiently long, these separated layers may reattach onto the surface, so that separation will occur again at the downwind edges of the roof and sides. Whether the building is long or short, these separated layers will eventually curve inward toward the wake axis, forming a rather imprecisely defined region called a {open_quotes}cavity.{close_quotes} It is bounded upwind and above by the separation streamline emanating from the roof edge, and downwind by a reattachment streamline. Unlike two-dimensional flows, the separation streamline is not the same as the reattachment streamline. The {open_quotes}cavity{close_quotes} is also bounded laterally by the streamlines emanating from the corners. Within this roughly ellipsoidal-shape cavity, the flow is of exceptionally high turbulence intensity and small mean velocity, and frequently reverses direction.
TL;DR: An experimental study of the local mass transfer over the entire surface of a wall-mounted cube is performed with a particular emphasis on the effects of flow angles-of-attack (0 deg≤α≤45 deg).
Abstract: An experimental study of the local mass transfer over the entire surface of a wall-mounted cube is performed with a particular emphasis on the effects of flow angles-of-attack (0 deg≤α≤45 deg). Invoking an analogy between heat and mass transfer, the presently obtained mass transfer results can be transformed into their heat transfer counterparts. Reynolds number based on the cube height and mean free-stram velocity varies between 3.1×10 4 and 1.1×10 5 . To substantiate the mass transfer results, streakline patterns are visualized on the cube surfaces as well as the endwall using the oil-graphite technique. Significantly different flow regimes and local mass transfer characteristics are identified as the angle-of-attack varies
TL;DR: In this article, the body surface pressure fluctuation along the stagnation streamlines of several wing-body junctions was measured with microphones with a nominal reference velocity of 32.5 m/s and Reynolds number based on approach momentum thickness of 4450.
Abstract: The body surface pressure fluctuation along the stagnation streamlines of several wing-body junctions were measured with microphones. The wings shapes are of a 3:2 semielliptical-nosed NACA-0020-tailed body, a parallel centerbody model, a tear drop shape, Sand 1850, NACA-0015, and NACA-0012. The oil-flow visualizations revealed the limiting streamline structure on the wall where the models were mounted. Measurements were conducted at a nominal reference velocity of 32.5 m/s and Reynolds number based on approach momentum thickness of 4450
TL;DR: In this article, the local and mean natural convection heat transfer characteristics and flow fields were studied experimentally and numerically in an air-filled, differentially heated enclosure with a cross-sectional aspect ratio of one.
Abstract: The local and mean natural convection heat transfer characteristics and flow fields were studied experimentally and numerically in an air-filled, differentially heated enclosure with a cross-sectional aspect ratio of one. The enclosure is rotated above its longitudinal horizontal axis. A Mach-Zehnder interferometer was employed to reveal the entire temperature field, which enable the measurement of the local and mean Nusselt numbers at the hot and cold surfaces. Laser sheet flow visualization was employed to observe the flowfield. The result showed that the Coriolis and centrifugal buoyancy forces arising from rotation have a remarkable influence on the local heat transfer when compared with the nonrotating results
TL;DR: The author has developed iterative least squares algorithms to improve the realism of streamlines and has applied the algorithms to velocity data obtained from a flow phantom and the carotid arteries of normal volunteers.
Abstract: Streamline display is a unique alternative to cross-sectional slice or projection display, because streamlines more clearly show the patterns of blood flow within the vessel. Flow patterns associated with atherosclerosis, such as streamline separation and recirculation, can be quickly identified with this display. Streamlines can be calculated using velocity data obtained from 3-D phase contrast angiographic pulse sequences. However, these streamlines often pass through the wall of vessel or show intraluminal sources and sinks of blood. The author has developed iterative least squares algorithms to improve the realism of streamlines. The velocity data is modified so that the resulting streamlines do not pass through the vessel wall and there are no intraluminal sources or sinks. He has applied the algorithms to velocity data obtained from a flow phantom and the carotid arteries of normal volunteers. Streamlines derived from the processed velocity fields are more realistic and provide more precise flow quantitation.
TL;DR: In this article, the dynamics of passively advected Lagrangian tracers undergoing small vertical oscillations around an horizontal reference density surface, in an Eulerian velocity field depending only on the horizontal coordinates.
TL;DR: In this paper, the authors used a finite-volume method and the k-e turbulence model for the flow in a circular model settling tank with and without swirls, and compared the results with experimentally determined streamlines and flow-through curves as well as with previous computations.
Abstract: Axisymmetric numerical simulation with a finite‐volume method and the k‐e turbulence model is described for the flow in a circular model settling tank with and without swirl. The geometry of the model tank requires the use of a nonorthogonal boundary fitted grid. Results are compared with experimentally determined streamlines and flow‐through curves as well as with previous computations. For flow without swirl, the numerical simulations are in good agreement with the experimental data, and significant improvement for a critical geometrical configuration was achieved by use of the low‐diffusive HLPA discretization scheme for convection. The inclusion of swirl allows the model to account for the influence of the circumferential removal procedure as well as for the effect of swirl inducing vanes at the inlet. The simplification introduced in modeling the removal equipment impairs somewhat the accuracy of the predicted flow‐through curves. For further improvement, a more realistic and detailed modeling of the...
TL;DR: In this paper, the authors derive and analyze several low dimensional Hamiltonian normal forms describing system symmetry breaking in ideal hydrodynamics, which are motivated by three-dimensional instabilities of rotating columnar fluid flows with circular streamlines (such as the Burger vortex) subjected to precession, elliptical distortion or off-center displacement.
TL;DR: In this paper, a linearized solution of the Laplace equation with linearized boundary conditions is presented for unsteady flow through a rectangular aquifer, and the results are compared with those of the linearized Boussinesq equation.
