An analysis is presented for two-dimensional flow of a thin layer of power-law fluid down an inclined plane. Integration of the equations of motion using lubrication approximations shows that for both pseudoplastic and dilatant fluids, the rate of advance of a blob of fluid of given volume decreases with increasing time. The analysis further reveals that for dimensionless time less than about $0.50$, a blob of the fluid (of fixed volume) with given exponent $n$ moves faster than a fluid of same volume with larger $n$. However, thereafter, a blob of the latter fluid moves faster than the former fluid.

## References

References
1.
Batchelor
,
G. K.
, 1967,
An Introduction to Fluid Dynamics
,
Cambridge University Press
,
Cambridege, UK
.
2.
Simpson
,
J. E.
, 1982, “
Gravity Currents in the Laboratory, Atmosphere and Ocean
,”
Ann. Rev. Fluid Mech.
,
14
, pp.
213
214
.
3.
Didden
,
M.
, and
Maxworthy
,
T.
, 1982, “
The Viscous Spreading of Plane and Axisymmetric Gravity Currents
,”
J. Fluid Mech.
,
121
, pp.
27
42
.
4.
Huppert
,
H. E.
, 1982, “
The Propagation of Two-Dimensional and Axisymmetric Viscous Gravity Currents over a Rigid Horizontal Surface
,”
J. Fluid Mech.
,
121
, pp.
43
58
.
5.
Huppert
,
H. E.
, 1986, “
The Intrusion of Fluid Mechanics into Geology
,”
J. Fluid Mech.
,
173
, pp.
557
594
.
6.
Bird
,
R. B.
,
Stewart
W. E.
, and
Lightfoot
,
E. N.
, 1960,
Transport Phenomena
,
John Wiley and Sons. Inc.
,
New York
.
7.
Metzner
,
A. B.
, 1956,
,
,
New York
, Vol.
1
.
8.
Wilkinson
,
W. L.
, 1960,
Non-Newtonian Fluids
,
Pergamon Press
,
London
.
9.
Johnson
,
M. W.
, and
Mangkoesoebroto
,
S.
, 1993, “
Analysis of Lubrication Theory for the Power-Law Fluid
,”
ASME J. Tribol.
,
115
, pp.
71
77
.
10.
Balmforth
,
N. J.
,
Craster
,
R. V.
,
Rust
A. C.
, and
Sassi
R
, 2006, “
Viscoplastic Flow Over an Inclined Surface
,”
J. Non-Newtonian Fluid Mech.
,
139
, pp.
103
127
.