Flow of a Blood Analogue Solution through Microchannels with Bifurcations

P.C. Sousa*1), F.T. Pinho2), M.A. Alves1) and M.S.N. Oliveira1)

1) DEQ, CEFT, FEUP, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal 2) DEMec, CEFT, FEUP, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal *E-mail: psousa@fe.up.pt Abstract

We investigate the flow patterns of Newtonian and viscoelastic fluids in microchannels containing bifurcations. The Newtonian fluid used as a reference is de-ionized water, while the non-Newtonian fluid used in the experiments has a shear rheology similar to that of human blood. The geometrical shape of the channels used reproduce bifurcating vessels, typically encountered in microcirculation networks. Visualizations of the flow patterns were performed for a wide range of flow rates using streak photography. For the viscoelastic fluid flow, recirculations appear upstream of the bifurcating point, which increase in size when the elasticity of the flow is increased. On the other hand, for the Newtonian fluid flow, no recirculations were observed within the flow rate range under investigation. 1. Introduction

Biological and bioengineered materials exhibit frequently nonlinear viscoelastic properties, which are crucial for proper biological functioning [1]. In particular, blood exhibits non-Newtonian properties, such as viscoelasticity, thixotropy and shear-thinning of the viscosity due to the cellular elements it carries [2, 3]. Since many pathological conditions in the cardiovascular system are influenced by the flow characteristics of blood it is very important to obtain a thorough characterization of blood rheology and blood flow dynamics in order to prevent cardiovascular diseases, to plan adequately vascular surgeries, understand the transport of drugs through the circulatory system and for the development of cardiovascular equipments, such as blood pumps, heart valves or stents [4]. Moreover, it is desirable to obtain a more in-depth understanding on the role of the non-Newtonian characteristics of blood rheology upon the dynamics in microcirculation.

The manipulation of blood may not always be practical, primarily due to safety reasons; therefore, blood analogue solutions have been used in many investigations to mimic the properties of blood. In a previous work we investigated the effect of elasticity on the flow behaviour of blood analogue solutions flowing in hyperbolic contractions under a strong extensional flow field [5]. In the current investigation we analyze the flow of a well-established blood

analogue solution flowing in microchannels which include in their design branch points characteristic of microvascular networks. These branch features are mostly bifurcations, in which the blood flowing in two daughter vessels merge into a single parent vessel (known as a converging bifurcation) or reversely the flow through the parent vessel is divided into two daughter vessels (known as a diverging bifurcation) [6]. Both situations are analyzed here. 2. Experimental

2.1. Microchannel fabrication and geometry

The planar microchannels used in this work are fabricated in polydimethylsiloxane (PDMS) using standard soft-lithography techniques and SU-8 photo-resist molds [7]. The PDMS polymer is widely employed for replica molding [8] due to its optical properties, such as transparency, essential to access the flow visually and also due to the straightforward, rapid, well documented and inexpensive fabrication method, which produces microchannels with well-defined features and sizes. In addition, PDMS is chemically inert, has a homogeneous structure and is biocompatible.

The microgeometry used in this investigation is composed of a straight channel which divides into two branches forming a bifurcated channel. The three channels have the same width, D, of 105 µm and form bifurcation angles of α = 45º and β = 157.5°, as illustrated in Figure 1. The depth, h, of the microchannel is 100 µm.

Fig. 1. Optical micrograph of the bifurcated channel

used in the experiments.

D αααα

ββββ ==== ππππ −−−− αααα //// 2222

100 µm

2.2. Experimental set-up and techniques

The flow behavior of Newtonian and non-Newtonian fluids was investigated for a wide range of flow rates at room temperature (average temperature of 298.4 K). For that purpose, a syringe pump (Nemesys, Cetoni GmbH) was used to precisely impose the inlet flow rate and control the outlet flow rate.