Abstract: A solution of the Laplace equation with linearized boundary conditions is presented for unsteady flow through a rectangular aquifer. The results are compared with those of the linearized Boussinesq equation. The linearized solution based on the Laplace equation is as, easy to use as Boussinesq's solution, has a wider range of application, and allows accurate computation of streamlines.
TL;DR: In this article, the rolling-up of the separated shear layer is modelled by a point vortex whose time-dependent circulation is predicted by an unsteady Kutta condition.
Abstract: Active circulation control of the two-dimensional unsteady separated flow past a semiinfinite plate with transverse motion is considered. The rolling-up of the separated shear layer is modelled by a point vortex whose time-dependent circulation is predicted by an unsteady Kutta condition. A suitable vortex shedding mechanism introduced. A control strategy able to maintain constant circulation when a vortex is present is derived. An exact solution for the nonlinear controller is then obtained. Dynamical systems analysis is used to explore the performance of the controlled system. The control strategy is applied to a class of flows and the results are discussed. A procedure to determine the position and the circulation of the vortex, knowing the velocity signature on the plate, is derived. Finally, a physical explanation of the control mechanism is presented.
TL;DR: In this article, vortex shedding in unsteady flow past a thin plate placed normal to the flow it studied using a Taylor-Galerkin/pressure-correction finite element algorithm is considered over restricted time periods starting from some initial steady state, eventually encountering a time after which vortices are shed, prior to the onset of regular periodic shedding.
01 Jan 1994
TL;DR: In this article, the buoyancy-induced flows of non-Newtonian fluids in a horizontal fluid saturated porous layer are studied analytically and numerically using the power-law model to characterize the non-newtonian fluid behavior.
Abstract: The buoyancy-induced flows of non-Newtonian fluids in a horizontal fluid saturated porous layer is studied analytically and numerically using the power-law model to characterize the non-Newtonian fluid behavior. A constant heat flux is applied for heating and cooling the two opposing walls of the layer while the other two walls are insulated. On the basis of a modified Darcy equation the problem is solved analytically, in the limit of a thin layer, using a parallel flow approximation and an integral form of the energy equation. Solutions for the flow and temperature fields, and Nusselt numbers are obtained explicitly in terms of the modified Rayleigh numberR and the power-law indexn. A numerical study of the same phenomenon, obtained by solving the complete system of governing equations, is also conducted. A good agreement is found between the analytical prediction and the numerical simulation.
TL;DR: In this article, the slow motion of a Newtonian fluid past a porous spherical shell has been examined and the streamlines for the flow outside of the inner core and around the spherical shell have been depicted graphically and compared with the corresponding streamlines around a non-porous sphere.
Abstract: Slow motion of a Newtonian fluid past a porous spherical shell has been examined. The flow in the free fluid region (inside the core and outside the shell) is governed by the Navier-Stokes equations whereas the flow in the porous region (shell region) is governed by the Brinkman model. The exact solution has been found under Stokes' approximation. The drag experienced by the shell has been discussed numerically for a range of values of governing parameters. The streamlines for the flow outside of the inner core and around the spherical shell have been depicted graphically and compared with the corresponding streamlines around a non-porous sphere.
TL;DR: In this article, large-eddy simulations were performed to study the turbulent reacting flows in a simulated solid-fuel combustion chamber and the effects of combustion on the unsteady flow structure and the mean flameholder recirculation zone were documented in terms of the density contours, vorticity dynamics, streamlines, mean-velocity vector fields, temperature profiles, flame position, and fuel blowing velocity.
TL;DR: In this paper, the authors used trajectory analysis to understand the effect of hydrodynamic and nonhydrodynamic forces on colloidal stability, and showed that the type of hydroynamic flow is an important determinant of the aggregation behavior of colloidal particles.
TL;DR: In this paper, the Stokes equations were used to describe the flow field generated by axial oscillations of a finite-length cylinder in an incompressible viscous fluid.
Abstract: The flow field generated by axial oscillations of a finite-length cylinder in an incompressible viscous fluid is described by the unsteady Stokes equations and computed with a first-kind boundary-integral formulation. Numerical calculations were conducted for particle oscillation periods comparable with the viscous relaxation time and the results are contrasted to those for an oscillating sphere and spheroid. For high-frequency oscillations, a two-term boundary-layer solution is formulated that involves two, sequentially solved, second-kind integral equations. Good agreement is obtained between the boundary-layer solution and fully numerical calculations at moderate oscillation frequencies. The flow field and traction on the cylinder surface display several features that are qualitatively distinct from those found for smooth particles. At the edges, where the base joins the side of the cylinder, the traction on the cylinder surface exhibits a singular behaviour, characteristic of steady two-dimensional viscous flow. The singular traction is manifested by a sharply varying pressure profile in a near-field region. Instantaneous streamline patterns show the formation of three viscous eddies during the decelerating portion of the oscillation cycle that are attached to the side and bases of the cylinder. As deceleration proceeds, the eddies grow, coalesce at the edges of the particle, and thus form a single eddy that encloses the entire particle. Subsequent instantaneous streamline patterns for the remainder of the oscillation cycle are insensitive to particle geometry: the eddy diffuses outwards and vanishes upon particle reversal; a simple streaming flow pattern occurs during particle acceleration. The evolution of the viscous eddies is most apparent at moderate oscillation frequencies. Qualitative results are obtained for the oscillatory flow field past an arbitrary particle. For moderate oscillation frequencies, pathlines are elliptical orbits that are insensitive to particle geometry; pathlines reduce to streamline segments in constant-phase regions close to and far from the particle surface.