96
S. Lee et al.
general polydisperse slurry segregation models in helical domains. Furthermore,
such equilibrium models are the building blocks for the development of implicit flux
functions for dynamic transport models [14, 16, 26]. The current bidensity theory
may lead to new dynamic models that could predict multilayer stratified flows as
observed in [10].
Acknowledgments This work is supported by NSF grants DMS-1312543 and DMS-1048840 and
UC Lab Fees Research Grant 09-LR-04-116741-BERA.
References
1. Breedveld, V., van den Ende, D., Tripathi, A., Acrivos, A.: The measurement of the shearinduced particle and fluid tracer diffusivities in concentrated suspensions by a novel method.
J. Fluid Mech. 375, 297–318 (1998)
2. Cook, B.P.: Theory for particle settling and shear-induced migration in thin-film liquid flow.
Phys. Rev. E 78, 045303 (2008)
3. Couturier, É., Boyer, F., Pouliquen, O., Guazzelli, É.: Suspensions in a tilted trough: second
normal stress difference. J. Fluid Mech. 686, 26–39 (2011)
4. Davis, R.H., Acrivos, A.: Sedimentation of noncolloidal particles at low Reynolds numbers.
Annu. Rev. Fluid Mech. 17, 91 (1985)
5. Eckstein, E.C., Bailey, D., Shapiro, A.H.: Self-diffusion of particles in shear flow of a suspension. J. Fluid Mech. 79, 191–208 (1977)
6. Gadala-Maria, F., Acrivos, A.: Shear induced structure in a concentrated suspension of solid
spheres. J. Rheol. 24(6), 799–814 (1980)
7. Krishnan, G.P., Beimfohr, S., Leighton, D.T.: Shear-induced radial segregation in bidisperse
suspensions. J. Fluid Mech. 321, 371–393 (1996)
8. Lee, S., Stokes, Y.M., Bertozzi, A.L.: A model for particle laden flow in a spiral concentrator. In:
23rd International Congress of Theoretical and Applied Mechanics (ICTAM) Procedia IUTAM
(2012)
9. Lee, S., Stokes, Y.M., Bertozzi, A.L.: Behavior of a particle-laden flow in a spiral channel.
Phys. Fluids 26, 043302 (2014)
10. Lee, S., Mavromoustaki, A., Urdaneta, G., Huang, K., Bertozzi, A.L.: Experimental investigation of bidensity slurries on an incline. Granul. Matter 16(2), 269–274 (2014)
11. Leighton, D., Acrivos, A.: Viscous resuspension. Chem. Eng. Sci. 41, 1377–1384 (1986)
12. Leighton, D., Acrivos, A.: Shear-induced migration of particles in concentrated suspensions.
J. Fluid Mech. 181, 415 (1987)
13. Leighton, D., Acrivos, A.: Measurement of shear-induced self-diffusion in concentrated suspensions of spheres. J. Fluid Mech. 177, 109–131 (1987)
14. Mavromoustaki, A., Bertozzi, A.L.: Hyperbolic systems of conservation laws in gravity-driven,
particle-laden thin-film flows. J. Eng. Math. 88, 29–48 (2014)
15. Murisic, N., Ho, J., Hu, V., Latterman, P., Koch, T., Lin, K., Mata, M., Bertozzi, A.L.: Particleladen viscous thin-film flows on an incline: experiments compared with an equilibrium theory
based on shear-induced migration and particle settling. Physica D 240, 1661–1673 (2011)
16. Murisic, N., Pausader, B., Peschka, D., Bertozzi, A.L.: Dynamics of particle settling and resuspension in viscous liquid films. J. Fluid Mech. 717, 203–231 (2013)
17. Nott, P.R., Brady, J.F.: Pressure-driven flow of suspensions: simulation and theory. J. Fluid
Mech. 275, 157–199 (1994)
18. Oron, A., Davis, S.H., Bankoff, S.G.: Long-scale evolution of thin liquid films. Rev. Mod.
Phys. 69, 931 (1997)
S. Lee et al.
general polydisperse slurry segregation models in helical domains. Furthermore,
such equilibrium models are the building blocks for the development of implicit flux
functions for dynamic transport models [14, 16, 26]. The current bidensity theory
may lead to new dynamic models that could predict multilayer stratified flows as
observed in [10].
