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TECHNICAL PAPERS

The Surface-Tension-Driven Flow of Blood From a Droplet Into a Capillary Tube

[+] Author and Article Information
Wei Huang, Yuan Cheng Fung

Department of Bioengineering, University of California, San Diego, La Jolla, CA 92093-0412

Raghbir S. Bhullar

Roche Diagnostics Corporation, Indianapolis, IN 46206

J Biomech Eng 123(5), 446-454 (Apr 17, 2001) (9 pages) doi:10.1115/1.1389096 History: Received September 02, 2000; Revised April 17, 2001
Copyright © 2001 by ASME
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References

Figures

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A capillary tube drawing blood from a droplet. The tube is cylindrical with circular or rectangular cross section. The velocity profiles shown are those in a plane of symmetry.
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Front surface of the blood and the streamlines of flow in the early stages
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Pattern of the velocity vectors in flow into a capillary tube from a droplet
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Lew–Fung 9 theoretical results on the additional local resistance to flow in the entry region of the tube flow caused by the radial velocity and disturbed axial velocity. The function f(x/a) is defined in Eq. (18), and is called the fractional increase of resistance.
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Integrated fractional increased resistance to flow in the entry regime from x=0 to x=X as defined by Eq. (19). ΔR(X/a) is the equivalent added axial length due to resistance of entry flow defined by Eq. (20).
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Flow in the capillary tube in early stages of entry before a region of Poiseuille flow is established. At this stage, the entry length L3 is shorter than the value where the flow can be said to deviate from Poiseuillean profile by less than 1 percent. The length of the meniscus traction regime, L1 is approximately equal to L3. The total length X=L1+L3 is smaller than twice the characteristic entry length, which is approximately equal to 0.7 times the radius of a circular cylindrical capillary tube, or 0.7 times the half thickness of a narrow rectangular tube. Hence the condition shown in Fig. 6 occurs when X is smaller than 1.4 times the radius of the tube or 1.4 times the half thickness of a narrow rectangle.
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Top panels: (1) Time course of the theoretical velocity (dX/dt) and acceleration (d2X/dt2) of fluid flowing into a circular cylindrical capillary with radius a=0.05 mm, and a narrow rectangular capillary with height H=0.05 mm. The fluid properties were: ρ=1000 kg/m3,μ=4cp=0.004 kg/(m⋅s),Γ=0.04 kg/s2, and θ=0 deg. The velocity and acceleration were computed from X=0 to X=100. The displacement history is presented in Figs. 89101112. Bottom panel: (2) The acceleration history in the initial 0.20 ms period is shown in magnified time scale for the cases of a cylindrical tube with radius a=0.05 mm and a narrow slit with H=0.1 mm.
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Theoretical results on the time course of fluid front flowing into a circular capillary tube. The radius a of the circular cross section was 0.05, 0.1, and 0.5 mm, respectively. The properties of fluid were: ρ=1000 kg/m3,μ=4cp=0.004 kg/(m⋅s),Γ=0.04 kg/s2, and θ=0 deg.
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Theoretical results on the time course of fluid front flowing into a narrow rectangular capillary. The height H of the narrow rectangular cross section was 0.05 and 0.1 mm, respectively. The properties of fluid were: ρ=1000 kg/m3,μ=4cp=0.004 kg/(m⋅s),Γ=0.04 kg/s2, and θ=0 deg.
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Effect of aspect ratio (Width/Height or W/H) in the time course of fluid front flowing into a narrow rectangular capillary. The height H of the narrow rectangular cross section was 0.05 mm. The properties of fluid in the computation were: ρ=1000 kg/m3,μ=4cp=0.004 kg/(m⋅s),Γ=0.04 kg/s2, and θ=0 deg. The aspect ratios were 1, 2, 3, 4, 5, 10, and ∞, respectively.
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Effect of fluid viscosity (μ) in the time course of fluid front flowing into a narrow rectangular capillary. The height H of the narrow rectangular cross section was 0.05 mm. The properties of fluid were: ρ=1000 kg/m3,Γ=0.04 kg/s2, and θ=0 deg. The viscosities were 0.001, 0.002, 0.003, 0.004, 0.005, 0.010, and 0.1 kg/(ms).  
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Effect of contact angle θ in the time course of fluid front flowing into a narrow rectangular capillary of the height H=0.05 mm. The properties of fluid in the computation were: ρ=1000 kg/m3,μ=4cp=0.004 kg/(m⋅s), and Γ=0.04 kg/s2.

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