Download Shear strain: a short history

Shear Rate Summary 1
Shear rate: a short history
25 May 2004
Bagnold, 1954
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dU/dy, a term in the dimensionless shear strain group, represents the rate of
shearing of the grains over one another
if dU/dy is large, grain inertia dominates
if dU/dy is small, fluid viscosity dominates
Assumptions:
- uniform shear strain and the grains are moving with the fluid
- dU/dy constant through time, driven by external forces
- kinetic energy is constant
- grain motion includes collisions
- elastic grains
- the movement of the displaced fluids is of a random nature in relation to that of
the grains (density of fluid does not enter)
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“successions of glancing collisions as one layer overtakes the next slower layer”
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Pressure = force/area = mass*acceleration/area = (momentum/time)/area
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 dU 
 , enters into the momentum and into the
Mean relative velocity U  kbD
 dy 
expression for the number of collisions per time
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 1  f  U 
Py   
2mU cos  i  = (grain/area)(1/time)(mass)(velocity)
s
 bd 

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 dU 
 cos  i
Py  aif  D 
dy


2
2
Shear Rate Summary 2