Experimental Study on the Viscoelastic Flow Mixing in Microfluidics

Microfluidic technology uses micro-scaled channels, chambers and valves to control and manipulate single-phased or multiphased fluids in the microliter to picoliter volume range, and deliver, mix or synthesize substances in the fluid. The fluid manipulation is confined to the micrometerscaled space and therefore offers many advantages which has not been realized in traditional methods. It requires much less sample liquid, allows rapid diffusion and has a faster reaction in the micro-chambers to save time for testing or synthesizing. The designable microchannel structure also offers large freedom to control the liquid flow. Since its emergence, microfluidic technology has attracted much research attention in different areas including fluid dynamics, nanotechnology, biochemistry, biotechnology and clinical applications. The integration of microfluidic technology with biotechnology and clinical research has promoted a lot of applications in tissue engineering [1, 2], disease diagnosis [3, 4] and gene delivery and transfer [5]; some examples are listed in Table 1. Among the aforementioned biotechnology and clinical applications, the mixing of substances in the microfluidics is one important process. In the microfluidic mixer, the synthesis and delivery of lipid or drugloaded nanoparticles [6, 7] or microgels [8] are realized. For example, lipid nanoparticles containing small interfering RNA (siRNA) are synthesized by microfluidic mixing for enabling therapeutic applications [9]. The nanoparticles are also used for lipofection of plasmid DNA into human mast cell lines [10]. In addition, the microfluidic mixer promotes the biosensing applications. An active mixing method was proposed to increase the capture efficiency in a heterogeneous microfluidic immunosensor [11]. A micro-mixing system was later developed for the detection of immunoagglutination [12] and rapid labeling of immune cells with antibodies [13]. Simultaneous genetic detection of multiple plant viruses was also realized through an autonomous microfluidic sample mixing device [14]. More importantly, the microfluidic mixing technology has already manifested great potential in diagnosis and therapy applications. A microfluidic device was developed to tunably mix reactive oxygen species for optimizing photodynamic therapy [15]. The control of drug release was also realized 1The First Affiliated Hospital of Sun Yat-Sen University, Sun Yat-Sen University, Guangzhou 510080, China


