Author:
HUANG XIN,GARCÍA MARCELO H.
Abstract
The spreading and sediment deposit of a two-dimensional, unsteady,
laminar mud flow
from a constant-volume source on a relatively steep slope is studied theoretically
and
experimentally. The mud under consideration has the rheological properties
of a
Herschel–Bulkley fluid. The flow is of low-Reynolds-number type and
has a
well-formed wave front moving a substantial distance downslope. Due to
the nonlinear
rheological characteristics, a set of nonlinear partial differential equations
is needed for
this transient problem. Depth-integrated continuity and momentum equations
are
derived by applying von Kármán's momentum
integral method. A matched-asymptotic
perturbation method is implemented analytically to get asymptotic solutions
for both
the outer region away from, and the inner region near, the wave front.
The outer
solution gives accurate results for spreading characteristics, while the
inner solution,
which is shown to agree well with experimental results of Liu & Mei
(1989) for a
Bingham fluid, predicts fairly well the free-surface profile near the wave
front. A
composite solution uniformly valid over the whole spreading length is then
achieved
through a matching of the inner and outer solutions in an overlapping region.
The
range of accuracy of the solution and the size of the inner and overlapping
regions are
quantified by physical scaling analyses. Rheological and dynamic measurements
are
obtained through laboratory experiments. Theoretical predictions are compared
with
experimental results, showing reasonable agreement. The impact of shear
thinning on
the runout characteristics, free-surface profiles and final deposit of
the mud flow is
examined. A mud flow with shear thinning spreads beyond the runout distance
estimated by a Bingham model, and has a long and thin deposit.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
256 articles.
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