Visualizations of the flow patterns were undertaken at the center-plane, i.e. at mid-distance between the top and bottom planar bounding walls of the microchannel. For this purpose, the fluids were seeded with inert 1µm fluorescent tracer particles (Nile Red, Molecular Probes, Invitrogen, Ex/Em: 520/580 nm). The optical set-up employed consists of an inverted epi-fluorescence microscope (Leica Microsystems GmbH, DMI 5000M) equipped with a CCD camera (Leica Microsystems GmbH, DFC350 FX), a filter cube (Leica Microsystems GmbH, excitation BP 530-545 nm, dichroic 565 nm, barrier filter 610-675 nm) and a 100 W mercury lamp light source. 3. Fluids and rheological characterization

A Newtonian and a viscoelastic fluid were used in

this investigation. The Newtonian fluid is de-ionized water and the viscoelastic fluid is an aqueous solution of polyacrylamide (Sigma-Aldrich; average molecular weight, Mw = 1.8 × 107 g mol-1) at a concentration of 125 ppm (w/w), which was proposed as a blood analogue solution [3,5,9]. The density, ρ, of the viscoelastic solution is 998.2 kg m-3 at 293.2 K.

The rheology of the non-Newtonian fluid was

measured in both extensional and shear flows. The extensional flow characterization used a capillary break-up extensional rheometer (Haake CaBER 1, Thermo Scientific) and a characteristic relaxation time λ = 0.038 s was measured. For the shear flow rheological characterization, a shear rheometer (Anton Paar, model Physica MCR301) was used with a cone-plate geometry (75mm diameter and 1º angle)

operating in the shear rate range of 1 ≤ γɺ /s-1 ≤ 7×103.

Figure 2 shows the master curve obtained at the reference temperature (T = 293.2 K) by using the time-temperature superposition method [10]. The variation of the viscosity with temperature can be described using an Arrhenius equation of the form

0ln( ) ( / ) (1 / 1 / )Ta H R T T∆= − . Since the range of

temperatures of the measurements is small, the shift

factor, aT, can be simplified to 0( ) / ( )Ta T Tη η= .

Furthermore, in Figure 2 we also show the shear viscosity variation with shear rate, measured for the human blood at 310.2 K [11]. The experimental data obtained for the PAA viscoelastic fluid was fitted using a Carreau model:

0

2 (1 ) / 2

( )

[1 ( ) ] n

η ηη ηΛγ

∞∞ −

−= +

+ ɺ

. (1)

and the parameters obtained were: η0 = 0.5 Pa s, ηS = 0.002 Pa s, Λ = 29 s and n = 0.33.

10-2 10-1 100 101 102 103 1041E-3

0.01

0.1

1

10Blood analogue

283.2 K 288.2 K 293.2 K 298.2 K 303 K

Human Blood 310.2 K

Human blood(ii)

(η /

a T) /

Pa

s

γ aT / s-1

0.001(i)

.

Blood analogue

Fig. 2. Master curve of the steady shear viscosity for the blood analogue solution at 293.2 K and rheological shear data for human blood at 310.2 K [11]. The symbols represent experimental data and the solid line represents a fit to a Carreau model. (i) Miniumum measurable shear viscosity calculated from 20× the minimum measurable torque of the rheometer; (ii) onset of secondary flow due to Taylor instabilities. 4. Results

To characterize the flow we use the Reynolds (Re)

and the Deborah (De) numbers. The Reynolds number is defined as Re = ρUD/η, where U is the average velocity in the upstream channel and η is the shear viscosity at the characteristic shear rate,γɺ =U/D. The

Deborah number is defined as De =λγɺ , where λ is the

relaxation time measured with the CaBER. In Figure 3 we show streak images obtained at the

same flow rate in the converging bifurcation (two inlets and one outlet) with different configurations for the reference fluid (Figure 3a) and for the blood analogue fluid (Figure 3b). As can be seen, the viscoelastic fluid flow revealed a different and more complex flow pattern than the Newtonian fluid flow. In both configurations presented, when elasticity becomes important, recirculations appear in the inlet channels for the viscoelastic fluid flow. Oppositely, for the Newtonian fluid flow, no recirculations are visible within the range of flow conditions studied. Furthermore, when the flow rate is increased further, the recirculations increase in size (not shown here).