Introduction
Microfluidic technology uses micro-scaled channels, chambers and valves to control and manipulate single-phased or multi-phased fluids in the microliter to picoliter volume range, and deliver, mix or synthesize substances in the fluid. The fluid manipulation is confined to the micrometer-scaled space and therefore offers many advantages which has not been realized in traditional methods. It requires much less sample liquid, allows rapid diffusion and has a faster reaction in the micro-chambers to save time for testing or synthesizing. The designable microchannel structure also offers large freedom to control the liquid flow. Since its emergence, microfluidic technology has attracted much research attention in different areas including fluid dynamics, nanotechnology, biochemistry, biotechnology and clinical applications. The integration of microfluidic technology with biotechnology and clinical research has promoted a lot of applications in tissue engineering [1,2], disease diagnosis [3,4] and gene delivery and transfer [5]; some examples are listed in Table 1.
Among the aforementioned biotechnology and clinical applications, the mixing of substances in the microfluidics is one important process. In the microfluidic mixer, the synthesis and delivery of lipid or drugloaded nanoparticles [6,7] or microgels [8] are realized. For example, lipid nanoparticles containing small interfering RNA (siRNA) are synthesized by microfluidic mixing for enabling therapeutic applications [9]. The nanoparticles are also used for lipofection of plasmid DNA into human mast cell lines [10]. In addition, the microfluidic mixer promotes the biosensing applications. An active mixing method was proposed to increase the capture efficiency in a heterogeneous microfluidic immunosensor [11]. A micro-mixing system was later developed for the detection of immunoagglutination [12] and rapid labeling of immune cells with antibodies [13]. Simultaneous genetic detection of multiple plant viruses was also realized through an autonomous microfluidic sample mixing device [14]. More importantly, the microfluidic mixing technology has already manifested great potential in diagnosis and therapy applications. A microfluidic device was developed to tunably mix reactive oxygen species for optimizing photodynamic therapy [15]. The control of drug release was also realized through stabilized polymeric nanoparticles generated in an efficient microfluidic mixing system [16]. A passive mixing microfluidic urinary albumin chip was later demonstrated for chronic kidney disease assessment [17].
In the aforementioned works, a conventional Newtonian fluid is usually used as the fluid carrier in microfluidic mixing devices. However, most body fluids, especially blood, have different hydrodynamic properties with conventional Newtonian fluids. Such liquids process both viscosity and elasticity, and are categorized as viscoelastic fluids. The viscoelastic fluid plays an important role in the circulation system of the human body; the study of its flow properties will greatly help to understand the human physiology. The flow of blood in vessels has been widely studied in both theoretical and experimental aspects [18][19][20][21]. In one study, Chakravarty and Mandal investigated the blood flow in overlapping stenosed vessels, the wall of which is assumed to be elastic and deformable [22]. The blood flow through the overlapping stenosed vessels was also numerically and analytically studied by Riahi et al. [23]. The fluid in the aforementioned model is assumed to be Newtonian; however, in a realistic situation, the blood flow in vessels is viscoelastic. Therefore, fluid models with both viscosity and elasticity are proposed to study these flows. Different non-Newtonian characteristics such as yield stress, pseudo-plasticity and viscoelasticity [24] are investigated at different shear rates.
The mixing of viscoelastic fluid in the microfluidic system was also intensively studied and found to be much larger than that of the Newtonian fluid [33]. The enhanced mixing is usually achieved by generating vortex in the viscoelastic microfluidic flow due to the elastic stress in the fluid, which is not observed in the Newtonian flow even at high flow rate conditions [34][35][36]. An early experiment found a significant difference between Newtonian and non-Newtonian fluids, and concluded that the shear thinning behavior of the blood could be the dominant non-Newtonian property [37]. On the other hand, a work discusses the importance of extensional rheology, in addition to the shear rheology of solutions when mimicking the blood circulation system [38]. New technologies such as the micro-particle image velocimetry (PIV) technique were then applied to analyze the human blood flow [39]. A recent study investigated the unidirectional large-amplitude oscillatory shear flow of the blood to assess its non-Newtonian behaviors, which describes well the unidirectional pulsatile flow in veins and arteries [40]. Here, we studied the viscoelastic flow in a T-shaped microchannel structure, which mimics the blood flow in the bifurcated vessels as shown in Figure 1A. Two streams of viscoelastic fluid are injected into a T-shaped microchannel and pumped with periodical pulse, mimicking the pulse of blood in vessels. Specifically, the flow pattern and mixing of the two streams are monitored transiently. The integration of microfluidic technology with the blood flow research could not only provide a new approach to understand the related disease mechanism, but also be used to analyze the drug mixing and delivery in the blood flow.

