Quiescent Newtonian Fluid Research Articles

On the dynamics and wakes of a freely settling Platonic polyhedron in a quiescent Newtonian fluid

We investigate systematically the free settling of a single Platonic polyhedron in an unbounded domain filled with an otherwise quiescent Newtonian fluid. We consider a particle–fluid density mimicking a rock in water. Five Platonic polyhedrons of increasing sphericity are studied for a range of Galileo numbers $10 \leqslant \mathcal {G}a \leqslant 300$ . We construct a regime map in the parameter space of Galileo number and particle volume fraction ( $\mathcal {G}a, \phi$ ), highlighting how the angularity of the Platonic polyhedron impacts its settling path and the onset of instabilities. We find that the initial angular position solely affects the transient settling process. All the Platonic polyhedrons maintain a stable settling angular position at low $\mathcal {G}a$ . Higher angularity leads to path unsteadiness at lower $\mathcal {G}a$ . Path instability progresses from steady vertical to unsteady vertical, followed by oblique settling observed for highly spherical particles, but helical settling (HS) for more angular particles. The particle autorotation is found to be the pivotal factor influencing path instability and the regime transition of angular particles. Beginning in the unsteady oblique and helical regimes, particle autorotation becomes more prevalent, escalating further in the chaotic regime as $\mathcal {G}a$ increases. The particle angular velocity vector is shown to be predominantly situated in the horizontal plane. A thorough force balance in the horizontal plane reveals that the Magnus force is the primary driving force of the HS regime. Additionally, we establish two new empirical correlations to predict the particle settling velocity and the disturbed wake length that solely require the physical properties of the system ( $\mathcal {G}a$ and $\phi$ ). Our numerical results suggest that an increase of the density ratio from $2$ to $3$ exerts only a marginal impact on the path instability of the most angular particle, the settling tetrahedron.

Computational fluid dynamic investigating the reactive species transfer across the interface of a single rising bubble

This study implements a new solver (reactiveInterFoam) to simulate the component mass transfer alongside deformable gas–liquid interfaces. Mass transfer from the rising bubble in a quiescent Newtonian fluid is simulated. An effect of bubble hydrodynamics on the simultaneous diffusion reaction and selectivity of the cyclohexane oxidation process is investigated on a two-dimensional axisymmetric domain. The color function volume of fluid (CF-VoF) technique is applied to capture the deformable interface, and the continuous species transfer method is used to monitor the gas–liquid mass transfer behavior. Several simulations have been conducted to validate the model reliability to forecast component mass transfer from the bubble to the liquid phase, bubble shape, and flow field. Simulation findings approved that the rate of mass transfer is a function of boundary’s concentration, layer thickness, and bubble surface area. Furthermore, the selectivity increases by decreasing bubble diameter in both spherical and ellipsoidal regimes. The small bubbles with a lower Reynolds number have higher average selectivity. Comparing the simulated bubble shape and the grace chart indicates that the suggested numerical method can perfectly predict bubble regimes. The absolute average relative deviation (AARD%) of 14.59% has been observed between the terminal velocities predicted by the numerical simulation and six experimental measurements.

Transient and passage to steady state in fluid flow and heat transfer within fractional models

PurposeThe classical integer derivative diffusionmodels for fluid flow within a channel of parallel walls, for heat transfer within a rectangular fin and for impulsive acceleration of a quiescent Newtonian fluid within a circular pipe are initially generalized by introducing fractional derivatives. The purpose of this paper is to represent solutions as steady and transient parts. Afterward, making use of separation of variables, a fractional Sturm–Liouville eigenvalue task is posed whose eigenvalues and eigenfunctions enable us to write down the transient solution in the Fourier series involving also Mittag–Leffler function. An alternative solution based on the Laplace transform method is also provided.Design/methodology/approachIn this work, an analytical formulation is presented concerning the transient and passage to steady state in fluid flow and heat transfer within the diffusion fractional models.FindingsFrom the closed-form solutions, it is clear to visualize the start-up process of physical diffusion phenomena in fractional order models. In particular, impacts of fractional derivative in different time regimes are clarified, namely, the early time zone of acceleration, the transition zone and the late time regime of deceleration.Originality/valueWith the newly developing field of fractional calculus, the classical heat and mass transfer analysis has been modified to account for the fractional order derivative concept.

