2.1 The microfluidic chip

The microfluidic chip is shown schematically in Fig.1. It consists of the reservoir channel, T-jump channel and sample-detection channel. The microchannels were fabricated in a 2 mm-thick PMMA substrate by micromill technique. The reservoir channel, 1 mm (w)× 0.8 mm(h), is in an invariable temperature environment by an external thermoelectric cooler. To ensure a constant flow rate and heating efficiency, the T-jump channel is of a trapezoid- rectangle-trapezoid shape of 11 mm(w)×0.1 mm(h). The sample-detection channel is a 1 mm(w)×1 mm(h)×30 mm(l) groove, being sealed on both sides by 20 μm-thick Kapton film that allows X-ray beams to pass through. Adhered to the substrate is a 1 mm-thick PMMA cover plate, with two holes for connecting the channel ends to Telflon tubing and a pumping system (Hamilton, Switzerland) that provides a steady flow rate for the microfluidics.

Fig.1.Full-screen View

Schematic 3-D view of the T-jump microfluidic chip.

2.2 The T-jump channel

The area where the T-jump channel connects the reservoir channel forms a sudden dimensional change, hence enlarging the area of active heating. Different configurations of the T-jump channel were proposed (Fig.2). Three-dimensional steady state analysis models were built to evaluate performance of the three types of channels, and their heat transfer characteristics were analyzed by fluid dynamics analysis software ANSYS CFX. The Navier-Stokes and continuity equations were solved by coupling with heat transfer equations under the following boundary conditions: (1) constant mass flow rate at microchannel inlet and 1atm pressure at microchannel outlet; (2) constant front wall heat flux and adiabatic wall for others; (3) specific temperature of inlet fluid; (4) no-slip condition at the walls; and (5) incompressible fluid.

Fig.2.Full-screen View

Schematic view of T-jump microchannels. (a)rectangular (b) semielliptic (c) trapezoid

CFD analysis of the T-jump channels was investigated using water as working fluid. The flow characteristic was evaluated by the Reynolds number (Re) calculated by Eq.(1)

where ρ is the fluid density, v is the average fluid velocity, μ is the fluid viscosity and D is the hydraulic diameter defined as

where a is the channel width and b is the channel height. In CFD analysis, the flow behavior is in laminar regime with Reynolds number below 2000. For the range of flow rate used in this work, Re is not larger than 20. The heat transfer characteristic was analyzed the Nusselt number (Nu) as:

where h is the heat transfer coefficient and λ is the thermal conductivity of fluid.

To compare performance of the three microchannel configurations, CFD analysis was conducted under the inlet flow rate of 10 μL/s at 35℃ and heat flux of 70 kW/m². Under these conditions, the heat is transferred to the fluid by forced convection heat transfer. Fig.3 shows the Nusselt number as a function of inlet flow temperature in rectangle, semiellipse and trapezoid T-jump channels. Comparing the three sets of data, one sees that Nu of the trapezoid channel is the highest of all the channels. Although the Nu of trapezoid channel decreases slightly with increasing temperature, it keeps a strong micro-scale effect. The results of simulations at different heat fluxes and flow rates are similar. This shows that the channel geometry has great effect on heat transfer characteristics of microchannels. That the trapezoid channel performs the best in heat transfer can be attributed to the constantly change of cross-sectional area. Due to the steady contraction of cross-sectional area, the flow in trapezoid channel experiences thermally developing laminar flow with significant entrance effect. In addition, the structure leads to some perturbation that aids to improve local heat transfer coefficient in the laminar flow.

Fig.3.Full-screen View

The correlation of Nusselt number with inlet temperature.

2.3 The microheater

Considering thermal efficiency and non-disposable recyclability, a Pt film heater line is used. It is independent of the microfluidic chip, fastened on the PMMA substrate. When an electrical current passes through the resistance heater, the heat generated is transferred to the fluid in the microchannel. In this case, two main points, power generation and electromigration, should be taken into account in designing the dimensions of the heater ^[19]. The amount of heat, Q, transferred to the microfluidics can be estimated by

where C is the specific heat capacity, m is the mass flow, and ΔT is the temperature change of fluid. To be specific, it can also be expressed in terms of power requirement:

where P $$ is the power consumption of heater, η is the thermal efficiency, m_r is the mass flow rate of microfluidics.

The resistance of the heater, R_H, is given by

where V is the supply voltage. The dimensions of the Pt film heater can be determined by Eq.(7)

where l, w and t are length, width and thickness of the Pt film heater, respectively, and ρ_f is resistivity of the Pt film which is different from bulk Pt owing to influence of mean free path of electrons.

