NUMERICAL ESTIMATION OF PLASMA LAYER THICKNESS IN BRANCHED MICROCHANNEL USING A MULTI-LAYER

MODEL OF BLOOD FLOW K. Morimoto1*, D. Kato and S. Konishi

1Ritsumeikan University, JAPAN ABSTRACT

This paper presents a CFD (Computational Fluid Dynamics) -based modeling of blood flow in branched microfluidic channels, in order to enhance the effectiveness of conventional plasma skimming techniques. Here, we propose a multi-layer model of blood flow in branched microchannels, with which the thickness of the plasma layer could be estimated more precisely than that based on the spatially-uniform distribution of the fluid viscosity. The thickness of each layer is identified by successive CFD simulations, dependent on the flow-rate ratios among the main and branch channels. The proposed approach is verified through pig blood separation tests using PDMS devices. KEYWORDS: Plasma Skimming, Branched Micochannel, CFD, Multi-Layer Model

INTRODUCTION

This paper presents CFD (Computational Fluid Dynamics) -based modeling of blood flow in branched microfluidic channels, in order to enhance the effectiveness of conventional plasma skimming techniques [1, 2]. The principle of the present plasma skimming technique is shown in Fig. 1a. The whole blood is supplied from the inlet of the main channel and the plasma component is collected from the outlet of the branch channels. In microfluidic channels, the Reynolds number is extremely low, so that the motion of fluids is characterized by stable laminar flow and the particles move along the streamlines. When small solid particles are considered, the route followed by a particle at a bifurcation is de-termined by whether the particle's center is included in the inflow layer (“plasma layer”) to the branch channel.

For optimizing the performance of this branching mechanism, we perform CFD simulations taking into consideration the spatial change of the fluid viscosity. PDMS devices are fabricated by the standard soft lithography technique as shown in Fig. 1b. In this study, we propose a multi-layer model of blood flow in branched microchannels, with which the thickness of the plasma layer could be estimated more precisely than that based on the spatially-uniform distribution of the fluid viscosity. Owing to the fact that no theoretical flow profile is available for bifurcating channels in compari-son to the case of the simple straight channel [3], we perform CFD analyses to obtain streamline distributions under var-ious design conditions. In our proposed approach, the thickness of each layer is identified by successive CFD simula-tions, dependent on the flow-rate ratios among the main (sample-solution supplied) and branch (liquid-extracting) channels. The results of the present simulation are verified through separation tests using pseudo blood and pig blood. CFD SIMULATION

We investigate the effects of the flow ratio r (= Qmain/Qbranch) between the flow rate of the main channel (Qmain) and that of the branch channel (Qbranch) and of the geometry of the channel (height h and main channel width w). In the present study, a software package COMSOL Multiphysics 3.4 was employed to perform 3D computation using the in-compressible Navier-Stoke equation as the governing equation. The boundary conditions used were P = 0 (atmospheric pressure) for the inlet of the channel (Inlet) and no-slip conditions for the surfaces of the channel walls; the flow rate conditions for the channel outlets (Outlet 1 and Outlet 2) are based on the given flow-rate ratios. The total flow rate (Qmain + Qbranch) was set at 10 µl/min. The diameter of the branch channel was set at 10 µm, roughly the same as the size of blood cells.

Figure 2 shows the schematic of the present multi-layer model. The whole region inside the channel consists of three layers with different viscosity: plasma layer, blood cell layer (the initial viscosity is bl = 3.8 10-3 Pa·s, and increasing at every bifurcation), and transition layer (the thickness is prescribed as x1 = y1 = 2 m). We incorporate the present vis-cosity model into the flow simulation.

Boundary Streamline

Main Flow

Branched Flow

Outlet 2Outlet 1

Inlet

3 mm

l 3 mm

lb

wb

Figure 1: Principle of the present blood separation (plasma skimming) using branched structure (a) and presently fabricated PDMS device (b).

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978-0-9798064-3-8/µTAS 2010/$20©2010 CBMS 378 14th International Conference onMiniaturized Systems for Chemistry and Life Sciences

3 - 7 October 2010, Groningen, The Netherlands

Figure 3 shows the streamline visualization for different flow rate ratios of the main and branch channels with spa-tially-uniform viscosity model. The thickness of the plasma layer is defined as L. It is seen that L is strongly dependent on the flow rate ratio, and the key factor in the present separation. By increasing the flow rate ratio r, L can be reduced below the desired threshold distance (L < 4 m for human or pig blood).

