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Research Papers

# The Effects of Vibrations on Particle Motion in a Viscous Fluid Cell

[+] Author and Article Information
Samer Hassan

Department of Chemical Engineering and Applied Chemistry,  University of Toronto, Toronto, ON, M5S 3E5, Canada

Masahiro Kawaji1

Department of Chemical Engineering and Applied Chemistry,  University of Toronto, Toronto, ON, M5S 3E5, Canadakawaji@ecf.utoronto.ca

1

Corresponding author.

J. Appl. Mech 75(3), 031012 (May 01, 2008) (7 pages) doi:10.1115/1.2839658 History: Received November 29, 2005; Revised November 13, 2007; Published May 01, 2008

## Abstract

The effects of small vibrations on particle motion in a viscous fluid cell have been investigated experimentally and theoretically. A steel particle was suspended by a thin wire at the center of a fluid cell, and the cell was vibrated horizontally using an electromagnetic actuator and an air bearing stage. The vibration-induced particle amplitude measurements were performed for different fluid viscosities ($58.0cP$ and $945cP$), and cell vibration amplitudes and frequencies. A viscous fluid model was also developed to predict the vibration-induced particle motion. This model shows the effect of fluid viscosity compared to the inviscid model, which was presented earlier by Hassan (2004, “The Effects of Vibrations on Particle Motion in an Infinite Fluid Cell  ,” ASME J. Appl. Mech., 73(1), pp. 72–78) and validated using data obtained for water. The viscous model with modified drag coefficients is shown to predict well the particle amplitude data for the fluid viscosities of $58.5cP$ and $945cP$. While there is a resonance frequency corresponding to the particle peak amplitude for oil $(58.0cP)$, this phenomenon disappeared for glycerol $(945cP)$. This disappearance of resonance phenomenon is explained by referring to the theory of mechanical vibrations of a mass-spring-damper system. For the sinusoidal particle motion in a viscous fluid, the effective drag force has been obtained, which includes the virtual mass force, drag force proportional to the velocity, and the Basset or history force terms.

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## Figures

Figure 1

Experimental setup

Figure 3

Experimental and theoretical variations of particle amplitude with cell vibration frequency; cell amplitude: 1.0mm, steel particle diameter: 12.7mm

Figure 4

Experimental and theoretical variations of particle amplitude with dimensionless vibration frequency; cell amplitude: 1.0mm; steel particle diameter: 12.7mm

Figure 5

Experimental and theoretical variations of particle amplitude with dimensionless cell frequency for glycerol oil (945cP) and for different values of k; cell amplitude: 1.0mm

Figure 2

Instantaneous displacement of a particle for different viscosities and vibration frequencies: (a) oil (58.0cP, f=1.0Hz, a=1.0mm); (b) oil (58.0cP, f=2.0Hz, a=1.0mm); (c) glycerol (945cP, f=0.75Hz, a=8.0mm), and (d) glycerol (945cP, f=3.0Hz, a=1.0mm)

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