Effect of Laser-Induced Heating on Raman Measurement within a Silicon Microfluidic Channel
Abstract
:1. Introduction
2. Numerical Simulations
2.1. Preliminaries Prior to Modeling
2.2. Physical Model, Computational Equations and Boundary Conditions
- (1)
- Steady-state (its reasonableness is discussed in Section 4.4), laminar and incompressible flow;
- (2)
- Negligible radiation heat transfer;
- (3)
- Negligible buoyancy;
- (4)
- Constant fluid and solid (silicon) properties;
- (5)
- Negligible viscous heating;
- (6)
- Pyrex glass layer was not explicitly modeled due to its low thermal conductivity;
- (7)
- Only half of the geometry was represented due to the symmetry of the domain;
- (8)
- Gaussian laser beam profile.
- Uniform velocity profile at the inlet (the difference between the uniform and parabolic assumption has been proven to be negligible in our case);
- Constant pressure of 1 bar at the outlet;
- Non-Slip boundary conditions at all walls.
- Constant temperature (T = 296.15 K) at the inlet and dT/dx = 0 at the outlet;
- Adiabatic condition at the fluid-Pyrex boundary (top of the chip);
- The continuity of the temperature and heat flux is automatically used in the CFX code as conjugate boundary conditions to couple the energy equations for the fluid and solid phases. It is defined as Equation (5) at the fluid–solid interface.
- Heat source: a heat flux centered on the solid side of the fluid-solid interface (marked in Figure 1). The heat flux was specified as the absorbed energy with a function of r. The function was conducted from the laser beam intensity form with Gaussian profile:
- The energy absorbed in the solid is:
- Adiabatic condition at the silicon-Pyrex boundary;
- Free convective heat transfer with surrounding air at the lateral walls and underside of the solid. Both the ambient and initial solid temperature was 296.15 K. The free convective heat transfer coefficient hfc was estimated at 10 W·m−2·K−1. This hfc value is close enough due to the relatively minor effect of the heat loss [33].
2.3. Methodology of Orthogonal Array (OA) Analysis
Simulations | Factors | Simulations | Factors | ||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A | B | C | D | E | F | G | H | I | J | K | A | B | C | D | E | F | G | H | I | J | K | ||
No. 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | No. 26 | 1 | 1 | 1 | 4 | 5 | 4 | 3 | 2 | 5 | 2 | 3 |
No. 2 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | No. 27 | 1 | 2 | 2 | 5 | 1 | 5 | 4 | 3 | 1 | 3 | 4 |
No. 3 | 1 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | No. 28 | 1 | 3 | 3 | 1 | 2 | 1 | 5 | 4 | 2 | 4 | 5 |
No. 4 | 1 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | No. 29 | 1 | 4 | 4 | 2 | 3 | 2 | 1 | 5 | 3 | 5 | 1 |
