Elastohydrodynamic theory for wet oblique collisions

Kantak, Advait A.; Davis, Robert H.

doi:10.1016/j.powtec.2006.07.006

Cited by 24 publications

(31 citation statements)

References 21 publications

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“…(Colour online) Restitution coefficient for normal (head-on) collisions for case µ med x 0,large ss a large compared for the current theory, Davis (1987), and Kantak & Davis (2006). which particles only rebound due to surface roughness, has the simple form…”

Section: Methodsmentioning

confidence: 90%

“…Lubrication The viscous (lubrication) force that resists the relative motion of the particles acts in both the normal and the tangential directions. For small deformations and for x a, the normal component of the lubrication force has been derived by Kantak & Davis (2006) for liquid-coated spheres as…”

Section: Solid Particlementioning

confidence: 99%

“…Two other theories are also compared to experimental results. The theory of Kantak & Davis (2006) uses a complete treatment of elastohydrodynamics to model a wetted collision, but with constant viscosity. The theoretical predictions of Kantak & Davis (2006) have a somewhat fortuitous match of St * n , since not including the glass transition provides for closer approach and more resistance that balances the lack of (known) resistance upon rebound due to presumed cavitation; however, e w,n is underpredicted for St n > St * n .…”

Section: Reversal Criteriamentioning

confidence: 99%

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Agglomeration and de-agglomeration of rotating wet doublets

et al. 2012

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In this work, experiments using a pendulum apparatus were conducted for two particles engaged in oblique, wetted collisions over a range of impact angles, impact velocities, coating thicknesses, liquid viscosities, particle materials, and particle radii. From previous studies on normal or head-on collisions, the two particles bounce apart if the Stokes number (a ratio of particle inertia to viscous forces) exceeds a critical value, whereas they stick together if the Stokes number is below this critical value. However, for oblique collisions, an additional outcome is observed at moderate Stokes numbers and impact angles, in which the spheres initially stick together, rotate as a doublet, and then separate due to centrifugal forces. We refer to this outcome as 'stick-rotate-separate'. For subcritical Stokes numbers exhibiting this new outcome, the experimental results for the apparent coefficient of normal restitution and angle of rotation from impact to separation show only weak dependence on the fluid viscosity and thickness and the dry restitution coefficient, whereas they both decrease with increasing particle radius. These results are in contrast with those for supercritical Stokes numbers in which the spheres bounce upon impact. An accompanying theory based on lubrication forces, the glass transition of the liquid layer, and solid deformation and rebound agrees well with experimental results and gives insight into the observed trends.

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Section: Methodsmentioning

confidence: 90%

Section: Solid Particlementioning

confidence: 99%

Section: Reversal Criteriamentioning

confidence: 99%

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Agglomeration and de-agglomeration of rotating wet doublets

et al. 2012

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“…The capillary forces are generally negligible for high-inertia collisions and have therefore been neglected in the model for restitution coefficient presented in Kantak and Davis. 9 The outcome of collisions between two wet particles has been detailed in previous studies. To summarize, Davis et al 1 gave the first criterion for predicting whether spheres colliding while fully immersed in a liquid will stick or rebound.…”

Section: Introductionmentioning

confidence: 99%

Initial rates of aggregation for dilute, granular flows of wet particles

2009

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Molecular dynamics (MD) simulations are used to determine the agglomeration rates of wet grains (particles coated with a viscous, liquid layer) engaged in simple shear flow under dilute conditions. In this work, a closed-form model derived from the elastohydrodynamic theory describes the normal restitution coefficient for binary collisions. Unlike previous MD studies, the particle deformation is not assumed to depend on a particle “overlap” (penetration), but instead depends on the formal coupling of Hertzian deformation theory with lubrication theory. The initial rate of doublet formation is studied as a function of system properties and the energy input to the system. In addition to the system properties, the distribution of relative velocities in the system is found to be a key factor influencing the initial rates of clustering. A theory based on estimating the collision frequency and the critical velocity below which no rebound is observed—due to viscous dissipation—is found to provide a good approximation of the initial aggregation rate. The rate of aggregation is found to increase with increasing number of particles in the system, increasing solid fraction, decreasing overall Stokes number, and decreasing compliance parameter.

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“…A comprehensive model for oblique impacts was presented in further work by Kantak & Davis (2006). Donahue et al (2010) investigated three-particle collisions using a Stokes' cradle, comparing their results to the theory of a series of two-particle collisions.…”

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confidence: 99%

Cavitation structures formed during the collision of a sphere with an ultra-viscous wetted surface

et al. 2016

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We investigate the inception of cavitation and resulting structures when a sphere collides with a solid surface covered with a layer of non-Newtonian liquid having a kinematic viscosity of up to ν 0 = 20 000 000 cSt. We show the existence of shear-stress-induced cavitation during sphere approach towards the base wall (i.e. the pressurization stage) in ultra-viscous films using a synchronized dual-view high-speed imaging system. For the experimental parameters employed, liquids having viscoelastic properties of De O(1) are shown to enable sphere rebound without any prior contact with the solid wall. Cavitation by depressurization (i.e. during rebound) in such non-contact cases is observed to onset after a noticeable delay from when the minimum gap distance is reached. Also, the cavities created originate from remnant bubbles, being the remains of the primary bubble entrapment formed by the lubrication pressure of the air during film entry. Cases where physical contact occurs (contact cases) in 10 000 cSt ν 0 1000 000 cSt films produce cavities attached to the base wall, which extend into an hourglass shape. In contrast, strikingly different structures occur in the most viscous liquids due to the disproportionality in radial expansion and longitudinal extension along the cavity length. Horizontal shear rates calculated using particle image velocimetry (PIV) measurements show the apparent fluid viscosity to vary substantially as the sphere approaches and rebounds away from the base wall. A theoretical model based on the lubrication assumption is solved for the squeeze flow in the regime identified for shear-induced cavity events, to investigate the criterion for cavity inception in further detail.

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Elastohydrodynamic theory for wet oblique collisions

Cited by 24 publications

References 21 publications

Agglomeration and de-agglomeration of rotating wet doublets

Agglomeration and de-agglomeration of rotating wet doublets

Initial rates of aggregation for dilute, granular flows of wet particles

Cavitation structures formed during the collision of a sphere with an ultra-viscous wetted surface

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