Anomalous rolling of spheres down an inclined plane

Liu, Y.J.; Nelson, James R.; Feng, James J.; Joseph, Daniel D.

doi:10.1016/0377-0257(93)80036-b

Cited by 43 publications

(36 citation statements)

References 9 publications

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“…This direction of rotation can be characterized as reverse-contact, i.e. the particle rotates as if it is rolling up the tube near the closest contact (Liu et al 1993). If the particle is restrained from this rotation, the resultant torque acting on it can be called a 'reverse-contact torque'.…”

Section: Motion Of a Spheroid Without Inertia In Stokes Flowmentioning

confidence: 99%

Sedimentation of an ellipsoid inside an infinitely long tube at low and intermediate Reynolds numbers

Swaminathan

Mukundakrishnan

2006

J. Fluid Mech.

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The motion of a heavy rigid ellipsoidal particle settling in an infinitely long circular tube filled with an incompressible Newtonian fluid has been studied numerically for three categories of problems, namely, when both fluid and particle inertia are negligible, when fluid inertia is negligible but particle inertia is present, and when both fluid and particle inertia are present. The governing equations for both the fluid and the solid particle have been solved using an arbitrary Lagrangian-Eulerian based finite-element method. Under Stokes flow conditions, an ellipsoid without inertia is observed to follow a perfectly periodic orbit in which the particle rotates and moves from side to side in the tube as it settles. The amplitude and the period of this oscillatory motion depend on the initial orientation and the aspect ratio of the ellipsoid. An ellipsoid with inertia is found to follow initially a similar oscillatory motion with increasing amplitude. Its orientation tends towards a flatter configuration, and the rate of change of its orientation is found to be a function of the particle Stokes number which characterizes the particle inertia. The ellipsoid eventually collides with the tube wall, and settles into a different periodic orbit. For cases with non-zero Reynolds numbers, an ellipsoid is seen to attain a steady-state configuration wherein it falls vertically. The location and configuration of this steady equilibrium varies with the Reynolds number.

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Section: Motion Of a Spheroid Without Inertia In Stokes Flowmentioning

confidence: 99%

Sedimentation of an ellipsoid inside an infinitely long tube at low and intermediate Reynolds numbers

Swaminathan

Mukundakrishnan

2006

J. Fluid Mech.

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“…As soon as it deviates from the centreline, the particle acquires a rotation in the 'normal' sense, i.e. as if rolling down the nearer wall (Liu et al 1993). This regime has two remarkable features: suppression of vortex shedding and destabilization of sedimentation along the centreline.…”

Section: Cold Particlementioning

confidence: 99%

Direct numerical simulation of the sedimentation of solid particles with thermal convection

et al. 2003

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Dispersed two-phase flows often involve interfacial activities such as chemical reaction and phase change, which couple the fluid dynamics with heat and mass transfer. As a step toward understanding such problems, we numerically simulate the sedimentation of solid bodies in a Newtonian fluid with convection heat transfer. The two-dimensional Navier-Stokes and energy equations are solved at moderate Reynolds numbers by a finite-element method, and the motion of solid particles is tracked using an arbitrary Lagrangian-Eulerian scheme. Results show that thermal convection may fundamentally change the way that particles move and interact. For a single particle settling in a channel, various Grashof-number regimes are identified, where the particle may settle straight down or migrate toward a wall or oscillate laterally. A pair of particles tend to separate if they are colder than the fluid and aggregate if they are hotter. These effects are analysed in terms of the competition between the thermal convection and the external flow relative to the particle. The mechanisms thus revealed have interesting implications for the formation of microstructures in interfacially active two-phase flows. Dispersed two-phase flows often involve interfacial activities such as chemical reaction and phase change, which couple the fluid dynamics with heat and mass transfer. As a step toward understanding such problems, we numerically simulate the sedimentation of solid bodies in a Newtonian fluid with convection heat transfer. The twodimensional Navier-Stokes and energy equations are solved at moderate Reynolds numbers by a finite-element method, and the motion of solid particles is tracked using an arbitrary Lagrangian-Eulerian scheme. Results show that thermal convection may fundamentally change the way that particles move and interact. For a single particle settling in a channel, various Grashof-number regimes are identified, where the particle may settle straight down or migrate toward a wall or oscillate laterally. A pair of particles tend to separate if they are colder than the fluid and aggregate if they are hotter. These effects are analysed in terms of the competition between the thermal convection and the external flow relative to the particle. The mechanisms thus revealed have interesting implications for the formation of microstructures in interfacially active two-phase flows. Disciplines Engineering | Mechanical Engineering

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“…To end with, the work of Liu et al (1995) is of interest in this context as well. They performed experiments with spheres rolling in a viscoelastic fluid down an inclined wall and observed that the sense of the rotation is in the other direction compared with a sphere rolling down an inclined plane in a Newtonian fluid (in which case it rotates as in air).…”

Section: B History Of the Subjectmentioning

confidence: 99%

Viscoelastic flow past a confined cylinder of a polyisobutylene solution

Baaijens

Peters

Baaijens

et al. 1995

Journal of Rheology

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SynopsisViscoelastic constitutive equations are evaluated using the benchmark problem of the planar flow past a confined cylinder for a well-characterized solution of S%(w/w) polyisobutylene in tetradecane. The ratio of channel height to cylinder diameter is equal to two. We compare finite element simulations with point-wise measured velocities and stresses obtained by means of laser Doppler anemometry and a flow-induced birefringence technique, respectively. The Deborah number (De) ranges from 0.25 to 2.32. In the case of the geometry with a symmetrically confined cylinder, computations were made with a generalized Newtonian model and with both a single-and a four-mode Phan-Thien and Tanner (PlT) model. All model parameters were determined in simple shear flow. A similar analysis is presented in case of an asymmetrically confined cylinder (with De = 1.87). Impressively good agreement was found between the predictions of the four-mode P'IT model and the measured velocities and stresses. The agreement was even excellent in the geometry with the asymmetrically confined cylinder. 0 I995 Society of Rheology.

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Anomalous rolling of spheres down an inclined plane

Cited by 43 publications

References 9 publications

Sedimentation of an ellipsoid inside an infinitely long tube at low and intermediate Reynolds numbers

Sedimentation of an ellipsoid inside an infinitely long tube at low and intermediate Reynolds numbers

Direct numerical simulation of the sedimentation of solid particles with thermal convection

Viscoelastic flow past a confined cylinder of a polyisobutylene solution

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