Figure 4 shows the present procedure of estimating the plasma layer thickness. The horizontal axis means the speci-fied plasma layer thickness for each simulation and the vertical axis corresponds to the calculated values of L. The esti-mated values of the thickness from the present multi-layer model are obtained as intersections of each profile and the dotted line. It is found that the single-layer model with uniform viscosity underestimates the thickness for each flow rate. In the present branched channel, the plasma layer thickness is estimated to be 3.5 µm and 2.7 µm for Qbranch = 0.09 and 0.06 µl/min, respectively. EXPERIMENTAL VERIFICATION

Figure 5 shows experimental results obtained in PDMS devices with the present branching mechanism. For pseudo blood, a mixed solution of glass beads with particle diameters of 1.75 µm and 10 µm, and a 40% water solution of glyce-rol was used. From the experiment using a PDMS device having 5 branch channels (Fig. 5(a)), it is verified that only particles with the diameter of 1.75 µm enter each of the branch channels. Thus, in the case of pseudo blood, the present device works as effectively as the single-layer model predicts.

On the other hand, in the case of pig blood, L becomes larger for the same flow rate as in the pseudo blood, so that red blood cells enter the branch (Figs. 5(b, c)). We regulate the flow rate in the branch channel, and examined the effec-tiveness of our computational model. As shown in Figs. 5(d-g), the purity of the plasma is increased successfully with decreasing Qbranch as the present multi-layer model predicts: plasma layer thickness is reduced up to 2.7 µm for Qbranch = 0.06 µl/min, preventing the blood cells from flowing into the branch channel.

y

x

pl

bl0 bl1

x1

y1

Blood cell layer

Plasma layer

Transition layer

Figure 2: Two-dimensional representation of the present multi-layer model of spatially-varying viscosity. The viscosity of the blood cell layer and the plasma layer is assumed respectively as bl = 3.8 10-3 Pa·s (increasing with bifurcation) and pl = 1.2 10-3 Pa·s (constant).

Figure 3: Streamline distribution and effect of the flow rate in the branch channel Qbranch: (a) flow rate ratio r (= Qmain/Qbranch) = 3, (b) r =10, (c) the plasma layer thickness L versus Qbranch.

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1.21.00.80.60.40.20.0

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h = 20 m, w = 108 m h = 25 m, w = 76 m h = 30 m, w = 58 m h = 35 m, w = 46 m

Upper Limit: L = 4 m

(c)

Figure 4: Estimation of the plasma layer thickness from the proposed multi-layer model. (a) Whole view, (b) magnified view.

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Lca

l [m

]

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Qbranch = 0.09 l/min

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Qbranch = 0.03 l/min

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CONCLUSION In order to enhance the effectiveness of conventional plasma skimming techniques, we proposed a three-layer model

of blood flow in branched microchannels. With the present model, the thickness of the plasma layer is estimated for giv-en channel geometry and flow-rate conditions. The simulation result is verified through plasma separation tests using pig blood. Since the thickness of the plasma layer is critically important for increasing the separation efficiency, the present approach would be of great value for the design optimization. ACKNOWLEDGEMENT

This research was supported by the Ministry of Education, Science, Sports and Culture of Japan (MEXT), through the Grant-in-Aid for Cooperation of Innovative Technology and Advanced Research in City Area Program in the Southern Area of Lake Biwa, 2007-2009.

REFERENCES [1] M. Yamada & M. Seki, "Hydrodynamic filtration for on-chip particle concentration and classification utilizing mi-

crofluidics," Lab Chip, 5, 1233 (2005). [2] S. Yang, et al., "A microfluidic device for continuous, real time blood plasma separation," Lab Chip, 6, 871 (2006). [3] M. Sharan & A.S. Popel, "A two-phase model for flow of blood in narrow tubes with increased effective viscosity

near the wall," Biorheology , 38, 415 (2001). CONTACT *K. Morimoto, tel: +81-77-561-5847; kmrmt@se.ritsumei.ac.jp

Figure 5: Experimental results of blood plasma separation: (a) pseudo blood sample containing different sizedparticles, (b-g) pig blood samples diluted with saline solution (the viscosity is adjusted to that of human blood). The width of the main and branch channels is respectively designed to 81.2 m and 10 m with a constant height of 35 m: (b, c) Qbranch = 0.11 l/min, (d, e) Qbranch = 0.09 l/min, (f, g) Qbranch = 0.06 l/min.

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