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Analysis of peristaltic two-phase flow with application to ureteral biomechanics

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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 incompressible, 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 amplitude/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.

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Abbreviations

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

q λ :

Flow rate characteristic value in moving frame

Q :

Time-averaged flow rate in fixed frame

\({\widehat Q}\) :

Instantaneous flow rate in fixed frame

(r, z):

Spatial coordinates in moving frame

(R, Z):

Spatial coordinates in fixed frame

R b :

Wave radius

Re 0 :

Liquid Reynolds number

\({\overline {Re}}\) :

Modified Reynolds number

S :

Stokes drag coefficient

t :

Time

(u, v):

Axial and radial velocity in moving frame

(U, V):

Axial and radial velocity in fixed frame

α :

= ρ p /ρ f , Density ratio between phases

\({\epsilon}\) :

= R b /b, Nondimensional wave slope

η :

Equation of wall in moving frame

λ:

Axial length

μ :

Viscosity

μ 0 :

Fluid viscosity

ρ :

Density

τ :

Viscous stress tensor

\({\phi}\) :

= a b /R b , Amplitude ratio

ψ :

Stream-function

f :

Fluid phase

p :

Particle phase

r :

Relative

s :

Suspension

* :

Dimensional quantities

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Author notes

  1. Edmundo Corona

    Present address: Sandia National Laboratories, Albuquerque, NM, 87185, USA

Authors and Affiliations

  1. Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    Joel Jiménez-Lozano, Mihir Sen & Edmundo Corona

Authors
  1. Joel Jiménez-Lozano
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  2. Mihir Sen
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  3. Edmundo Corona
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Corresponding author

Correspondence to Mihir Sen.

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Jiménez-Lozano, J., Sen, M. & Corona, E. Analysis of peristaltic two-phase flow with application to ureteral biomechanics. Acta Mech 219, 91–109 (2011). https://doi.org/10.1007/s00707-010-0438-y

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  • DOI: https://doi.org/10.1007/s00707-010-0438-y

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