Equip the gut with a coordinate system with coordinates and let
be the direction pointing along the length of the gut. Write
for the velocity of the chyme. Here
is the component of the velocity in the direction of the
-axis and
and
are the velocity components in the other two directions. Write
for the viscosity of the chyme (a measure of its stickiness) and
for the pressure forcing the chyme to flow down the intestine. The Stokes equations relate velocity, pressure and viscosity as follows:
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Here is the vector
, where
(similarly for
and
).
The expression stands for the vector
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and is defined as
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