No. 5 | 1 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | No. 30 | 1 | 5 | 5 | 3 | 4 | 3 | 2 | 1 | 4 | 1 | 2 |
No. 6 | 2 | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | No. 31 | 2 | 1 | 2 | 1 | 3 | 3 | 2 | 4 | 5 | 5 | 4 |
No. 7 | 2 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | 1 | No. 32 | 2 | 2 | 3 | 2 | 4 | 4 | 3 | 5 | 1 | 1 | 5 |
No. 8 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | 1 | 2 | No. 33 | 2 | 3 | 4 | 3 | 5 | 5 | 4 | 1 | 2 | 2 | 1 |
No. 9 | 2 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | No. 34 | 2 | 4 | 5 | 4 | 1 | 1 | 5 | 2 | 3 | 3 | 2 |
No. 10 | 2 | 5 | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | No. 35 | 2 | 5 | 1 | 5 | 2 | 2 | 1 | 3 | 4 | 4 | 3 |
No. 11 | 3 | 1 | 3 | 5 | 2 | 4 | 4 | 1 | 3 | 5 | 2 | No. 36 | 3 | 1 | 3 | 3 | 1 | 2 | 5 | 5 | 4 | 2 | 4 |
No. 12 | 3 | 2 | 4 | 1 | 3 | 5 | 5 | 2 | 4 | 1 | 3 | No. 37 | 3 | 2 | 4 | 4 | 2 | 3 | 1 | 1 | 5 | 3 | 5 |
No. 13 | 3 | 3 | 5 | 2 | 4 | 1 | 1 | 3 | 5 | 2 | 4 | No. 38 | 3 | 3 | 5 | 5 | 3 | 4 | 2 | 2 | 1 | 4 | 1 |
No. 14 | 3 | 4 | 1 | 3 | 5 | 2 | 2 | 4 | 1 | 3 | 5 | No. 39 | 3 | 4 | 1 | 1 | 4 | 5 | 3 | 3 | 2 | 5 | 2 |
No. 15 | 3 | 5 | 2 | 4 | 1 | 3 | 3 | 5 | 2 | 4 | 1 | No. 40 | 3 | 5 | 2 | 2 | 5 | 1 | 4 | 4 | 3 | 1 | 3 |
No. 16 | 4 | 1 | 4 | 2 | 5 | 3 | 5 | 3 | 1 | 4 | 2 | No. 41 | 4 | 1 | 4 | 5 | 4 | 1 | 2 | 5 | 2 | 3 | 3 |
No. 17 | 4 | 2 | 5 | 3 | 1 | 4 | 1 | 4 | 2 | 5 | 3 | No. 42 | 4 | 2 | 5 | 1 | 5 | 2 | 3 | 1 | 3 | 4 | 4 |
No. 18 | 4 | 3 | 1 | 4 | 2 | 5 | 2 | 5 | 3 | 1 | 4 | No. 43 | 4 | 3 | 1 | 2 | 1 | 3 | 4 | 2 | 4 | 5 | 5 |
No. 19 | 4 | 4 | 2 | 5 | 3 | 1 | 3 | 1 | 4 | 2 | 5 | No. 44 | 4 | 4 | 2 | 3 | 2 | 4 | 5 | 3 | 5 | 1 | 1 |
No. 20 | 4 | 5 | 3 | 1 | 4 | 2 | 4 | 2 | 5 | 3 | 1 | No. 45 | 4 | 5 | 3 | 4 | 3 | 5 | 1 | 4 | 1 | 2 | 2 |
No. 21 | 5 | 1 | 5 | 4 | 3 | 2 | 4 | 3 | 2 | 1 | 5 | No. 46 | 5 | 1 | 5 | 2 | 2 | 5 | 3 | 4 | 4 | 3 | 1 |
No. 22 | 5 | 2 | 1 | 5 | 4 | 3 | 5 | 4 | 3 | 2 | 1 | No. 47 | 5 | 2 | 1 | 3 | 3 | 1 | 4 | 5 | 5 | 4 | 2 |
No. 23 | 5 | 3 | 2 | 1 | 5 | 4 | 1 | 5 | 4 | 3 | 2 | No. 48 | 5 | 3 | 2 | 4 | 4 | 2 | 5 | 1 | 1 | 5 | 3 |
No. 24 | 5 | 4 | 3 | 2 | 1 | 5 | 2 | 1 | 5 | 4 | 3 | No. 49 | 5 | 4 | 3 | 5 | 5 | 3 | 1 | 2 | 2 | 1 | 4 |
No. 25 | 5 | 5 | 4 | 3 | 2 | 1 | 3 | 2 | 1 | 5 | 4 | No. 50 | 5 | 5 | 4 | 1 | 1 | 4 | 2 | 3 | 3 | 2 | 5 |
Level | Factors | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
A | B | C | D | E | F | G | H | I | J | K | |
1 | 0.5 | 1 | 0.01 | 494 | 0.1 | 1.05 | 0.104 | 30 | 100 | 25 | 0.49 |
2 | 1 | 2 | 0.025 | 867 | 0.55 | 1.72 | 0.151 | 60 | 300 | 64 | 0.64 |
3 | 2.5 | 3 | 0.05 | 997 | 0.89 | 2.36 | 0.268 | 80 | 500 | 100 | 1 |
