Acta Mech 219, 91–109 (2011)
DOI 10.1007/s00707-010-0438-y
Joel Jiménez-Lozano · Mihir Sen · Edmundo Corona
Analysis of peristaltic two-phase flow with application
to ureteral biomechanics
Received: 19 May 2010 / Published online: 26 January 2011
© Springer-Verlag 2011
Abstract Fluid flow in the ureter is sometimes accompanied by solid particles that are produced in the
kidneys or result from the breakup of larger kidney stones; ureteral peristalsis is affected by the presence of these
solids. Peristaltic flow is analyzed for a solitary traveling wave in an axisymmetric tube with an incompress-
ible, Newtonian fluid in which identical, solid spherical particles are distributed. A two-phase flow model is
used in conjunction with a perturbation method based on a small radius to length ratio of the wave to obtain
a closed-form solution of the flow and particle velocities. The phenomenon of trapping in which closed fluid
recirculation streamlines in a moving coordinate frame occurs is discussed. Peristaltic pumping is affected
as particle volume fraction is increased. The pressure drop diminishes as the amplitude ratio (wave ampli-
tude/wave radius) decreases. The pressure in the contracted part of the ureter increases as the particle volume
fraction is increased. It is suggested that certain pathological and physiological manifestations on the ureter
can be related to these findings. The results may also be relevant to the transport of other physiological fluids
and industrial applications in which peristaltic pumping is used.
List of symbols
a Particle radius
a
b
Wave amplitude
b Characteristic length
c Wave velocity
C Volume fraction
H Equation of wall in fixed frame
M Drag force per unit volume
p Pressure
P Pressure rise over characteristic length
q Flow rate in moving frame
q
c
Critical flow rate for bifurcation in moving frame
J. Jiménez-Lozano · M. Sen (B ) · E. Corona
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
E-mail: Mihir.Sen.1@nd.edu
Present Address:
E. Corona
Sandia National Laboratories, Albuquerque, NM 87185, USA