Preferential accumulation of particles in periodic channels

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Table of contents

1 STATE OF THE ART 
1.1 Particle-ladenows: Basic concepts
1.1.1 Denition of particle inertia
1.1.2 Particle transport in closed channel ows
1.1.3 Focusing phenomena in closed channels
1.1.3.a. Lift-induced inertial migration
1.1.3.b. Preferential accumulation of particles in periodic channels
1.2 Flow in channels with at and corrugated walls
1.2.1 Modeling ow in rough fractures
1.2.2 Inertial eects in fracture ows
1.2.3 Idealized model of fracture geometry
2 SINGLE PHASE FLOW THROUGH FRACTURES 
2.1 Geometrical description of fractures with corrugated walls
2.2 Governing equations
2.2.1 Flow between parallel at walls: the cubic law
2.2.2 Flow between corrugated walls: the local cubic law
2.2.3 Flow velocity components in corrugated channels
2.3 Inuence of the fracture geometry on its hydraulic aperture
2.3.1 x eect
2.3.2 eect
2.4 Inuence of the fracture geometry on the validity of the LCL for dierent Reynolds numbers
2.4.1 Numerical Method
2.4.2 Low Re (< 1)
2.4.2.a. Relative error between the LCL and NS solutions for three reference geometries
2.4.2.b. Inuence of , 0, and x on the relative error between the
LCL and NS solutions
2.4.3 High Re (> 1)
2.4.3.a. Relative error between the LCL and NS solutions for the reference geometries
2.4.3.b. Inuence of , 0, and x on the relative error between the LCL and NS solutions
2.5 Discussions
2.5.1 Relation between the hydraulic and the mean apertures
2.5.2 Validity of the local cubic law for dierent Reynolds numbers
2.6 Conclusion
3 TRANSPORT AND DEPOSITION OF WEAKLY-INERTIAL PARTI- CLES IN FRACTURE FLOWS 
3.1 Governing equations
3.1.1 Forces acting on each particle
3.1.2 Particle motion equation and particle trajectory equation
3.1.2.a. Focusing of weakly inertial particles in channels with periodic walls
3.1.2.b. Trajectory equation of inertia-free particles
3.1.2.c. Channel with at walls
3.1.2.d. Channel with sinusoidal walls
3.2 Numerical verication
3.2.1 Simulation procedure
3.2.2 Results
3.2.2.a. Particle focusing
3.2.2.b. Particle trajectories
3.3 Particle transport regime diagrams
3.3.1 Channel with at walls
3.3.2 Corrugated channel with sinusoidal walls
3.3.2.a. Channel with in phase walls
3.3.2.b. Channel with out of phase identical walls
3.3.2.c. Channel with maximum phase lag between the walls
3.3.3 Summary
3.4 Conclusion
4 EXPERIMENTAL INVESTIGATION OF PARTICLE TRANSPORT IN FRACTURE FLOWS 
4.1 Experimental setup and procedure
4.1.1 Open channel with closed circuit ow
4.1.2 Fractures with at and sinusoidal walls
4.1.3 Liquid properties
4.1.4 Visualization and image treatment
4.2.4.a. Lighting
4.2.4.b. Camera and bench
4.1.5 Experimental procedure and image treatment
4.2 Preliminary results with poppy seeds
4.2.1 Particle properties
4.2.2 Transport with water as the operating liquid
4.3.2.a. Trajectory of a single particles
4.3.2.b. Inertial focusing of two particles
4.2.3 Transport with water-glycerin mixture as the operating liquid
4.3.3.a. Fracture with two at walls
4.3.3.b. Fracture with aat wall and a sinusoidal wall
4.3.3.c. Fracture with two sinusoidal walls
4.3 Conclusion
CONCLUSION AND PERSPECTIVES