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Research Papers: Fundamental Issues and Canonical Flows

Deviations Due to Non-Newtonian Influences Within a Miniature Viscous Disk Pump

[+] Author and Article Information
Phil Ligrani

Oliver L. Parks Endowed Chair
Director of Graduate Programs
e-mail: pligrani@slu.edu

Jae Sik Jin

Department of Aerospace and
Mechanical Engineering,
Saint Louis University,
St. Louis, MO 63103

1Corresponding author.

Manuscript received July 21, 2012; final manuscript received January 7, 2013; published online February 22, 2013. Assoc. Editor: Prashanta Dutta.

J. Fluids Eng 135(3), 031205 (Feb 22, 2013) (12 pages) Paper No: FE-12-1339; doi: 10.1115/1.4023408 History: Received July 21, 2012; Revised January 07, 2013; Accepted January 08, 2013

A miniature viscous disk pump (VDP) is utilized to characterize and quantify non-Newtonian fluid deviations due to non-Newtonian influences relative to Newtonian flow behavior. Such deviations from Newtonian behavior are induced by adding different concentrations of sucrose to purified water, with increasing non-Newtonian characteristics as sucrose concentration increases from 0% (pure water) to 10% by mass. The VDP consists of a 10.16 mm diameter disk that rotates above a C-shaped channel with inner and outer radii of 1.19 mm, and 2.38 mm, respectively, and a channel depth of 200 μm. Fluid inlet and outlet ports are located at the ends of the C-shaped channel. Within the present study, experimental data are given for rotational speeds of 1200–2500 rpm, fluid viscosities of 0.001–0.00134 Pa s, pressure rises of 0–220 Pa, and flow rates up to approximately 0.00000005 m3/s. The theory of Flumerfelt is modified and adapted for application to the present VDP environment. Included is a new development of expressions for dimensionless volumetric flow rate, and normalized local circumferential velocity for Newtonian and non-Newtonian fluid flows. To quantify deviations due to the magnitude non-Newtonian flow influences, a new pressure rise parameter is employed, which represents the dimensional pressure rise change at a particular flow rate and sucrose concentration, as the flow changes from Newtonian to non-Newtonian behavior. For 5% and 10% sucrose solutions at rotational speeds of 1200–2500 rpm, this parameter increases as the disk dimensional rotational speed increases and as the volumetric flow rate decreases. Associated magnitudes of the pressure difference parameter show that the fluid with the larger sucrose concentration (by mass) produces significantly larger differences between Newtonian and non-Newtonian fluid flow, for each value of dimensional volumetric flow rate. For each disc rotational speed, compared to Newtonian data, dimensional pressure rise variations with dimensional volumetric flow rate, which are associated with the non-Newtonian data, are generally lower when compared at a particular volumetric flow rate. Agreement with analytic results, for any given flow rate, rotational speed, and flow passage height, validates the shear stress model employed to represent non-Newtonian behavior, as well as the analytic equations and tools (based upon the Navier–Stokes equations) which are employed to predict measured behavior over the investigated range of experimental conditions.

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Figures

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Fig. 1

Cross-sectional view and side view of the viscous disk pump. All dimensions are given in millimeters.

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Fig. 2

Configuration of the single-disk viscous pump, including coordinate system. The shaded region of the pump chamber is used for the Stokes flow analysis. The z coordinate is directed normal to the surface, and measured from the halfway location between the surface and the disk, at the horizontal center plane of the flow passage.

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Fig. 3

Photograph of the viscous disk pump flow passage. The pump chamber depth or gap height h is 200 μm, with a pump chamber outer radius of 2.38 mm.

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Fig. 4

Test setup for the single-disk viscous pump. All dimensions are given in millimeters. (a) Test components. (b) Elevations of different components.

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Fig. 5

Dimensional pressure rise variation with dimensional volumetric flow rate for pure water for disc rotational speeds of 1200–2500 rpm. The chamber height of the single-disk viscous pump is 200 μm. N = Newtonian fluid analytic result; nN = non-Newtonian fluid analytic result; E = experimental data.