Regarding the flow of the blood analogue solution in

the diverging bifurcation (one inlet and two outlets), in Figure 4 we present a binary image obtained by

adjusting the threshold level. It is possible to see that under high elasticity flow conditions, the tracer particles tend to form aggregated structures near the bifurcation point and that the size of these aggregates increases in time.

Fig. 3. Flow patterns obtained with the Newtonian (a) and blood analogue fluid (b) flowing in the converging bifurcated microchannel. For the viscoelastic case, the recirculations are highlighted by the red dashed lines.

Fig. 4. Binary image obtained by adjusting the

threshold for Re = 39.5 and De = 479.

The dynamics of this phenomenon can be compared to what occurs in the microvascular networks, in which platelets or other cellular elements, such as fatty material tend to accumulate narrowing the blood vessel available for blood flow. 5. Conclusions

In this work, the flow of a Newtonian and a well-established blood analogue solution with viscoelastic properties was investigated in microchannels containing different types of bifurcations. We have shown that at the microscale, Newtonian and non-Newtonian fluids reveal a markedly different flow behavior. In particular, the flow of the blood analogue solution through converging bifurcations, reveal the development of recirculations upstream of the bifurcating point whereas for the Newtonian fluid, no flow separation was observed in the Reynolds number range investigated. The recirculations are usually associated with low velocities and shear stresses, and are therefore regions where the local accumulation of particles or other products are recurrent. Acknowledgements

The authors acknowledge the financial support provided by Fundação para a Ciência e a Tecnologia (FCT), COMPETE and FEDER through projects PTDC/EQU-FTT/113811/2009, PTDC/SAU-BEB/108728/2008, PTDC/EME-MFE/099109/2008, REEQ/262/EME/ 2005 and REEQ/928/EME/2005. References [1] Ewoldt RH, Hosoi AE and McKinley GH. Nonlinear viscoelastic biomaterials: meaningful characterization and engineering inspiration. Integr. Comp. Biol. 49, 40-49, 2009. [2] Stuart J and Kenny MW. Blood rheology. J. Clin Pathol. 33, 417-429, 1980. [3] Vlastos G, Lerche, D, Koch B, Samba O and Pohl M. The effect of parallel combined steady and

a1) Re = 2.20

b1) Re = 2.20 De = 19.2

b2) Re = 2.20 De = 19.2

a2) Re = 2.20

oscillatory shear flows on blood and polymer solutions. Rheologica Acta 36, 160−172, 1997. [4] Yilmaz F, Gundogdu MY. A critical review on blood flow in large arteries; relevance to blood rheology, viscosity models, and physiologic conditions. Korea-Australia Rheology Journal 20, 197-211, 2008. [5] Sousa PC, Pinho FT, Oliveira, MSN and Alves MA. Extensional flow of blood analogue solutions in microfluidic devices. Biomicrofluidics 5, 014108-1-19, 2011. [6] Tuma RF, Duran WN and Ley K. Handbook of physiology. Microcirculation. Academic Press, 2nd Edition, USA, 2008. [7] McDonald JC, Dufy DC, Anderson JR, Chiu DT, Wu H and Whitesides GM. Fabrication of microfluidic systems in poly(dimethylsiloxane). Electrophoresis 21, 27-40, 2000.

[8] Sia SK and Whitesides GM. Microfluidic devices fabricated in poly(dimethylsiloxane) for biological studies. Electrophoresis 24, 3563–3576, 2003. [9] Thurston GB. Viscoelastic Properties of Blood and Blood Analogs. Advances in Hemodynamics and hemorheology 1, 1-30, 1996. [10] Dealy J and Plazek D. Time-temperature superposition – A users guide. Rheology Bulletin 78, 16-31, 2009. [11] Chien S. Shear dependence of effective cell volume as a determinant of blood viscosity. Science 168, 977−979, 1970.