Path instabilities of a freely rising or falling sphere

Path instabilities of a sphere rising or falling in a quiescent Newtonian fluid have been studied experimentally. The rich palette of possible instabilities is dependent upon two dimensionless quantities, namely the Galileo number (Ga) and the particle/fluid mass density ratio (ρ¯). In recent literature, several (Ga,ρ¯) regime maps have been proposed to characterize path instabilities, based on both numerical and experimental studies, with substantial disagreements among them. The present study attempts to shed light on path instabilities for which previous studies disagree. A detailed experimental investigation has been conducted for 219 different combinations of Ga and ρ¯, grouped around four values of ρ¯ (∼ 0.87, 1.12, 3.19 and 3.9) and Ga in the range of ∼ 100 to 700. Our results agree well with literature for the low Ga range in which a particle takes a steady vertical or steady oblique path and for which all previous studies agree with each other. For the higher and more controversial Ga range, we discuss consensus and disagreements with previous studies. Some regimes, which were only recently observed in numerical simulations, have been observed experimentally for the first time. Also, intriguing bi-stable regimes (i.e., coexistence of two stable asymptotic states) have been observed. For all four investigated density ratios, an update of the regime map is proposed. Finally, for both the rising and falling spheres, the drag coefficient as function of terminal settling Reynolds number has been determined, which for the investigated density ratios does not differ significantly from that of flow past a fixed sphere.

On the dynamic behaviors of freely falling annular disks at different Reynolds numbers

Freely falling or rising objects in quiescent Newtonian fluid have been frequently encountered in nature or industry, such as the spreading of seeds from a tree or the movement of ores in deep sea mining. The dynamic behaviors of freely moving objects can provide a significant understanding of the evolution of the body wake and the resulting path instability. In this study, we present numerical simulations of freely falling annular disks released from quiescent water for relatively low Reynolds numbers from 10 to 500 while keeping the non-dimensional moment of inertia I* and inner to outer diameter ratio η constant. The falling stage experiences a variation from quasi-one-dimensional mode, steady oblique motion (SO motion), to the fully three-dimensional mode, helical motion. The stage diagram is plotted to show the variation tendency with the increment of Reynolds numbers. The detailed characteristics of the trajectories and orientation of the annular disks for different motions are analyzed. The corresponding vortical structures are presented, and an analog of the wingtip vortex is found at the outer rim of the disk for transitional and helical motion. A steady recirculation region of SO motion is observed, which is similar to that of a stationary disk but with complex multilayer structures formed by the combined effects of both the inner and outer rims. The limit streamline and pressure coefficient are investigated, demonstrating that the asymmetrical pressure distribution that exerts fluid forces and torques on the disk plays a crucial role in the dynamic response of the disk. Furthermore, combining the flow fields and fluid forces, the physical mechanism responsible for the diverse falling patterns is explored in detail.

Path instabilities of oblate spheroids

In the present paper, we investigate the path instabilities and the transition scenario for oblate homogeneous spheroids falling (or ascending) freely in a quiescent and unconfined Newtonian fluid under the action of gravity, buoyancy and hydrodynamic forces. The problem depends on three independent external parameters: the aspect ratio $\unicode[STIX]{x1D712}=d/a$, where $d$ is the diameter and $a$ the length of the axisymmetry axis of the spheroid; the non-dimensionalized mass $m^{\ast }=m/(\unicode[STIX]{x1D70C}d^{3})$, $m$ being the mass of the spheroid and $\unicode[STIX]{x1D70C}$ the fluid density; and the Galileo number, defined as $G=\sqrt{(m^{\ast }-V^{\ast })gd^{3}}/\unicode[STIX]{x1D708}$. In the definition of the Galileo number, $V^{\ast }=V/d^{3}$ is the non-dimensionalized volume, $g$ the gravitational acceleration and $\unicode[STIX]{x1D708}$ is the kinematic viscosity. Asymptotic solutions (regimes) are investigated in seven $\unicode[STIX]{x1D712}=\text{const}.$ parameter planes going from $\unicode[STIX]{x1D712}=10$ (very flat spheroid) to $\unicode[STIX]{x1D712}=1.1$ (an almost spherical shape), for $m^{\ast }$ going from 0 to 5 and Galileo numbers up to 300 (i.e. Reynolds numbers roughly up to 500). The obtained results provide a link between the known scenario of a homogeneous disk and that, well known, of a sphere. The scenario of the flat spheroid of aspect ratio 10 has many common features with that of an infinitely thin disk, but the finite thickness brings about significant quantitative differences. At the opposite side of the investigated aspect ratio interval, the dynamics of the spheroid of aspect ratio 1.1 is found very close to that of a perfect sphere except for small density ratios (smaller than approximately 0.5). Very light spheroids of aspect ratio 1.1 move along vertical zig-zagging trajectories. At intermediate aspect ratios, the strong subcritical effects and the characteristic zig-zagging and fluttering motion, typical for flat bodies, progressively disappear. The tumbling regime remains remarkably stable and is shown to be present down to $\unicode[STIX]{x1D712}=2$. An interesting result consists in the evidence of the first two bifurcations typical for the sphere scenario (leading to steady oblique and oblique oscillating trajectories) present both for very flat and thick spheroids but absent at intermediate aspect ratios. The results pertaining to spheroids might be more useful in practical applications than those obtained for too idealized thin disks and perfect spheres.

