Lubrication analysis of interacting rigid cylindrical particles in confined shear flow

Journal Article · Wed Jul 15 00:00:00 EDT 2015 · Physics of Fluids (1994)

DOI:https://doi.org/10.1063/1.4927219· OSTI ID:22482467

Cardinaels, R., E-mail: [e-mail] ^[1]; Soft Matter Rheology and Technology, Department of Chemical Engineering, KU Leuven, Celestijnenlaan 200f, P.O. Box 2424, BE3001 Leuven ^[2]; Department of Mechanical and Aerospace Engineering, Princeton University, D328 Engineering Quadrangle, Princeton, New Jersey 08544 ^[3]; Stone, H. A., E-mail: [e-mail] ^[4]

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1. Polymer Technology, Department of Mechanical Engineering, TU Eindhoven, Den Dolech 2, 5612 AZ, P.O. Box 513, 5600 MB Eindhoven (Netherlands)
2. (Belgium)
3. (United States)
4. Department of Mechanical and Aerospace Engineering, Princeton University, D328 Engineering Quadrangle, Princeton, New Jersey 08544 (United States)

Lubrication analysis is used to determine analytical expressions for the elements of the resistance matrix describing the interaction of two rigid cylindrical particles in two-dimensional shear flow in a symmetrically confined channel geometry. The developed model is valid for non-Brownian particles in a low-Reynolds-number flow between two sliding plates with thin gaps between the two particles and also between the particles and the walls. Using this analytical model, a comprehensive overview of the dynamics of interacting cylindrical particles in shear flow is presented. With only hydrodynamic interactions, rigid particles undergo a reversible interaction with no cross-streamline migration, irrespective of the confinement value. However, the interaction time of the particle pair substantially increases with confinement, and at the same time, the minimum distance between the particle surfaces during the interaction substantially decreases with confinement. By combining our purely hydrodynamic model with a simple on/off non-hydrodynamic attractive particle interaction force, the effects of confinement on particle aggregation are qualitatively mapped out in an aggregation diagram. The latter shows that the range of initial relative particle positions for which aggregation occurs is increased substantially due to geometrical confinement. The interacting particle pair exhibits tangential and normal lubrication forces on the sliding plates, which will contribute to the rheology of confined suspensions in shear flow. Due to the combined effects of the confining walls and the particle interaction, the particle velocities and resulting forces both tangential and perpendicular to the walls exhibit a non-monotonic evolution as a function of the orientation angle of the particle pair. However, by incorporating appropriate scalings of the forces, velocities, and doublet orientation angle with the minimum free fraction of the gap height and the plate speed, master curves for the forces versus orientation angle can be constructed.

• OSTI ID: 22482467
• Journal Information: Physics of Fluids (1994), Vol. 27, Issue 7; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-6631
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONFINEMENT
DIAGRAMS
HYDRODYNAMIC MODEL
LUBRICATION
ORIENTATION
PARTICLES
PLATES
REYNOLDS NUMBER
SHEAR
VELOCITY
WALLS