# Electrode Cooling Effect on Out-Of-Phase Electrothermal Streaming in Rotating Electric Fields

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Basic Design of the Circulating Electrode Structure

_{1}= $A\mathrm{cos}\left(\omega t\right)$, V

_{2}= $A\mathrm{cos}\left(\omega t+90\xb0\right)$, V

_{3}= $A\mathrm{cos}\left(\omega t+180\xb0\right)$, and V

_{4}= $A\mathrm{cos}\left(\omega t+270\xb0\right)$, respectively. Here, A is the voltage amplitude, ω is the angular field frequency of the applied voltage wave (Table 1). On this basis, electric field vector at the center of circulating electrode array is approximately of the following form:

#### 2.2. Chip Fabrication

#### 2.3. Sample Preparation and Experimental Setup

#### 2.4. Flow Components of Electrothermal Streaming in Rotating Electric Fields

_{c2}= $\frac{\sqrt{5}\sigma}{2\pi \epsilon}$. In addition, within low-frequency ranges f < f

_{c1}, fluid motion of TWET whirlpool diminishes, while that of vertical SWET streaming enhances, which would exert a negative impact on the rotating flow pattern of out-of-phase induction vortex. Specifically, the horizontal TWET whirlpool shrinks in size, and exhibits more helical flow streamlines cascading downward at lower field frequencies.

#### 2.5. Computational Model

_{Au}= 340 W·m

^{−1}·k

^{−1}, considerably higher than that of water solution k

_{water}= 0.6 W·m

^{−1}·k

^{−1}and glass substrate k

_{glass}= 1 W·m

^{−1}·k

^{−1}, so that the electrode structures can be treated as ideal thermal conductors which are effectively isothermal bodies. Then, for inputting voltage signals from function generator to the microelectrode arrays, external wire connection has to be achieved by fabricating large-scale electrode pads of millimeter dimension, as shown in Figure 1a,b. In similar device configurations, heat exchange between metal electrode bars and ambient environment has a propensity to occur due to external natural convection. Since gold electrodes are good thermal conductors, they can transfer cooling energy from ambient environment to the device internal, which would make the electrode bars not only an isothermal body but also fixed at the referential temperature T

_{0}= 293.15 K of atmospheric condition for a sufficiently large heat transfer coefficient. That is, because gold microelectrodes of excellent heat dissipation capability are connected to external wires by large-scale metal pads, electrode cooling due to external natural convection ought to be taken into consideration and modeled by setting the electrode surface at the ambient temperature T

_{electrode}= T

_{0}= 293.15 K in the simulation analysis.

_{glass}= 1 [W·m

^{−1}·k

^{−1}], with the bottom surface of the fluidic device set at ambient temperature due to strong natural convection at the microscope platform.

^{−10}[F/m] and thermal conductivity k

_{water}= 0.6 [W·m

^{−1}·k

^{−1}], where several large-voltage effects including nonlinear Joule heating source, temperature-dependent dynamic viscosity and improved electrothermal body force are taken into account [34,50].

## 3. Results and Discussion

#### 3.1. Experimental Observation of ROT-ETF Fluid Motion

_{glass}= 1 [W·m

^{−1}·K

^{−1}] is used to construct the insulating base for supporting the circulating electrode array. The low heat dissipation capability of glass material effectively makes the hot spots due to electric heating generation located right on the electrode surface, namely, the maximum temperature rise takes place right in the electrode plane, thereby actuating a repulsion-type induction vortex (Figure 3b in [34]). In this sense, preliminary theoretical analysis goes against the counterclockwise rotating whirlpool captured in our experiment with a high-speed CCD camera.

#### 3.2. Electrode Cooling Effect on Rotating Direction of Induction Whirlpool

_{si}= 140 [W·m

^{−1}·k

^{−1}] is able to remove the internal Joule heating to exterior of the device with high efficiency. Under such circumstance, the maximum temperature rise takes place in the medium bulk at some vertical distance above the electrode array rather than right on the channel bottom surface. Accordingly, electrolyte solution on the electrode surface has a lower conductivity than that at the hot spots on top of the electrode array, resulting in an attraction-type induction fluidic device.