Methods
In this paper, the polyacrylamide (PAM) solution is used as the viscoelastic fluid to mimic the blood flow in the microchannel structure. Here, we use the PAM solution of 200 ppm molecular weight. As shown in Figure 1B, the microchannel is a T-shaped structure, which is fabricated on a poly-(dimethylsiloxane) (PDMS) layer through the typical soft lithography method. The PDMS layer is then bonded with a glass slide as shown in Figure 1C. In the experimental setup, the solution is injected into both inlet A and inlet B, which are noted as fluid A and fluid B with injection flow rates of Q A and Q B , respectively. The flow rates are controlled by two flow pumps independently. After entering the microchannel, the two fluids first meet at the center of the "injection channel" and then pass through a narrow "bottleneck channel" before entering the abruptly expanded "mixing channel". To evaluate the mixing effect between the two pumped fluids, the fluorescent dye rhodamine B is pre-mixed with fluid A. Rhodamine B can be excited by a 435-nm-wavelength laser and radiate fluorescent light. The fluorescence intensity of the fluid changes as the two fluids mix with each other in the microchannel, and can thus be used to assess the mixing degree in the microchannel.
The fluorescent light intensity is recorded as a gray value at each pixel point in the mixing channel for a long enough time, and the fluid mixing degree is analyzed according to the gray values. In this experiment, the flow patterns are  [27] Surface antigen bonding method in microfluidic channels [3] Vortex chip for high-throughput and label-free cell purification [28] Biomarker detection One-step multiplexed pathogen detection with nano-biosensors [4] Microfluidic droplets as bioreactors for enzymatic amplification [29] Gene delivery and therapy Gene transfection Deliver genes into cells in microfluidic electroporation systems [30] Generate inertial vortex to enhance gene transfection efficiency [31] Production of gene carriers Microfluidic system to improve the production of retroviral vectors [5] Biosynthesis reactor for synthesizing DNA-polycation complex [32] recorded by a high-speed camera with 2048 pixels × 2048 pixels, and the resolution of each pixel is 0.769 µm.
The relaxation time and shear rate of the PAM solution used here are 100/s and 0.12 s, respectively. The concentration of rhodamine B fluorescent dye in fluid A is 10 µg/mL. At such a low concentration, its effect on mixing can be ignored. The size of the T-shaped microchannel is as follows: the length and width of the "injection channel", "bottleneck channel" and "mixing channel" are L 1 = 2 mm, W 1 = 100 µm, L 2 = 600 µm, W 2 = 50 µm, L 3 = 2 mm and W 3 = 600 µm, respectively. The end of the "mixing channel" is connected to the microchannel outlet. In the T-shaped design, the channel design is symmetrical to simplify the analysis. The mixing is further enhanced by an abrupt expansion of the micro channel with W 3 = 12 W 2 . In the experimental records, the microscope focused at the central plane of the flow.

Mixing in the constant injection condition
Before the study of the viscoelastic fluid mixing in the microchannel, we first investigated the mixing of a Newtonian fluid. The glycerol solution is injected into inlet A and inlet B and the corresponding flow rates Q A and Q B are first controlled at a same constant value Q 0 . Figure 2A presents the contour map of the fluorescent dye concentration when Q 0 = 100 µL/h. The color bar represents the normalized dye fluorescent intensity with an arbitrary unit. The red region at the fluid A side stands for concentration 1, and the blue region at the fluid B side stands for concentration 0. The two fluids flow through the bottleneck channel and enter into the mixing channel. The dye concentration profile is stable and a smooth boundary region (green color) is observed in between, which is due to the diffusion of the fluorescent dye during the mixing between fluid A and fluid B. When the injected flow rate increases from 100 µL/h to 500 µL/h as shown in Figure 2B, the diffusion effect decreases and the mixing region shrinks. While for the viscoelastic PAM solution, the mixing is much different from that of the glycerol solution as shown in Figure 2C and 2D. When the PAM solution is injected into the microchannel at Q 0 = 100 µL/h, the mixing region is significantly larger than that in the glycerol solution. The florescence concentration decreases at the fluid A side and increases at the fluid B side compared to the glycerol solution mixing case, indicating an enhanced mixing of the two fluids. PAM has the same viscosity as glycerol; therefore, the mixing increase must stem from the non-zero elasticity in PAM. The elasticity of PAM arises from the interaction between its molecular structure and the flow. The flow conditions induce force on the polymers in the fluid and the polymer chains are stretched and oriented. This non-equilibrium configuration imposes large anisotropic normal stresses, which themselves influence the flow field and the mixing effect, and also explain the relatively rough boundary between the two side fluids. As Q 0 increases to 500 µL/h, the elastic interaction between the two

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Original Article side fluids is further enhanced and a "wave" shaped boundary is observed. The "wave" shape propagates forward in the microchannel and therefore the fluorescent dye distribution at one specific cross-section keeps changing. This special boundary is due to the stronger elastic force between the two fluids. Now the dye concentration profile keeps changing as the "wave" shaped boundary moves forward. The mixing region becomes smaller than that when Q 0 = 100 µL/h; the decreased mixing efficiency is due to the lowered diffusion at the higher flow rate condition.