Acknowledgments This work is supported by NSF grants DMS-1312543 and DMS-1048840 and
UC Lab Fees Research Grant 09-LR-04-116741-BERA.
References
1. Breedveld, V., van den Ende, D., Tripathi, A., Acrivos, A.: The measurement of the shearinduced particle and fluid tracer diffusivities in concentrated suspensions by a novel method.
J. Fluid Mech. 375, 297–318 (1998)
2. Cook, B.P.: Theory for particle settling and shear-induced migration in thin-film liquid flow.
Phys. Rev. E 78, 045303 (2008)
3. Couturier, É., Boyer, F., Pouliquen, O., Guazzelli, É.: Suspensions in a tilted trough: second
normal stress difference. J. Fluid Mech. 686, 26–39 (2011)
4. Davis, R.H., Acrivos, A.: Sedimentation of noncolloidal particles at low Reynolds numbers.
Annu. Rev. Fluid Mech. 17, 91 (1985)
5. Eckstein, E.C., Bailey, D., Shapiro, A.H.: Self-diffusion of particles in shear flow of a suspension. J. Fluid Mech. 79, 191–208 (1977)
6. Gadala-Maria, F., Acrivos, A.: Shear induced structure in a concentrated suspension of solid
spheres. J. Rheol. 24(6), 799–814 (1980)
7. Krishnan, G.P., Beimfohr, S., Leighton, D.T.: Shear-induced radial segregation in bidisperse
suspensions. J. Fluid Mech. 321, 371–393 (1996)
8. Lee, S., Stokes, Y.M., Bertozzi, A.L.: A model for particle laden flow in a spiral concentrator. In:
23rd International Congress of Theoretical and Applied Mechanics (ICTAM) Procedia IUTAM
(2012)
9. Lee, S., Stokes, Y.M., Bertozzi, A.L.: Behavior of a particle-laden flow in a spiral channel.
Phys. Fluids 26, 043302 (2014)
10. Lee, S., Mavromoustaki, A., Urdaneta, G., Huang, K., Bertozzi, A.L.: Experimental investigation of bidensity slurries on an incline. Granul. Matter 16(2), 269–274 (2014)
11. Leighton, D., Acrivos, A.: Viscous resuspension. Chem. Eng. Sci. 41, 1377–1384 (1986)
12. Leighton, D., Acrivos, A.: Shear-induced migration of particles in concentrated suspensions.
J. Fluid Mech. 181, 415 (1987)
13. Leighton, D., Acrivos, A.: Measurement of shear-induced self-diffusion in concentrated suspensions of spheres. J. Fluid Mech. 177, 109–131 (1987)
14. Mavromoustaki, A., Bertozzi, A.L.: Hyperbolic systems of conservation laws in gravity-driven,
particle-laden thin-film flows. J. Eng. Math. 88, 29–48 (2014)
15. Murisic, N., Ho, J., Hu, V., Latterman, P., Koch, T., Lin, K., Mata, M., Bertozzi, A.L.: Particleladen viscous thin-film flows on an incline: experiments compared with an equilibrium theory
based on shear-induced migration and particle settling. Physica D 240, 1661–1673 (2011)
16. Murisic, N., Pausader, B., Peschka, D., Bertozzi, A.L.: Dynamics of particle settling and resuspension in viscous liquid films. J. Fluid Mech. 717, 203–231 (2013)
17. Nott, P.R., Brady, J.F.: Pressure-driven flow of suspensions: simulation and theory. J. Fluid
Mech. 275, 157–199 (1994)
18. Oron, A., Davis, S.H., Bankoff, S.G.: Long-scale evolution of thin liquid films. Rev. Mod.
Phys. 69, 931 (1997)