Effects of inertia and viscoelasticity on sedimenting anisotropic particles

An axisymmetric particle sedimenting in an otherwise quiescent Newtonian fluid, in the Stokes regime, retains its initial orientation. For the special case of a spheroidal geometry, we examine analytically the effects of weak inertia and viscoelasticity in driving the particle towards an eventual steady orientation independent of initial conditions. The generalized reciprocal theorem, together with a novel vector spheroidal harmonics formalism, is used to find closed-form analytical expressions for the$O(\mathit{Re})$inertial torque and the$O(\mathit{De})$viscoelastic torque acting on a sedimenting spheroid of an arbitrary aspect ratio. Here,$\mathit{Re}=UL/{\it\nu}$is the Reynolds number, with$U$being the sedimentation velocity,$L$the semi-major axis and${\it\nu}$the fluid kinematic viscosity, and is a measure of the inertial forces acting at the particle scale. The Deborah number,$\mathit{De}=({\it\lambda}U)/L$, is a dimensionless measure of the fluid viscoelasticity, with${\it\lambda}$being the intrinsic relaxation time of the underlying microstructure. The analysis is valid in the limit$\mathit{Re},\mathit{De}\ll 1$, and the effects of viscoelasticity are therefore modelled using the constitutive equation of a second-order fluid. The inertial torque always acts to turn the spheroid broadside-on, while the final orientation due to the viscoelastic torque depends on the ratio of the magnitude of the first ($N_{1}$) to the second normal stress difference ($N_{2}$), and the sign (tensile or compressive) of$N_{1}$. For the usual case of near-equilibrium complex fluids – a positive and dominant$N_{1}$($N_{1}>0$,$N_{2}<0$and$|N_{1}/N_{2}|>1$) – both prolate and oblate spheroids adopt a longside-on orientation. The viscoelastic torque is found to be remarkably sensitive to variations in${\it\kappa}$in the slender-fibre limit (${\it\kappa}\gg 1$), where${\it\kappa}=L/b$is the aspect ratio,$b$being the radius of the spheroid (semi-minor axis). The angular dependence of the inertial and viscoelastic torques turn out to be identical, and one may then characterize the long-time orientation of the sedimenting spheroid based solely on a critical value ($\mathit{El}_{c}$) of the elasticity number,$\mathit{El}=\mathit{De}/\mathit{Re}$. For$\mathit{El}<\mathit{El}_{c}~({>}\mathit{El}_{c})$, inertia (viscoelasticity) prevails with the spheroid settling broadside-on (longside-on). The analysis shows that$\mathit{El}_{c}\sim O[(1/\text{ln}\,{\it\kappa})]$for${\it\kappa}\gg 1$, and the viscoelastic torque thus dominates for a slender rigid fibre. For a slender fibre alone, we also briefly analyse the effects of elasticity on fibre orientation outside the second-order fluid regime.

Analytical study on accelerating falling of non-spherical particle in viscous fluid

Unsteady motion of a vertically falling non-spherical particle has attracted considerable attention due to its frequent applications in nature and industry. A series of semi-analytical methods have been used to raise the results' accuracy as well as widening the region of convergence. The current study pursued a new analytical solution for the unsteady motion of a rigid non-spherical particle in a quiescent Newtonian fluid, based on the Optimal Homotopy Analysis Method. With a view towards obtaining the highest level of accuracy and ensuring the convergence of the analytical results, the averaged residual errors were obtained and minimized. In addition to flexibility, it was also proven that the proposed method can lead to completely reliable and precisely accurate results. Based on the series solution, the effects of physical parameters on the terminal settling velocity (i.e. the greatest velocity that a falling body may reach) and the acceleration time (i.e. the time that a particle reaches the settling velocity) are investigated.

