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Research Papers: Flows in Complex Systems

A Structural and Fluid-Flow Model for Mechanically Driven Peristaltic Pumping With Application to Therapeutic Drug Delivery

[+] Author and Article Information
Kevin Krautbauer

Department of Mechanical Engineering,
University of Minnesota,
111 Church Street SE,
Minneapolis, MN 55455
e-mail: krau0232@umn.edu

Eph Sparrow

Department of Mechanical Engineering,
University of Minnesota,
111 Church Street SE,
Minneapolis, MN 55455
e-mail: esparrow@umn.edu

John Gorman

Department of Mechanical Engineering,
University of Minnesota,
111 Church Street SE,
Minneapolis, MN 55455
e-mail: gorma157@umn.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 4, 2016; final manuscript received July 7, 2017; published online August 10, 2017. Assoc. Editor: Kwang-Yong Kim.

J. Fluids Eng 139(11), 111104 (Aug 10, 2017) (7 pages) Paper No: FE-16-1137; doi: 10.1115/1.4037282 History: Received March 04, 2016; Revised July 07, 2017

The primary focus of this research is the design of wall-driven peristaltic pumps based on first principles with minimal simplifying assumptions and implementation by numerical simulation. Peristaltic pumps are typically used to pump clean/sterile fluids because crosscontamination with exposed pump components cannot occur. Some common biomedical applications include pumping IV fluids through an infusion device and circulating blood by means of heart-lung machines during a bypass surgery. The specific design modality described here involves the structural analysis of a hyperelastic tube-wall medium implemented by numerical simulation. The numerical solutions yielded distributions of stresses and mechanical deflections. In particular, the applied force needed to sustain the prescribed rate of compression was determined. From numerical information about the change of the volume of the bore of the tube, the rate of fluid flow provided by the peristaltic pumping action was calculated and several algebraic equation fits are presented. Other results of practical utility include the spatial distributions of effective stress (von Mises) at a succession of times during the compression cycle and the corresponding information for the spatial and temporal evolution of the displacements.

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Figures

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Fig. 1

Three stages of an expulsor-type linear peristaltic pumping action: (a) start of expulsion cycle, (b) closing of isolation valves, and (c) expulsion of fluid

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Fig. 2

Initial shape (left) and final deformed cross-sectional shape (right) as utilized in conventional (simplified) expulsor-type modeling

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Fig. 3

Schematic cross-sectional diagram of the initial configuration of the compressible tubing and the plates used for the compression

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Fig. 4

Timewise motion of the expulsor plate and symmetry plate. Zero displacement represents the starting location.

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Fig. 5

Display of the discretized solution space in the undeformed state

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Fig. 6

Timewise variation of the volume of the bore in ratio form, where V(t) denotes the instantaneous volume and V(0) is the initial undeformed volume

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Fig. 7

Volumetric fluid flow rates resulting from the peristaltic action. Each number attached to a curve denoting the degree of the polynomial.

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Fig. 8

Force per unit axial length required to compress the tubing uniformly with time

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Fig. 9

At left: rate of decrease of the interplate space h and at right: notation

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Fig. 10

Variations of the wall thickness of the compressed tube at selected circumferential locations

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Fig. 11

Distributions of the effective (von Mises) stress at selected time intervals throughout the peristaltic compression cycle. The stresses are in units of MPa. (a) t = 0.06 s, (b) t = 0.12 s, (c) t = 0.24 s, (d) t = 0.36 s, (e) t = 0.48 s, and (f) t = 0.59 s.

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Fig. 12

Quantitative characterization of the deformations at selected time intervals throughout the peristaltic compression cycle: (a) t = 0 s, (b) t = 0.12 s, (c) t = 0.24 s, (d) t = 0.36 s, (e) t = 0.48 s, and (f) t = 0.59 s

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Fig. 13

(a) Schematic diagram of the undeformed model used in the analytical solution with inner radius R and wall thickness w. (b) Schematic diagram of the fully deformed model used in the analytical solution with inner radius r, wall thickness w, and internal width x.

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