Elsevier

Powder Technology

Volume 381, March 2021, Pages 567-575
Powder Technology

Micro non-contact interaction between falling particles and plates in viscous fluids

https://doi.org/10.1016/j.powtec.2020.12.039Get rights and content

Highlights

  • Micro non-contact interaction of particle-plate in viscous fluid was investigated.

  • Rough surface of plates induces “braking effect” on settling particles.

  • Multi-peak of non-contact interaction force was observed.

  • Interaction height and non-contact interaction force were quantitatively evaluated.

Abstract

Frequent solid-solid interaction results in unpredicted hydrodynamic behaviors in solid-liquid two-phase flow, and the presence of liquid phases causes the interaction to be more complicated, giving rise to non-contact solid-solid interaction. In this work, we measured the micro non-contact interaction force between falling particles and plates in viscous fluids, the micro hydrodynamic behaviors of settling particles near plates were investigated, and interaction height, non-contact interaction force and collision force were quantitatively evaluated. When fluid moving front induced by settling particles contacts plates, non-contact interaction between them occurs, which is significantly strengthen by plate surface roughness, and “break effect” on interstitial fluid was observed, resulting in non-contact force peaks. Three correlations were established to quantitatively characterize the interaction height, non-contact interaction force and collision force, and good agreement is anticipated at the regimes of 9.93 < Re < 1248.35.

Introduction

Solid-liquid two-phase flow widely exists in a variety of fields of industry and nature, typic examples include fluidization bed, sand migration in river, proppant transport during hydraulic fracturing, and sewage discharge and treatment, etc. [[1], [2], [3]]. Due to the difference in physical properties between the two phases, the presence of solid phases causes the flow to be more unpredicted. Generally, complicated solid-liquid and solid-solid interactions occur, causing frequent momentum exchange that subsequently affects global hydrodynamic behavior. In addition, liquid phases intensify the complexity of solid-solid interaction, which is completely different from that of dry collisions, resulting in non-linear interaction and serious energy dissipation. Non-contact interaction between solid phases even occurs when they approach to each other, which would significantly affect the hydrodynamic behaviors of solid phases and finally change global flow of solid-liquid two phases [[4], [5], [6], [7]]. Therefore, it is of significant importance to accurately characterize the solid-solid interaction in liquid environment and evaluate the micro non-contact interaction between them, which would shed light on improving the understanding of the hydrodynamics of solid-liquid two-phase flow.

Particle collisions with the presence of liquid phases have been extensively investigated [[8], [9], [10]], which can be divided into two categories, particle colliding with liquid-coated plates and particle-plate collisions in a liquid environment. When particles fall and interact with a plate covered with a liquid layer [[10], [11], [12]], they would rebound after collision, and liquid bridge between them usually forms. However, this rebound depends on particle adhesion velocity, which increases with the increase in the thickness of liquid layer, and particle rebound is not observed when the incident velocity is smaller than the adhesion velocity. A coefficient of restitution (COR) was used to quantitatively describe the energy loss before and after collisions, which represents the ratio of particle rebound velocity to incident velocity. It is well known that liquid layers lead to smaller COR than that of dry collisions because of higher viscous damping, and COR decreases with the increase in liquid viscosity and the thickness of liquid layer, which also depends on pre-humidified objects especially in the conditions of high incidence velocity and large liquid viscosity [11]. Although the coefficient of restitution for dry collisions is independent of particle size, this scenario changes completely for wet particles. Because smaller particles correspond to larger specific surface area, stronger influence of viscous damping on small particles was observed [12]. Crüger et al. [10] confirmed this finding, and they further pointed out that particle dynamic behaviors in both tangential and normal directions depend on the thickness of liquid layers, collision angle and surface roughness. Generally, liquid phases reduce the friction between particles and plates, causing particle tangential COR to slightly increase comparing to that of dry conditions, and although it is independent of surface tension, its influence on the shape of liquid bridge and particle rotation after rebound cannot be ignored [13,14].