Mixing in the periodically pulsed injection condition
To mimic the pulsatile blood flow in veins and arteries, the injected flow rate of fluid A is pulsed with a square wave signal, while the flow rate of fluid B remains at a constant value, which can be expressed as: where f is the modulated frequency on fluid A and t is the flow time. The modulation of the driving stimulus can better integrate the microfluidic technology with the real blood flow study. The flow patterns of the viscoelastic solution in the microchannel at different modulated frequencies with Q 0 = 100 µL/h and Q 0 = 500 µL/h are illustrated in Figure 3A and 3B. At Q 0 = 100 µL/h, the distribution of the fluorescence in the microchannel remains almost unchanged as the modulation frequency f varies. In addition, when f = 0.1 Hz (T = 10 s), a small "wave" shaped boundary can be observed between fluid A and fluid B when the fluids flow into the mixing channel. This is because at this lower frequency, more fluid A and fluid B enter the mixing channel in one period and interact with each other elastically. At the relatively high flow rate of 500 µL/h, the fluorescence concentration distribution in the fluid showed a distinct "wave" shape at the boundary between fluid A and fluid B at different modulation frequencies including f = 0. The spatial "wave" period is equal to about 665 µm at different modulated frequencies, which is determined by the elasticity of the viscoelastic fluid itself. It can be observed that with the frequency modulation, the concentration of the fluorescent dye distributes differently. As the driving signal varies periodically in time, the flow in the microchannel and the mixing degree of fluid A and fluid B also change periodically. The transient mixing degree MD t is calculated to quantitatively analyze the mixing efficiency. On the cross-line at the flow distance S 0 after entering the mixing channel, the transient mixing degree at time t is expressed as: In equation (2), C i is the gray value of pixel i on the S 0 cross line at time t when the video is recorded under the microscope. There are a total of P pixels on the cross-line, and C 0 is the average gray value.
We investigated the transient mixing degree of both glycerol solution and PAM solution as shown in In the glycerol solution fluid with a constant flow rate (Figure 4A) or when the driving frequency f = 1 Hz (Figure 4B), the transient mixing degree was only around 10% for the most of the time at all tested flow rates from 100 µL/h to 1000 µL/h. As the modulation frequency varies to f = 0.2 Hz (Figure 4C) and f = 0.1 Hz (Figure 4D), the transient mixing degree remains at a low value when the flow rate Q 0 is at 100 µL/h and 200 µL/h condition. While at the f = 0.2 Hz and f = 0.1 Hz conditions with Q 0 = 500 µL/h and 1000 µL/h, it can be observed that a periodical high mixing degree of around 50% is obtained at the specific time when entering the mixing channel, the period of which equals to the modulating signal period. The increase in the transient mixing degree results from the unbalanced injection between fluid A and fluid B. At the lower modulation frequency and higher injection flow rate, the volume difference between the two fluids entering the microchannel is larger in every half cycle; therefore, there is a large unbalanced force between the two fluids. The direction of the force keeps changing as the injected flow rate of fluid A is modulated, which disturbs the flow and increases the mixing efficiency. The improvement in mixing recurs at every modulated period, and forms a periodical band in the contour map.
In contrast, as shown in Figure 5, the transient mixing degree of the PAM solution in the viscoelastic fluid is generally above 50% at different driving boundary conditions and injected flow rates, which is significantly higher than that of the Newtonian fluid glycerol solution. The increase in the mixing degree is caused by the elastic stress inside and mutual compression between fluid A and fluid B. For the constant flow rate injection case ( Figure 5A) and f = 1 Hz modulation condition (Figure 5B), a significant increase in the mixing degree is found at certain flow distance and flow time when the flow rate Q 0 increases to 1000 µL/h. This high mixing fluid region (the red color region) starts at the beginning of the mixing channel (flow distance = 0), and the mixing degree increases gradually as the fluid flows through the mixing channel. This is due to the elastic interaction between fluid A and fluid B, and the diffusion continues to contribute to the mixing effect. As the modulation frequency decreases to f = 0.2 Hz and f = 0.1 Hz, an obvious high mixing band can be observed at the high flow rate of Q 0 = 500 µL/h and Q 0 = 1000 µL/h, which changes periodically in time with period equaling to the modulation period. The increase in the mixing degree stems from the external driving force which periodically stretches and compresses the polymer inside fluid A