Temporal multiscale approach for nanocarrier motion with simultaneous adhesion and hydrodynamic interactions in targeted drug delivery

We present a fluctuating hydrodynamics approach and a hybrid approach combining fluctuating hydrodynamics with generalized Langevin dynamics to resolve the motion of a nanocarrier when subject to both hydrodynamic interactions and adhesive interactions. Specifically, using these approaches, we compute equilibrium probability distributions at constant temperature as well as velocity autocorrelation functions of the nanocarrier subject to thermal motion in a quiescent Newtonian fluid medium, when tethered by a harmonic spring force mimicking a tether due to a single receptor–ligand bond. We demonstrate that the thermal equipartition of translation, rotation, and spring degrees of freedom are preserved by our formalism while simultaneously resolving the nature of the hydrodynamic correlations. Additionally, we evaluate the potential of mean force (or free energy density) along a specified reaction coordinate to facilitate extensive conformational sampling of the nanocarrier motion. We show that our results are in excellent agreement with analytical results and Monte Carlo simulations, thereby validating our methodologies. The frameworks we have presented provide a comprehensive platform for temporal multiscale modeling of hydrodynamic and microscopic interactions mediating nanocarrier motion and adhesion in vascular targeted drug delivery.

Stability of the shape of a translating viscoelastic drop at low Reynolds number

We examine the stability of the shape of a viscoelastic drop translating in an immiscible, otherwise quiescent Newtonian fluid at low Reynolds number. Non-Newtonian stresses in the drop phase are characterized by the finitely extensible nonlinear elastic-Chilcott-Rallison model. A boundary integral method is used to numerically examine the time-evolution of initially perturbed drop shapes over a range of dimensionless parameters. For sufficiently small capillary numbers, the drop achieves an oblate spheroidal steady shape. For large initial deformations or capillary numbers, however, the drop deforms continuously and eventually breaks up through either the formation of an elongated tail or the development of a re-entrant cavity at its trailing end. These mechanisms of drop breakup are qualitatively similar to those reported earlier for Newtonian drops [C. J. Koh and L. G. Leal, Phys. Fluids A 1, 1309 (1989)10.1063/1.857359; C. Pozrikidis, J. Fluid Mech. 210, 1 (1990)10.1017/S0022112090001203; H. A. Stone, Annu. Rev. Fluid Mech. 26, 65 (1994)10.1146/annurev.fl.26.010194.000433]. Compared to the case of a Newtonian drop, drop phase elasticity is found to have a stabilizing (destabilizing) effect for initially oblate (prolate) shape perturbations, due to the development of polymeric stresses caused by deformation of polymer chains in alignment with streamlines of the flow. Polymer viscosity has a strong influence on the stability of the shape of drops, whereas polymer relaxation time and extensibility have relatively weak influences.

Natural Convection Heat and Mass Transfer in the Boundary Layer along a Vertical Cylinder with Opposing Buoyancies

The effects of opposing buoyancies on natural convection heat and mass transfer in the boundary layer over a vertical cylinder immersed in a quiescent Newtonian fluid are presented in this paper. The surface of the cylinder is maintained at a constant temperature and concentration. The homotopic transformation is proposed to transform the physical domain into a flat plate. The boundary layer equations and the boundary conditions are solved numerically using an implicit finite difference scheme and the Gauss-Seidel algorithm. The buoyancy ratio N, Prandtl number Pr and Schmidt number Sc are important parameters for this problem. The numerical results for Pr=Sc and Pr≠ Sc, including the velocity, temperature, concentration fields and the Nusselt number as well as the Sherwood number along the surface of the cylinder are discussed for aiding and opposing buoyancies. Results show that the Nusselt (Sherwood) number increases with positive or negative buoyancies ration N (N=Grc/Grt). Moreover, for opposing flows with Sc<Pr , the flow is completely downward, the thickness of the concentration layer is larger than that of the thermal layer . For Pr<Sc , the velocity are weak and the thermal layer thickness is much larger.

