Liquid Plug Flow in Straight and Bifurcating Tubes

[+] Author and Article Information
K. J. Cassidy

Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208

N. Gavriely

Department of Physiology, Technion—Israel Institute of Technology, Haifa, Israel

J. B. Grotberg

Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI 48109

J Biomech Eng 123(6), 580-589 (Jun 07, 2001) (10 pages) doi:10.1115/1.1406949 History: Received September 22, 1999; Revised June 07, 2001
Copyright © 2001 by ASME
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Grahic Jump Location
Experimental results for Case (ii).A: Dimensionless plug length, Λ=l/l0, versus dimensionless time, τ=(t−t0)/(l0/U1), for system 5 where h1/a=0.150±0.015,l0=2.5 cm: ▾ set h2/a=0.125±0.002 with linear fit [[dashed_line]] dΛ/dτ=4.6×10−2; ○ set h2/a=0.158±0.006 with linear fit [[dotted_line]] dΛ/dτ=2.27×10−4; • set h2/a=0.189±0.002 with linear fit – dΛ/dτ=−0.106.B: Trailing film thickness, h2/a, versus plug capillary number, Ca2: • system 5 (Ca1=0.0954,h1/a=0.150±0.015), ○ system 6 (Ca1=0.0345,h1/a=0.083±0.004); – linear regression lines for system 5 and system 6 data.
Grahic Jump Location
Experimental results for Case (iii). Local film thickness, h/a, versus local Ca, for system 7 (Ca<1) and system 8 (Ca>1). Each symbol set represents a family (symbol shape) at one CaP. ▪ Parent, □ daughter A or daughter B; – Theory of Halpern et al. 11.
Grahic Jump Location
Images of liquid plug passing through bifurcation region for Case (iv).A: test plug in parent, blockage in daughter A (lower). B: test plug has split into plugs in each daughter, trailing menisci just past the carina, and blockage starts to move. C: plug in daughter B travels faster than plug in daughter A.
Grahic Jump Location
Schematic of the experimental setup
Grahic Jump Location
Experimental results for Case (i). Film thickness, h/a, versus capillary number, Ca. ○ system 1, ▿ system 2, and □ system 3. The initial plug lengths 20<l/a<60. Semi-infinite bubble experiments from 19 for comparison: • LB400X and water, ▾ LB 1715 oil and water. Theoretical curve for semi-infinite bubbles – 11.
Grahic Jump Location
Schematic of flow types. A: semi-infinite bubble, B: dry-tube liquid plug, and C: wet tube liquid plug
Grahic Jump Location
Experimental results for Case (iv) where VBLK/aA3=10.4±2.5.A: Splitting ratio, lB/lA, versus CaP and B: Capillary ratio, CaB/CaA, versus CaP; ○ system 9, VP/aP3=35.0±6.0; □ system 9, VP/aP3=50.3±5.4; • system 10, VP/aP3≈90.C: Local film thickness, h/a, versus local Ca in each region; color set represents a system 9 family (color shade) at one flow setting. Flow in the • parent, ▪ daughter A, ▾ daughter B, and ♦ liquid blockage.
Grahic Jump Location
Experimental results for Case (iv) system 11 at CaP=1.0×10−2.A: Splitting ratio, lB/lA, versus ratio of liquid volume in the blockage to parent, VBLK/VP, and B: Capillary ratio, CaB/CaA, versus VBLK/VP; ▪ VP/aP3=21.6±3.4, • VP/aP3=36.4±3.7, ▴ VP/aP3=51.6±2.9.
Grahic Jump Location
Schematic of Case (iv) before (A) and after (B) the parent plug moves into the daughters, dividing along the central axis. P=Parent plug, BLK=Blockage plug, A=Daughter A plug, B=Daughter B plug.
Grahic Jump Location
Experimental results of liquid distribution for Case (iv) where VBLK/aA3=10.4±2.5. Mass Ratio (A) and Homogeneity index (B), before (closed symbol) and after (open symbol) the parent plug passes through the bifurcation central zone; • system 9, VP/aP3=35.0±6.0; ▴ system 9, VP/aP3=50.3±5.4; ▪ system 10, VP/aP3≈90.



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