_{Au}= 340 [W·m

^{−1}·k

^{−1}].

#### 3.3. Comparison between Theory and Experiment

_{c1}= 11 MHz, the multiple small in-phase SWET micro-vortices rotating orthogonal to the electrode surface are induced by the oppositely polarized electrodes with 180° phase difference and dominate over the horizontal out-of-phase TWET vortex. In Figure 5b, one large induction whirlpool is generated at the relaxation frequency, and it is not possible to find the vertical SWET flow components any longer. The out-of-phase induction vortex cascades downward with a helix flow profile, which coincides well with our experimental measurement in Figure 2e. According to simulation result in Figure 5c, the electrothermal flow field is completely stipulated by the horizontal out-of-phase TWET whirlpool at f = 35 MHz, with quite circular rotating streamlines. Since the field frequency 35 MHz surpasses the characteristic crossover frequency ${f}_{c2}=\sqrt{5}\sigma /2\pi \epsilon $ = 24.6 MHz for SWET, the SWET flow component in perpendicular orientation to the electrode plane decays considerably compared to the low-frequency limit, that is, the horizontal co-field TWET whirlpool governs the electrothermal flow field within the entire fluidic chamber at such high field frequencies. Consequently, the rotating electrothermal streamlines seem no longer to spiral downward, which can be validated by the experimental observation in Figure 2f as well.

#### 3.4. Numerical Prediction on the Effect of Electrical Conductivity

_{0}= 293.15 K of the ambient environment, due to, in part, external natural convection on the large-scale electrode pads of millimeter dimension for external wire connection. Under such electrode-cooling effect, the temperature field as well as the electrothermal flow field were calculated for different electrical conductivities of the suspending medium, where Fourier heat conduction in the presence of Joule medium heating has been taken into account.

## 4. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Experimental setup of the microfluidic chip for studying the behavior of electrothermal flow in a rotating electric field (ROT-ETF). (

**a**) An optical micrograph of the four-phase polynomial electrode configuration employed in this work; (

**b**) A picture of the experimental microfluidic device where Plant Design Management System (PDMS) microchamber is plasmally bonded to the glass substrate with desired circulating electrode patterns; (

**c**) Schematic of the applied 90°-phase-shifted sinusoidal voltage waves that produce a counterclockwise rotating electric field above the cross-shaped interelectrode gaps; (

**d**) The fully-developed co-field TWET induction whirlpool above the electrode array at the Debye frequency of electrolyte suspension.

**Figure 2.**Frequency-dependent flow field of ROT-ETF captured in experiment using a high-speed CCD camera, for given voltage amplitude A = 7.5 V. (

**a**) f = 1 MHz; (

**b**) f = 3 MHz; (

**c**) f = 7 MHz; (

**d**) f = 9 MHz; (

**e**) f = 11 MHz (relaxation frequency of the dielectric dispersion); (

**f**) f = 35 MHz. With increasing field frequency beyond the reciprocal charge relaxation time, rotating streamlines of the anticlockwise induction whirlpool become more circular and less helically cascading downward.

**Figure 3.**Construction of the 3-D simulation model: (

**a**) Schematic of the 3-D computational domain; (

**b**) A top view of the four-phase polynomial electrode configuration.

**Figure 4.**Influence of external natural convection-induced cooling of the gold microelectrodes on temperature field distribution and rotating direction of the central TWET whirlpool (unit: K). (

**a**) A volumetric arrow plot of electrothermal flow field and x-z cross-sectional surface plot of internal temperature field at y = −200 μm by ignoring the exchange heat flux on the electrode pads, where the anti-field induction vortex rotates clockwise; (

**b**) Under the influence of evident electrode cooling, out-of-phase induction EHD streaming transits from repulsion-type to attraction-type which is in the counterclockwise direction of signal-phase propagation.