The dynamics and rheology of a dilute suspension of periodically forced neutrally buoyant spherical particles in a quiescent Newtonian fluid at low Reynolds numbers

We study the effects of both convective and unsteady inertia on the dynamics and rheology of a dilute suspension of periodically forced neutrally buoyant spherical particles, at low Reynolds numbers, in a quiescent Newtonian fluid. The inclusion of inertia results in additional terms in the equation governing the dynamics of the particle that represent a fading memory of the entire history of the particle motion. The inclusion of convective inertia in the low Reynolds number limit makes the memory term nonlinear. Several tests were performed to show that the results presented in this paper are physically reasonable and correct. A perturbation analysis of the problem yields strong evidence that the results of our simulations are correct. It is observed that there is a preferred direction in this system which manifests itself in the properties of the solution. This preferred direction is identified as the direction of the initial motion of the particle. We present here results on the behavior of various parameters with respect to Reynolds numbers and the amplitude of the periodic force. These include phase-space plots between particle displacement and particle velocity and the variation of a rheological parameter, namely a ‘normal stress’ with respect to Reynolds number and the amplitude of the periodic force. We believe that our results may be technologically important since the rheological parameter depends strongly on controllable parameters such as the Reynolds number and the amplitude of the periodic force. Further, this system is one of the simplest systems whose rheology shows non-Newtonian behavior, such as the presence of a normal stress. In addition, this system represents a physically realizable system for experimentally testing the frameworks developed to calculate the collective behavior of systems of oscillators with memory.

Dynamics and ‘normal stress’ evaluation of dilute suspensions of periodically forced prolate spheroids in a quiescent Newtonian fluid at low Reynolds numbers

The problem of determining the force acting on a particle in a fluid where the motion of the fluid and the particle is given has been considered in some detail in the literature. In this work, we propose an example of a new class of problems where, the fluid is quiescent and the effect of an external periodic force on the motion of the particle is determined at low non-zero Reynolds numbers. We present an analysis of the dynamics of dilute suspensions of periodically forced prolate spheroids in a quiescent Newtonian fluid at low Reynolds numbers including the effects of both convective and unsteady inertia. The inclusion of both forms of inertia leads to a nonlinear integro — differential equation which is solved numerically for the velocity and displacement of the individual particle. We show that a ‘normal stress’ like parameter can be evaluated using standard techniques of Batchelor. Hence this system allows for an experimentally accessible measurable macroscopic parameter, analogous to the ‘normal stress’, which can be related to the dynamics of individual particles. We note that this ‘normal stress’ arises from the internal fluctuations induced by the periodic force. In addition, a preliminary analysis leading to a possible application of separating particles by shape is presented. We feel that our results show possibilities of being technologically important since the ‘normal stress’ depends strongly on the controllable parameters and our results may lead to insights in the development of active dampeners and smart fluids. Since we see complex behaviour even in this simple system, it is expected that the macroscopic behaviour of such suspensions may be much more complex in more complex flows.

Dynamic Simulation of Capillary Breakup of Nematic Fibers: Molecular Orientation and Interfacial Rupture

We simulate the breakup of cylindrical fibers of a nematic liquid crystal surrounded by a quiescent Newtonian fluid. The nematic is described by the Leslie-Ericksen theory, and the interfacial motion is captured by a phase-field method from the initial linear instability to final breakup. The focus is on the coupling between liquid crystal molecular orientation and the evolution of the interface. In particular, we examine how molecular anchoring on the interface and orientational distortion in the bulk affect the growth of capillary waves. Results show that the nematic order tends to hinder capillary wave development, in qualitative agreement with prior linear instability analysis. For typical materials, however, the effect becomes prominent only for nano-scale fibers. In addition, anisotropic viscosity plays a significant role in the growth rate of the capillary wave. In the nonlinear stage of the instability, neighboring waveforms grow at different speeds and lead to daughter drops of nonuniform sizes, which typically display the bipolar configuration with two boojum defects. Despite quantitative differences, the breakup of nematic fibers proceeds in mostly the same way as Newtonian ones. The numerical simulations are in general agreement with previous experimental observations.

The Dynamics of Periodically Forced Prolate Spheroids in a Quiescent Newtonian Fluid with Weak Inertia

The effects of convective and unsteady inertia on the dynamics of periodically forced neutrally buoyant prolate spheroids in a quiescent Newtonian fluid medium, at low Reynolds numbers have been modeled. The resulting nonlinear equations have been solved using appropriate numerical methods. Several tests including a perturbation analysis are performed to validate results. A preferred direction, which is identified as the initial direction of motion, is observed that manifests itself in the properties of the solution. Results of the behavior of various parameters with respect to the Reynolds number, aspect ratio of the spheroid and the amplitude of the periodic force are presented. The results are technologically important as they may lead to insights in the development of active dampeners and smart fluids.

