A continuum two-phase fluid-particle model accounting for particle-phase stresses and a body force due to the presence of a magnetic field is developed and applied to the problem of two-dimensional laminar hydromagnetic flow of a particulate suspension over a horizontal surface in the presence of a gravity field. Analytical solutions for the velocity distributions and the skin-friction coefficients of both phases are reported. Two cases of wall hydrodynamic (velocity) conditions corresponding to stationary and oscillatory velocity distributions are considered. Numerical evaluations of the analytical solutions are performed and the results are reported graphically to elucidate special features of the solutions. The effects of the particle-phase stresses and the magnetic field are illustrated through representative results for the horizontal velocity profiles, fluid-phase displacement thickness, and the complete skin-friction coefficient for various combinations of the physical parameters. It is found that the presence of the magnetic field increases the fluid-phase skin-friction coefficient for various particulate volume fraction levels while the presence of the particle-phase viscous stresses reduces it for various particle-to-fluid density ratios.

Issue Section:
Technical Papers
Keywords:
two-phase flow, suspensions, magnetohydrodynamics, magnetic field effects, sediments, magnetic fluids
Topics:
Flow (Dynamics), Fluids, Magnetohydrodynamics, Particulate matter, Gravity (Force), Magnetic fields, Two-phase flow, Skin friction (Fluid dynamics)
1.
Yiantsios
,
S. G.
, and
Karabelas
,
A. J.
,
1998
, “
The effect of gravity on the deposition of micron-sized particles on smooth surfaces
,”
Int. J. Multiphase Flow
,
24
, pp.
283
–
293
.
2.
Jia
,
X.
, and
Williams
,
R. A.
,
1990
, “
Particle/deposition at a charged solid/liquid interface
,”
Chem. Eng. Commun.
,
91
, pp.
127
–
198
.
3.
Ven van de, T. G. M., 1989, Colloidal Hydrodynamics, Academic Press, London.
4.
Yao
,
K. M.
,
Habibian
,
M. T.
, and
O’Melia
,
C. R.
,
1971
, “
Water and waste water filtration: concepts and applications
,”
Environ. Sci. Technol.
,
5
, pp.
1105
–
1112
.
5.
Adamczyk
,
Z.
, and
van de Ven
,
T. G. M.
,
1981
, “
Deposition of particles under external forces in laminar flow through parallel-plate and cylindrical channels
,”
J. Colloid Sci.
,
80
, pp.
340
–
356
.
6.
Adamczyk
,
Z.
, and
van de Ven
,
T. G. M.
,
1982
, “
Particle transfer to a plate in uniform flow
,”
Chem. Eng. Sci.
,
37
, pp.
869
–
880
.
7.
Marmur
,
A.
, and
Ruckenstein
,
E.
,
1986
, “
Gravity and cell adhesion
,”
J. Colloid Interface Sci.
,
114
, pp.
261
–
266
.
8.
Apazidis
,
N.
,
1985
, “
On two-dimensional laminar flows of a particulate suspension in the presence of a gravity field
,”
Int. J. Multiphase Flow
,
11
, pp.
657
–
698
.
9.
Apazidis
,
N.
,
1990
, “
Temperature distribution and heat transfer in a particle-fluid flow past a heated horizontal plate
,”
Int. J. Multiphase Flow
,
16
, pp.
495
–
513
.
10.
Dahlkild
,
A. A.
,
1997
, “
The motion of Brownian particles and sediment on an inclined plate
,”
J. Fluid Mech.
,
337
, pp.
25
–
47
.
11.
Chen
,
C. P.
, and
Wood
,
P. E.
,
1986
, “
Turbulence closure modeling of the dilute gas-particle axisymmetric jet
,”
AIChE J.
,
32
, pp.
163
–
166
.
12.
Drew
,
D. A.
, and
Segal
,
L. A.
,
1971
, “
Analysis of fluidized beds and foams using averaged equations
,”
Stud. Appl. Math.
,
50
, pp.
233
–
252
.
13.
Gidaspow
,
D.
,
1986
, “
Hydrodynamics of fluidization and heat transfer: super computer modelling
,”
Appl. Mech. Rev.
,
39
, pp.
1
–
23
.
14.
Tsuo
,
Y. P.
, and
Gidaspow
,
D.
,
1990
, “
Computation of flow patterns in circulating fluidized beds
,”
AIChE J.
,
36
, pp.
888
–
896
.
15.
Gadiraju
,
M.
,
Peddieson
,
J.
, and
Munukutla
,
S.
,
1992
, “
Exact solutions for two-phase vertical pipe flow
,”
Mech. Res. Commun.
,
19
, pp.
7
–
13
.
16.
Wallis, G. B., 1969, One-dimensional Two-phase Flow, McGraw-Hill, New York.
17.
Kynch
,
G. J.
,
1952
, “
A theory of sedimentation
,”
Trans. Faraday Soc.
,
48
, pp.
166
–
176
.
18.
Cramer, K. R., and Pai, S.-I., 1973, Magnetofluid Dynamics for Engineers and Applied Physicists, Scripta Publishing Company, Washington, D.C.
19.
Marble
,
F. E.
,
1970
, “
Dynamic of dusty gases
,”
Annu. Rev. Fluid Mech.
,
2
, pp.
397
–
446
.
20.
Tam
,
K. W.
,
1969
, “
The drag on a cloud of spherical particles in low Reynolds number flow
,”
J. Fluid Mech.
,
38
, pp.
537
–
546
.
21.
Soo, S. L., 1989, Particulates and Continuum Multiphase Fluid Dynamics, Hemisphere Publishing, New York, pp. 282 and 292.
22.
Chamkha
,
A. J.
,
1996
, “
Compressible dusty-gas boundary-layer flow over a flat surface
,”
ASME J. Fluids Eng.
,
118
, pp.
179
–
185
.
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