Balachandar, S.
2009
A scaling analysis for point-particle approaches to turbulent multiphase flows. Intl J. Multiphase Flow
35, 801–810.

Balachandar, S. & Eaton, J. K.
2010
Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech.
42, 111–133.

Basset, A. B.
1888
Treatise on Hydrodynamics. Deighton, Bell and Company.

Beylkin, G. & Monzón, L.
2005
On approximation of functions by exponential sums. Appl. Comput. Harmon. Anal.
19, 17–48.

Bombardelli, F. A., Gonzalez, A. E. & Nino, Y. I.
2008
Computation of the particle Basset force with a fractional-derivative approach. J. Hydraul. Eng.-ASCE
134 (10), 1513–1520.

Boussinesq, J.
1885
Sur la résistance qu’oppose un liquide indéfini au repos au mouvement varié d’une sphère solide. C. R. Acad. Sci. Paris
100, 935–937.

Brush, L. M., Ho, H. W. & Yen, B. C.
1964
Accelerated motion of a sphere in a viscous fluid. J. Hydraul. Engng
90, 149–160.

Clift, R., Grace, J. R. & Weber, M. E.
1978
Bubbles, Drops and Particles. Academic.

Daitche, Anton
2013
Advection of inertial particles in the presence of the history force: higher order numerical schemes. J. Comput. Phys.
254, 93–106.

Dorgan, A. J. & Loth, E.
2007
Efficient calculation of the history force at finite Reynolds numbers. Intl J. Multiphase Flow
33 (8), 833–848.

Elghannay, H. A. & Tafti, D. K.
2016
Development and validation of a reduced order history force model. Intl J. Multiphase Flow
85, 284–297.

Ferry, J. & Balachandar, S.
2001
A fast Eulerian method for disperse two-phase flow. Intl J. Multiphase Flow
27 (7), 1199–1226.

Ferry, J. & Balachandar, S.
2002
Equilibrium expansion for the Eulerian velocity of small particles. Powder Technol.
125 (2–3), 131–139.

Ferry, J., Rani, S. L. & Balachandar, S.
2003
A locally implicit improvement of the equilibrium Eulerian method. Intl J. Multiphase Flow
29 (6), 869–891.

van Hinsberg, M. A. T., Ten Thije Boonkkamp, J. H. M. & Clercx, H. J. H.
2011
An efficient, second order method for the approximation of the Basset history force. J. Comput. Phys.
230 (4), 1465–1478.

Landau, L. D. & Lifschitz, E. M.
1987
Fluid Mechanics, Course of Theroretical Physics, vol. 6. Butterworth-Heinemann.

Lee, H., Ha, M. Y. & Balachandar, S.
2012
Work-based criterion for particle motion and implication for turbulent bed-load transport. Phys. Fluids
24 (11), 116604.

Lee, H. & Hsu, I.
1994
Investigation of saltating particle motion. J. Hydraul. Engng
120 (7), 831–845.

Ling, Y., Parmar, M. & Balachandar, S.
2013
A scaling analysis of added-mass and history forces and their coupling in dispersed multiphase flows. Intl J. Multiphase Flow
57, 102–114.

Longhorn, A. L.
1952
The unsteady, subsonic motion of a sphere in a compressible inviscid fluid. Q. J. Mech. Appl. Maths
5, 64–81.

Lovalenti, P. M. & Brady, J. F.
1993a
The force on a sphere in a uniform-flow with small-amplitude oscillations at finite Reynolds-number. J. Fluid Mech.
256, 607–614.

Lovalenti, P. M. & Brady, J. F.
1993b
The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds-number. J. Fluid Mech.
256, 561–605.

Maxey, M. R. & Riley, J. J.
1983
Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids
26 (4), 883–889.

Mei, R.
1993
History force on a sphere due to a step change in the free-stream velocity. Intl J. Multiphase Flow
19 (3), 509–525.

Mei, R. W. & Adrian, R. J.
1992
Flow past a sphere with an oscillation in the free-stream velocity and unsteady drag at finite Reynolds number. J. Fluid Mech.
237, 323–341.

Michaelides, E. E.
1992
A Novel way of computing the Basset term in unsteady multiphase flow computations. Phys. Fluids A
4 (7), 1579–1582.

Mordant, N. & Pinton, J. F.
2000
Velocity measurement of a settling sphere. Eur. Phys. J. B
18 (2), 343–352.

Nino, I. & Garcia, M.
1998
Using Lagrangian particle saltation observations for bedload sediment transport modelling. Hydrol. Process.
12, 1197–1218.

Parmar, M., Balachandar, S. & Haselbacher, A.
2012a
Equation of motion for a drop or bubble in viscous compressible flows. Phys. Fluids
24, 056103.

Parmar, M., Balachandar, S. & Haselbacher, A.
2012b
Equation of motion for a sphere in non-uniform compressible flows. J. Fluid Mech.
699, 352–375.

Parmar, M., Haselbacher, A. & Balachandar, S.
2008
On the unsteady inviscid force on cylinders and spheres in subcritical compressible flow. Phil. Trans. R. Soc. Lond. A
366 (1873), 2161–2175.

Parmar, M., Haselbacher, A. & Balachandar, S.
2011
Generalized Basset–Boussinesq–Oseen equation for unsteady forces on a sphere in a compressible flow. Phys. Rev. Lett.
106 (8), 084501.

Prosperetti, A.
2011
Advanced Mathematics for Applications. Cambridge University Press.

Schmeeckle, M. W. & Nelson, J. M.
2003
Direct numerical simulation of bedload transport using a local, dynamic boundary condition. Sedimentology
50, 279–301.

Sobral, Y. D., Oliveira, T. F. & Cunha, F. R.
2007
On the unsteady forces during the motion of a sedimenting particle. Powder Technol.
178 (2), 129–141.

Taylor, G. I.
1928
The forces on a body placed in a curved or converging stream of fluid. Proc. R. Soc. Lond. A
120 (785), 260–283.

Tchen, C. M.1947 Mean value and correction problems connected with the motion of small particles suspended in a turbulent fluid. PhD thesis, Delft University, Hague.

Vojir, D. J. & Mchaelides, E. E.
1994
Effect of the history term on the motion of rigid spheres in a viscous-fluid. Intl J. Multiphase Flow
20 (3), 547–556.

Wood, I. R. & Jenkins, B. S.
1973
A numerical study of the suspension of a non-buoyant particle in a turbulent stream. In Proceedings of the IAHR International Symposium on River Mechanics, vol. 1, pp. 431–442. Asian Institute of Technology.