**Figure 5.**Simulation results of ROT-ETF flow field under distinct field frequencies where electrode cooling effect is taken into account: (

**a**) f = 1 MHz for low-frequency limit; (

**b**) f = 11 MHz at the characteristic dispersion frequency; (

**c**) f = 35 MHz within the high-frequency range.

**Figure 6.**Comparison of electrothermal flow velocity and temperature elevation between theory and experiment for both cooling and non-cooling cases. (

**a**) Frequency-dependence of maximum horizontal flow velocity; (

**b**) Voltage-dependence of maximum horizontal flow velocity; (

**c**) Voltage-dependence of maximum temperature rise within the medium bulk.

**Figure 7.**Numerical prediction on conductivity-dependence of the device performance, including (

**a**) the maximum temperature elevation; (

**b**) electrothermal flow velocity; and (

**c**) ideal operation frequency.

Symbol | Implication | Value or Unit |
---|---|---|

$\varphi $ | Electrostatic potential field | [V] |

E | Electric field vector | [V/m] |

T | Temperature field | [K] |

p | Hydrostatic pressure field | [Pa] |

u | Flow velocity vector | [m/s] |

ρ_{f} | Volumetric free charge distribution | [C/m^{3}] |

ρ_{b} | Volumetric bound charge distribution | [C/m^{3}] |

f_{ET} | Electrothermal body force | [N/m^{3}] |

ΔT | Temperature elevation within the bulk fluid | [K] |

$\epsilon $ | Liquid permittivity | 7.08 × 10^{−10} [F/m] |

$\sigma $ | Electrolyte conductivity | 0.05 [S/m] |

f_{c1} | Charge relaxation frequency | $\sigma /2\pi \epsilon $ = 11 [MHz] |

τ | Charge relaxation time | $\epsilon /\sigma $ = 1.42 × 10^{−8} [s] |

f_{c2} | Characteristic crossover frequency of SWET | $\sqrt{5}\sigma /2\pi \epsilon $ = 24.6 [MHz] |

f | Field frequency | 1~35 [MHz] |

ω | Angular field frequency | 2πf |

d | Nearest distance between oppositely polarized electrodes | 50 [μm] |

A | AC voltage amplitude | [V] |

E_{0} | Electric field magnitude | 2A/d |

T_{0} | Temperature of reference | 293.15 [K] |

k_{water} | Thermal conductivity of water | 0.6 [W·m^{−1}·K^{−1}] |

k_{PDMS} | Thermal conductivity of PDMS lid | 0.2 [W·m^{−1}·K^{−1}] |

k_{glass} | Thermal conductivity of glass substrate | 1 [W·m^{−1}·K^{−1}] |

k_{Si} | Thermal conductivity of silicon material | 140 [W·m^{−1}·K^{−1}] |

k_{Au} | Thermal conductivity of gold electrodes | 340 [W·m^{−1}·K^{−1}] |

η | Dynamic viscosity of water | 0.001 [Pa·s] |

H | Thickness of the fluid layer | 500 [μm] |

H_{Sub} | Thickness of glass substrate | 500 [μm] |

H_{Lid} | Thickness of PDMS lid | 100 [μm] |

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## Share and Cite

**MDPI and ACS Style**

Liu, W.; Ren, Y.; Tao, Y.; Chen, X.; Wu, Q.
Electrode Cooling Effect on Out-Of-Phase Electrothermal Streaming in Rotating Electric Fields. *Micromachines* **2017**, *8*, 327.
https://doi.org/10.3390/mi8110327

**AMA Style**

Liu W, Ren Y, Tao Y, Chen X, Wu Q.
Electrode Cooling Effect on Out-Of-Phase Electrothermal Streaming in Rotating Electric Fields. *Micromachines*. 2017; 8(11):327.
https://doi.org/10.3390/mi8110327

**Chicago/Turabian Style**

Liu, Weiyu, Yukun Ren, Ye Tao, Xiaoming Chen, and Qisheng Wu.
2017. "Electrode Cooling Effect on Out-Of-Phase Electrothermal Streaming in Rotating Electric Fields" *Micromachines* 8, no. 11: 327.
https://doi.org/10.3390/mi8110327