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Fig. 6

Dimensional pressure rise variation with dimensional volumetric flow rate for water with 1.0% sucrose solution for disc rotational speeds of 1200–2500 rpm. The chamber height of the single-disk viscous pump is 200 μm. N = Newtonian fluid analytic result; nN = non-Newtonian fluid analytic result; E = experimental data.

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Fig. 7

Dimensional pressure rise variation with dimensional volumetric flow rate for water with 5.0% sucrose solution for disc rotational speeds of 1200–2500 rpm. The chamber height of the single-disk viscous pump is 200 μm. N = Newtonian fluid analytic result; nN = non-Newtonian fluid analytic result; E = experimental data.

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Fig. 8

Dimensional pressure rise variation with dimensional volumetric flow rate for water with 10.0% sucrose solution for disc rotational speeds of 1200–2500 rpm. The chamber height of the single-disk viscous pump is 200 μm. N = Newtonian fluid analytic result; nN = non-Newtonian fluid analytic result; E = experimental data.

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Fig. 9

Magnitudes of effective absolute viscosity and power-law parameter for the local shear stress relationship, dependent upon sucrose solution concentration

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Fig. 10

Calculated nondimensional velocity profiles to illustrate (a) case I and (b) case II flow passage behavior for non-Newtonian fluid flow with 10% sucrose solution at a rotational speed of 2500 rpm

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Fig. 11

Pressure rise variation with dimensional disk rotational speed for 5% sucrose solution with zero volumetric flow rate, Q = 0. The viscous disk pump chamber height is 200 μm. nN = non-Newtonian analytic result.

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Fig. 12

Pressure rise variation with dimensional disk rotational speed for 10% sucrose solution with zero volumetric flow rate, Q = 0. The viscous disk pump chamber height is 200 μm. E = experimental data; nN = non-Newtonian analytic result.

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Fig. 13

Pressure difference (ΔP*) between Newtonian and non-Newtonian fluid flows as dependent upon dimensional volumetric flow rate (Q) for 10% sucrose solution for rotational speeds of 1200–2500 rpm. The viscous disk pump chamber height is 200 μm. E = experimental data; nN = non-Newtonian analytic result.

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Fig. 14

Pressure difference (ΔP*) between Newtonian and non-Newtonian fluid flows as dependent upon dimensional volumetric flow rate (Q) for 5% sucrose solution for rotational speeds of 1200–2500 rpm. The viscous disk pump chamber height is 200 μm. E = experimental data; nN = non-Newtonian analytic result.

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Fig. 15

Pressure difference (ΔP*) between Newtonian and non-Newtonian fluid flows as dependent upon dimensional volumetric flow rate (Q) for 5% and 10% sucrose solutions for a disk rotational speed of 2500 rpm. The viscous disk pump chamber height is 200 μm. E = experimental data; nN = non-Newtonian analytic result.

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Fig. 16

Analytically predicted pressure difference (ΔP*) between Newtonian and non-Newtonian fluid flows for zero dimensional volumetric flow rate (Q = 0) for different sucrose concentration solutions and different dimensional disk rotational speeds. The viscous disk pump chamber height is 200 μm.

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Fig. 17

Experimentally measured normalized pressure rise (ΔP**) as dependent upon dimensional volumetric flow rate (Q) for 5% and 10% sucrose solutions for disk rotational speeds of 1200–2500 rpm. The viscous disk pump chamber height is 200 μm.

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Fig. 18

Dimensional slopes of pressure rise variation with dimensional volumetric flow rate for different sucrose concentration solutions and different dimensional disk rotational speeds of 1200–2500 rpm. The chamber height of the single-disk viscous pump is 200 μm. N = Newtonian fluid analytic result; nN = non-Newtonian fluid analytic result; E = experimental data.

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