1. Peristaltic Pumping Steven A. Jones BIEN 501 Friday, April 18, 2008
Louisiana Tech University
Ruston, LA 71272

2. Geometry a – mean distance of wall from centerlineb a
h(t) R z
a – mean distance of wall from centerline
b – amplitude of wall motion
Louisiana Tech University
Ruston, LA 71272

3. Boundary Conditions for vZ(R,Z)
h(t) R Z
vZ(h,Z) = 0, vy(h,Z) = dh(t)/dt
dvZ(0,Z)/dZ = 0, vy(0,Z) = 0
Louisiana Tech University
Ruston, LA 71272

4. Conservation of Mass Conservation of mass: Symmetry Incompressible
Louisiana Tech University
Ruston, LA 71272

5. r-momentum symmetry Conservation of Momentum (r-component):
Louisiana Tech University
Ruston, LA 71272

6. Tangential Momentum vq = 0 Gravity is balanced by pressure gradient.
Conservation of Momentum ( -component):
vq = 0
Gravity is balanced by pressure gradient.
Louisiana Tech University
Ruston, LA 71272

7. Axial Momentum
Louisiana Tech University
Ruston, LA 71272

8. Summary of Equations The three equations:
Are more complicated than we would like them to be. However, a dimensional analysis will help.
Louisiana Tech University
Ruston, LA 71272

9. Analysis of Order
If vr and d/dz (hence d/dt) are small because wall motion is small and has large wavelength, we can get rid of terms of second order.
We can also get rid of terms on the left of the z-momentum equation if we assume low Re.
Louisiana Tech University
Ruston, LA 71272

10. Summary of Equations The three equations now reduce to:
Note that vr is on the order of bc.
Louisiana Tech University
Ruston, LA 71272