4 | 5 | 4 | 0.075 | 1261 | 1.53 | 3.06 | 0.285 | 100 | 600 | 144 | 1.5625 |
5 | 10 | 5 | 0.1 | 1584 | 1.92 | 4.19 | 0.6069 | 120 | 800 | 225 | 1.96 |
3. Experimental Section
4. Results and Discussion
4.1. General
4.2. OA Analysis
Factors | A | B | C | D | E | F | G | H | I | J | K |
---|---|---|---|---|---|---|---|---|---|---|---|
SS * | 961.935 | 315.083 | 62.373 | 23.04 | 24.621 | 18.631 | 31.063 | 36.248 | 27.455 | 21.068 | 13.979 |
Contribution | 62.6% | 20.5% | 4.1% | 1.5% | 1.6% | 1.2% | 2.0% | 2.4% | 1.8% | 1.4% | 0.9% |
4.3. Effects of Surface Power and Diameter of Illuminated Area
4.4. Effect of Exposure Time
4.5. Experimental Evidence of Temperature Rise
4.6. Estimation of the Laser-Induced Heating Effect
Dimensionless Group | Expression |
---|---|
π1 | (L·W)1/2)/d |
π2 | λs/(U·(L·W)1/2) |
π3 | ΔTmax·λs·(L·W) 1/2/(P·α) |
5. Conclusions
Acknowledgements
Author Contributions
Nomenclature
A | cross-sectional area along the axial direction, m2 |
cp | specific heat, kJ·kg−1·K−1 |
d | diameter of illuminated area, μm |
D | diffusion coefficient, m2·s−1 |
hfc | free convective heat transfer coefficient, W·m−2·K−1 |
h | height of the microchannel, μm |
I | laser intensity, W·m−2 |
L | length of the microfluidic chip, mm |
p | pressure, Pa |
P | surface power, mW |
q | heat flux, W·m−2 |
r | the distance with the spot center, μm |
T | temperature, K |
ΔTmax | maximum local temperature-rise of fluid, abbreviated as MLT, K |
u | velocity vector |
U | mean velocity, m·s−1 |
w | width of the microchannel, μm |
W | width of the microfluidic chip, mm |
Dimensionless groups
M | Maranzana number |
Pr | Prandtl number, cpfμf/λf |
Re | Reynolds number, 10−6ρfU 2(hw)/(h + w)/μf |
Greek symbols | |
---|---|
α | absorption coefficient |
λ | thermal conductivity, W·m−1·K−1 |
μ | dynamic viscosity, mPa s |
ρ | density, kg·m−3 |
ω0 | radius of laser spot, μm |
Subscripts | |
---|---|
0 | the center of laser spot |
a | ambient |
f | fluid |
s | solid |
Conflicts of Interest
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Lin, Y.; Yu, X.; Wang, Z.; Tu, S.-T.; Wang, Z. Effect of Laser-Induced Heating on Raman Measurement within a Silicon Microfluidic Channel. Micromachines 2015, 6, 813-830. https://doi.org/10.3390/mi6070813
Lin Y, Yu X, Wang Z, Tu S-T, Wang Z. Effect of Laser-Induced Heating on Raman Measurement within a Silicon Microfluidic Channel. Micromachines. 2015; 6(7):813-830. https://doi.org/10.3390/mi6070813
Chicago/Turabian StyleLin, Ying, Xinhai Yu, Zhenyu Wang, Shan-Tung Tu, and Zhengdong Wang. 2015. "Effect of Laser-Induced Heating on Raman Measurement within a Silicon Microfluidic Channel" Micromachines 6, no. 7: 813-830. https://doi.org/10.3390/mi6070813