Mixing in different geometric microchannels
The mixing is also studied in the T-shaped microchannel at different geometric parameters. We first increased the width of the mixing channel from 600 µm to 1400 µm as shown on the left side of Figure 6A.  the mixing channel width W 2 = 600 µm microchannel. This is due to a reduction in the mutual elastic stress between fluid A and fluid B in a wider "mixing channel" and the diffusion in the channel also decreases. Therefore, the transient mixing degree only remains around 40%. However, when the modulation frequency decreases to f = 0.2 Hz and f = 0.1 Hz, there is enough fluid A and fluid B interacting with each other in the bottleneck channel and forms a relatively high mixing region, so an obvious high mixing narrow band is formed in the mixing channel. For the most of the time, fluid A and fluid B are not well mixed when they enter the "mixing channel", and then gradually mix with each other due to the diffusion caused by the elastic interaction between them. The transient mixing degree therefore gradually increases as the fluid flows forward.
According to the previous analysis, the interaction between fluid A and fluid B in the bottleneck channel affects the mixing significantly. We investigated the length effect of the bottleneck channel by increasing it from 600 µm to 1400 µm as shown on the left side of Figure 6B. In this long bottleneck microchannel, the transient mixing degree of the PAM solution when Q 0 = 500 µL/h is shown on the right side of Figure 6B. The mixing degree fluctuation of the fluid in the long bottleneck microchannel is relatively small and the high mixing bands at different modulated frequencies are much less obvious compared to the cases when L 2 = 600 µm. This is because the interaction between fluid A and fluid B is constrained and stabilized in the long bottleneck channel.
As the interaction between fluid A and fluid B is constrained in the long bottleneck channel, we then propose a bent bottleneck channel, the side wall of which will exert an extra force on the fluids and therefore can increase the interaction between the fluids. The bent bottleneck microchannel is shown in Figure 7A. We compared the transient mixing of the PAM solution at the injection flow rate of 500 µL/h and 1000 µL/h as shown in Figure 7B and 7C. Compared with the mixing in the long straight bottleneck microchannel, it is obvious that high mixing bands are induced in the bent bottleneck microchannel, which is caused by the enhanced interaction in the bent bottleneck channel. At the constant injection condition, the high mixing region appears at around t = 4 s and t = 10 s when entering the mixing channel. As the fluid flows forward, the high mixing bands expand significantly. This is different from the mixing in the straight bottleneck microchannel; for example, the fluids in Figures 5 and 6 simply flow forward and the high mixing band does not expand much. The high mixing band in the bent bottleneck microchannel is even significant when the flow rate increases to 1000 µL/h. A higher centripetal force is induced at this higher flow rate condition; therefore, the mixing is increased and even the diffusion is affected at this high flow rate. At the driving frequency of f = 1 Hz, regular high mixing regions with the same period are observed when Q 0 = 500 µL/h. While for Q 0 = 1000 µL/h, the mixing is increased due to the stronger interaction between the fluids.

Conclusions
In conclusion, the flow of the viscoelastic fluid in the microchannel structure is studied to mimic the blood flow in vessels. Specifically, two streams of PAM fluids are confronted

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Original Article in a T-shaped microchannel, and the dye concentration profile and transient mixing between the two fluids are investigated. It demonstrates that the dye concentration profile in the viscoelastic flow changes with time even when the injection flow rate remains constant, which is due to the elastic interaction between the two streams. High transient mixing is observed periodically when the one side fluid is driven by periodical pulse stimulus. The approach to integrate microfluidic technology with the blood flow research will provide a new platform to understand the related biological mechanism, and the transient mixing degree of the flow can be used as a reference to investigate the blood flow in vessels.