14
B.
Derivation-Bulk Sticking Coefficient
The bulk sticking coefficient (K
sc
) is the ratio of the
force necessary to initiate sliding
(F
s
) of the
plate to
the normal force
(F
n
) on the plate.
Let Tu = average of reading from torque wrench (inch-pounds)
R = radius of plate (inches)
h = height above flat surface of cake around edge of plate (inches)
P = cell pressure, (psi) differential (inlet to outlet)
r
= variable radius
dr = incremental radius
τ
y
= shear on incremental area
F
s
= sliding force
F
n
= normal force on plate
K
sc
= bulk sticking coefficient
K
st
= stuck tendency coefficient
A = stuck area, radius'd plate
A
e
= stuck area, edge
1.
The Sliding Force (F
s
)
a. Calculation for use when neglecting edge effects is derived from the measured torque
Tu as follows:
NOTE:
R = 1 assumes cake sticking up to, but not around, the edge of the plate.