In this study, the power source for heater was generated by a digital DC power supply (0–60 V), the thermal efficiency η was estimated at 20% conservatively, the Pt film was 200 nm thick, and the mass flow rate of fluid was 10 mg/s. Resistivity of the Pt film was 2.8×10⁻⁷ Ω·m, and specific heat capacity of water is 4200 J·kg⁻¹·K⁻¹. Finally, the temperature increment of the fluid are presented as a function of width-length ratio of the Pt film heater line:

where α is a coefficient determined by

Fig.4 shows temperature increment of the passing flow as a function of the width-length ratio at different applied voltages. The temperature increment rises with the width-length ratio and the applied voltage. The range of temperature increment of the fluid in the channel at a certain range of applied voltage can be decided by the width-length ratio to optimize the heater performance. We chose the width-length ratio was 0.0052 in this design.

Fig.4.Full-screen View

The temperature increment vs width-length ratio of the Pt film heater line at different applied voltages. The orange dash marks the width-length ratio we used in the design.

Another issue is the transport of metallic atoms in conductor, which is driven by the interaction with electrons of passing current. This electromigration decreases reliability of thin-Pt-film electronic component at a current density up to 10⁷A/cm^{2 [21]}, which shall be the limit of current density of the heater line. Therefore, a zigzag heater line, spaced 100 μm apart with width of 200 μm, was designed and located at the trapezoid T-jump channel (Fig.5). With the use of lift-off technique, 50 nm Cr and 200 nm-thick thin Pt film was deposited on a 1mm-thick glass substrate. The room-temperature resistance of the heater, including lead wires, is roughly 300 Ω.

Fig.5.Full-screen View

Schematic drawing of the Pt heater on the microchannel.

3.1 Fluorescence measurement

Temperature-dependent fluorescence dye, rhodamine B, was used in temperature measurements. The fluorescence intensity of rhodamine B was measured and converted to temperature value according to the calibrated intensity- temperature curve. Prior to the measurement, rhodamine B (Sigma Aldrich, USA) was dissolved into 15 mmol/L Na₂CO₃ buffer. Filtered with a 0.2 μm syringe filter, the final concentration of rhodamine B was 87 $\text{μ}$mol/L. Fluorescence imaging was performed using a CCD camera (DP71, Olympus, Japan) and commercial fluorescence microscope (BX51, Olympus, Japan) equipped with a standard green fluorescence filter set. The exposure time was set to a constant manually and the white/black balance control was remained off throughout measurements.

In order to correlate the fluorescence intensity with temperature, a microfluidic chip integrated with a Pt100 thermal sensor (Heraeus, Germany) along the microchannel was fabricated. The microfluidic chip was fixed onto a silicone rubber thermostat (homemade) for a constant temperature environment of rhodamine B solution which was injected into the microchannel. The fluorescence images of the channel filled with dye solution were obtained at different temperatures of 25°C–80°C. To eliminate effects of background fluorescence inhomogeneity, background and room temperature images were acquired preferentially during the measurement. For each pixel, the intensity value was subtracted with the background, and normalized with the intensity value at room temperature.

3.2 Fluorescence experimental results

As shown in Fig.6, the correlation between intensity and temperature was established. The normalized intensity at each temperature was averaged from multi-measurement. The data can be fitted by Eq.(10), with R²=0.998:

Fig.6.Full-screen View

The calibrated intensity-temperature curve.

where T is the temperature of rhodamine B solution, and I is the normalized fluorescence intensity of rhodamine B solution after background subtraction.

The calibrated intensity-temperature relationship was used to explore thermal changes of fluid in the T-jump microchannel. A flow of the rhodamine B solution was continuously injected into the microfluidic chip and dissipated the heat energy provided by external Pt heater as described in Section 2.3. By changing the voltage applied on the Pt heater, various temperature increments of the fluid at each flow rate were obtained from the fluorescent images at the outlet of T-jump microchannel according to the intensity-temperature calibration curve.

The fluorescence inside the microchannel was measured at flow rates of 5 and 10 μL/s at 25°C of fluid in the reservoir channel. The temperature change, ΔT, was determined as a function of power input. Fig.7 shows the results at power input of 0.22–2.1 W at 5 and 10 μL/s, with ΔT = 4°C–30°C at the outlet of T-jump microchannel. As can be seen, higher heater power generated larger temperature increment.

Fig.7.Full-screen View

Temperature changes (with respect to 25°C) at the outlet of T-jump area as a function of power input.

It should be noted that from the flow rates of 5 μL/s to 10 μL/s, the temperature increment is reduced almost by half at the same power input. Higher flow rate resulted in smaller T-jump owing to the reduction of time in which the fluid contacted with Pt heater. In addition, the heating rate could be up to 180 and 210°C/s at the flow rates of 5 and 10 μL/s, respectively, for heater power ranging from 0.22 to 2.1 W.