Prandtl number scaling of unsteady natural convection boundary layers forPr&gt;1fluids under isothermal heating

In this paper, the scalings incorporating the Prandtl number (Pr) dependence have been obtained by a scaling analysis for the unsteady natural convection boundary layer of an initially quiescent isothermal Newtonian fluid of Pr>1 produced by the sudden imposition of a higher temperature on a vertical plate. It is shown that the transient flow behavior of the resulting boundary layer can be described by a three-region structure and at the start-up stage the boundary layer development is one dimensional and independent of height due to the dominance of pure conduction; however, at steady state it becomes two dimensional and height dependent as the flow becomes dominated by convection. Numerical results demonstrate that the scalings representing the thermal boundary layer development accurately represent their Pr dependence over the whole stage of flow development. The scalings representing the viscous boundary layer development are generally in good agreement with the numerical results with the Pr variation over the whole stage of flow development, although there are small deviations from the numerical results with the Pr variation that are within acceptable limits for scaling.

Harmonic oscillations of a circular cylinder moving with constant velocity in a quiescent fluid

The flow around an oscillating circular cylinder which moves with constant velocity in a quiescent Newtonian fluid with constant properties is analyzed. The influences of the frequency and amplitude oscillation on the aerodynamic loads and on the Strouhal number are presented. For the numerical simulation, a cloud of discrete Lamb vortices are utilized. For each time step of the simulation, a number of discrete vortices are placed close to the body surface; the intensity of theirs is determined such as to satisfy the no-slip boundary condition.

&lt;strong&gt;Harmonic oscillations of a circular cylinder moving with constant velocity in a quiescent fluid&lt;/strong&gt;&lt;br&gt; DOI: 10.5585/exacta.v6i1.663

The flow around an oscillating circular cylinder which moves with constant velocity in a quiescent Newtonian fluid with constant properties is analyzed. The influences of the frequency and amplitude oscillation on the aerodynamic loads and on the Strouhal number are presented. For the numerical simulation, a cloud of discrete Lamb vortices are utilized. For each time step of the simulation, a number of discrete vortices are placed close to the body surface; the intensity of theirs is determined such as to satisfy the no-slip boundary condition.

High Reynolds number oscillations of a circular cylinder

This paper concerns the numerical simulation of the flow around an oscillating circular cylinder, which moves with constant velocity in a quiescent Newtonian fluid with constant properties. For each time step of the simulation a number of discrete Lamb vortices is placed close to the body surface; the intensity of each of these is determined such as to satisfy the no-slip boundary condition. The aerodynamic loads acting on the surface of cylinder are computed using the integral formulation derived from the pressure Poisson equation. The influence of the frequency and amplitude oscillation on the aerodynamic loads and on the Strouhal number is presented and discussed.

On the motion of a porous sphere in a Stokes flow parallel to a planar confining boundary

An analysis is presented of the three-dimensional creeping flow in and around a porous sphere, modelled as a generalized Brinkman medium, near a smooth plane where the sphere (i) translates uniformly without rotating in an otherwise quiescent Newtonian fluid, (ii) rotates uniformly without translating in an otherwise quiescent Newtonian fluid, and (iii) is fixed in a shear field, which is uniform in the far field and has a linearly increasing velocity profile with increasing distance from the plane. The linear superposition of these three flow regimes is also considered for the special case of the free translational and rotational motion of a neutrally buoyant porous sphere in a shear field that is uniform in the far field. Exact series solutions to the momentum equations are derived for the velocity and pressure fields in the Brinkman and Stokes-flow regions. Coefficients in the series solutions for each flow regime are determined using recursion relations derived from the continuity equations in the Brinkman and Stokes-flow regions, from the interfacial boundary conditions on the porous spherical surface, and from the no-slip condition on the plane. Results are presented in terms of the drag force on the porous sphere and torque about the sphere centre as a function of the dimensionless clearance distance between the sphere and the rigid plane for several values of the dimensionless hydraulic permeability of the Brinkman medium. The free motion of the neutrally buoyant sphere is calculated by requiring that the net hydrodynamic drag force and torque acting on the sphere vanish. Results for this case are presented in terms of the dimensionless translational and rotational speeds of the porous sphere relative to the far-field shear rate as a function of the dimensionless clearance distance for several values of the dimensionless hydraulic permeability. The work is motivated by insights it offers into the behaviour of porous agglomerates, and by its potential utility in industrial, biological, biophysical, medicinal and environmental applications wherever gas or liquid suspensions of porous agglomerates might arise.