When particles collide with plates in a viscous liquid environment, i.e. immersion collision, viscous damping changes to be prominent, causing more complicated hydrodynamic and mechanical behaviors of particles. Similar to the collisions between particles and liquid-coated plates, particle rebound and energy dissipation were commonly evaluated in immersion collisions. Stokes number [[15], [16], [17]], the ratio of particle inertia force to viscous force, was used to predict particle rebound, and when it is smaller than a critical value (critical Stokes number), settling particles would be stuck on plate surfaces, while they rebound at higher Stokes number. Gondret et al. [16,18] observed the transient of particle collision from bounce-free to rebound with the increase in Stokes number, and they established the correlation between COR and Stokes number to estimate energy conversion and dissipation. Particle collisions at high Stokes number were evaluated by Joseph et al. [7], it was reported that the critical Stokes number is ca. 10, and particle rebound velocity is independent of nearby fluid when Stokes number is higher than 1000, then the COR approximately equals to that of dry collision, and this finding was also observed by other researchers [6,[19], [20], [21], [22]]. Accordingly, liquid phases cause more complicated solid-solid interaction, which significantly affects particle hydrodynamic and mechanical behaviors, and a deceleration process of settling particles before collision was observed [6,7], suggesting that non-contact interaction between settling particles and plates occurs because of interstitial liquid between them. The deceleration process when settling particles approach to a plate was also reported elsewhere [4,5], which is known as relating to the texture of plates. Yang and Hunt [6] evaluated the effect of surface roughness on energy dissipation, and they found that rough glass balls result in smaller energy loss than stainless steel balls. Ultimately, liquid phases increase energy dissipation of settling particles, and this inversely enhances the disturbance of flow field, causing vortex rings behind settling particles, which gradually grow into complex vortex ring system as particles approach to plates [[23], [24], [25]], causing complicated non-contact particle-plate interaction.

As mentioned above, it is clear that the collisions of settling particle with plates in a viscous liquid environment have been extensively studied [[26], [27], [28], [29]], and the deceleration behavior of settling particles near walls was observed. However, to the best of our knowledge, most of previous works mainly focused on macro evaluation of particle rebound and energy dissipation, and the microscopic hydrodynamic behavior of settling particles near walls was rarely reported, especially no quantitative characterization on this non-contact interaction was reported. Keep this in mind, here we investigated the micro hydrodynamic behavior of settling particles near rough plates, the non-contact force between settling particles and plates was measured, and interaction height, non-contact interaction force and collision force were quantitatively evaluated.

Section snippets

Experimental section

For particle-plate collisions in a liquid phase environment, an experimental setup (see in Fig. 1) was designed to accurately capture the micro hydrodynamic behaviors of settling particles near bottom plates. A cylindrical tube was used to contain glycerol solutions to mimic liquid phase environment, which is made of transparent plexiglass with the size of 240 mm in inner diameter, 10 mm in thickness and 350 mm in height. Experimental particles were artificially released using tweezers below

Measurement of micro non-contact interaction force

Fig. 3 shows the evolution of particle-plate interaction force before and after the first collision, and the green dash dot lines refer to collision point. Apparently, when particles settle in glycerol solutions, bottom plate exerts strong retardation effect on settling particles, resulting in non-contact force, which occurs when the clearance between them is less than a critical height. It is worth to note that the non-contact force is more prominent for high-viscosity fluids, so it can be

Conclusions

In liquid environment, the non-contact interaction between solid phases is anticipated, which would significantly affect particle hydrodynamic behaviors, causing complicated solid-liquid two-phase flow. To figure out the micro hydrodynamic behaviors of settling particles near plates, the non-contact force between them was measured using a dynamic force sensor, while local particle settling was recorded by a high-speed camera. When settling particles enter the action region of plates,

Declaration of Competing Interest

The authors declared that there is no conflict of interest.

Acknowledgments

This study was supported by National Natural Science Foundation of China (Grant No. 51804175, 21706269, 21978142), the Youth Innovation Talent Development Project for Universities of Shandong Province, the Taishan Scholar Project of Shandong Province (ts20190937), the Opening Fund of Key Laboratory of Unconventional Oil & Gas Development (China University of Petroleum (East China)), Ministry of Education (R1902016A), and the Fundamental Research Funds for the Central Universities.

References (36)

  • L. Wang et al.

    Dynamics and wear analysis of hydraulic turbines in solid-liquid two-phase flow

    Open Phys.

    (2019)
  • A. Mongruel et al.

    The approach of a sphere to a wall at finite Reynolds number

    J. Fluid Mech.

    (2010)
  • A. Mongruel

    Near-wall hydrodynamic interactions between a settling sphere and a wall

    J. Phys. Conf. Ser.

    (2012)
  • F.L. Yang et al.

    Dynamics of particle-particle collisions in a viscous liquid

    Phys. Fluids

    (2006)
  • G.G. Joseph et al.

    Particle-wall collisions in a viscous fluid

    J. Fluid Mech.

    (2001)
  • E.J. Hinch et al.

    The elastohydrodynamic collision of two spheres

    J. Fluid Mech.

    (1986)
  • P. Gondret et al.

    Experiments on the motion of a solid sphere toward a wall: from viscous dissipation to elastohydrodynamic bouncing

    Phys. Fluids

    (1999)
  • M.H. McLaughlin

    An Experimental Study of Particle-Wall Collision Relating to Flow of Solid Particles in Fluid

    (1968)
  • Cited by (0)

    View full text