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ABSTRACT
Electrothermal flow in a microfluidic system is a fast-developing technology because of the advancement in micro-electro-mechanical systems. The motion is driven by the electrothermal force generated by the AC electric field and non-uniform temperature distribution inside the system. Electrothermal force can be explored for pumps in microfluidic systems. In this paper, the lattice Boltzmann method (LBM) is used to simulate a 2D electrothermal pump. As an alternative numerical method for fluid dynamics, LBM has many advantages compared with traditional CFD methods, such as its suitability for parallel computation. With its parallel characteristic, LBM is well fitted to the parallel hardware in graphic processor units (GPU). To save computational time in parametric studies, a CUDA code was developed for executing parallel computation. The comparison of computational time between CPU and GPU is presented to demonstrate the advantage of using GPU. The effects of the frequency, thermal boundary conditions, electrode size, and gap between electrodes on volumetric flow rate were investigated in this study. It was shown that LBM is an effective approach to studying 2D electrothermal pumps on a CUDA platform.
Nomenclature
| c | = | lattice speed |
| ci | = | lattice speed in direction i |
| cp | = | specific heat capacity |
| cs | = | sound speed of the model, defined as |
| E | = | electric field |
| = | dimensionless electric field | |
| F | = | body force |
| Fb | = | buoyancy force |
| = | dimensionless buoyancy force | |
| Fe | = | electrothermal force |
| = | dimensionless electrothermal force | |
| Fi | = | discrete body force in direction i |
| fi | = | density distribution function in direction i |
| = | equilibrium distribution function of density in direction i | |
| g | = | gravitational acceleration |
| gi | = | distribution function of Laplace’s equation in direction i |
| = | equilibrium distribution function of Laplace’s equation in direction i | |
| hi | = | distribution function of Poisson’s equation in direction i |
| = | equilibrium distribution function of Poisson’s equation in direction i | |
| k | = | thermal conductivity |
| Lc | = | characteristic length |
| L2 | = | relative L2 error |
| N | = | number of grids along |
| Nx | = | block size in x direction on CUDA platform |
| Ny | = | block size in y direction on CUDA platform |
| n | = | number of lattice grids in horizontal direction |
| m | = | number of lattice grids in vertical direction |
| JH | = | Joule heating |
| = | dimensionless Joule heating | |
| k | = | thermal conductivity |
| p | = | pressure |
| = | dimensionless pressure | |
| pr | = | reference pressure |
| Q | = | volumetric flow rate per channel width |
| T | = | temperature |
| Tr | = | reference temperature |
| Tleft | = | Temperature on the left electrode |
| Tright | = | Temperature on the right electrode |
| t | = | time |
| u | = | velocity |
| = | dimensionless velocity | |
| = | dimensionless velocity in horizontal direction | |
| = | dimensionless velocity in vertical direction | |
| umax | = | maximum velocity in horizontal direction at x = 250 μm |
| vmax | = | maximum velocity in vertical direction at y = 50 μm |
| = | velocity of lattice Boltzmann method in test case | |
| = | analytical velocity in test case | |
| Vc | = | characteristic velocity |
| wi | = | weight coefficient in direction i |
| x | = | position vector |
| x | = | horizontal coordinate |
| = | dimensionless horizontal coordinate | |
| y | = | vertical coordinate |
| = | dimensionless vertical coordinate | |
| xmax | = | horizontal coordinate of vmax |
| ymax | = | vertical coordinate of umax |
| α | = | defined as |
| αg | = | lattice diffusivity of Laplace’s equation |
| αh | = | lattice diffusivity of Poisson’s equation |
| β | = | thermal expansion coefficient |
| ΔT | = | characteristic temperature |
| δσ | = | defined as |
| δϵ | = | defined as |
| δt | = | time step |
| δx | = | lattice space |
| ϵ | = | permittivity |
| ϵr | = | reference permittivity at Tr |
| ϕ | = | AC electric potential |
| = | dimensionless AC electric potential | |
| ϕ0 | = | applied potential |
| ϕleft | = | electric potential on left electrode |
| ϕright | = | electric potential on right electrode |
| μ | = | dynamic viscosity |
| θ | = | dimensionless temperature |
| θi | = | direction of lattice speed |
| ρ | = | density |
| = | density in LBM computation | |
| σ | = | conductivity |
| σr | = | reference conductivity at Tr |
| τ | = | charge relaxation time |
| τg | = | dimensionless relaxation time of Laplace’s equation |
| τh | = | dimensionless relaxation time of Poisson’s equation |
| τf | = | dimensionless relaxation time of density |
| υ | = | fluid kinematic viscosity |
| ω | = | AC voltage frequency |
Nomenclature
| c | = | lattice speed |
| ci | = | lattice speed in direction i |
| cp | = | specific heat capacity |
| cs | = | sound speed of the model, defined as |
| E | = | electric field |
| = | dimensionless electric field | |
| F | = | body force |
| Fb | = | buoyancy force |
| = | dimensionless buoyancy force | |
| Fe | = | electrothermal force |
| = | dimensionless electrothermal force | |
| Fi | = | discrete body force in direction i |
| fi | = | density distribution function in direction i |
| = | equilibrium distribution function of density in direction i | |
| g | = | gravitational acceleration |
| gi | = | distribution function of Laplace’s equation in direction i |
| = | equilibrium distribution function of Laplace’s equation in direction i | |
| hi | = | distribution function of Poisson’s equation in direction i |
| = | equilibrium distribution function of Poisson’s equation in direction i | |
| k | = | thermal conductivity |
| Lc | = | characteristic length |
| L2 | = | relative L2 error |
| N | = | number of grids along |
| Nx | = | block size in x direction on CUDA platform |
| Ny | = | block size in y direction on CUDA platform |
| n | = | number of lattice grids in horizontal direction |
| m | = | number of lattice grids in vertical direction |
| JH | = | Joule heating |
| = | dimensionless Joule heating | |
| k | = | thermal conductivity |
| p | = | pressure |
| = | dimensionless pressure | |
| pr | = | reference pressure |
| Q | = | volumetric flow rate per channel width |
| T | = | temperature |
| Tr | = | reference temperature |
| Tleft | = | Temperature on the left electrode |
| Tright | = | Temperature on the right electrode |
| t | = | time |
| u | = | velocity |
| = | dimensionless velocity | |
| = | dimensionless velocity in horizontal direction | |
| = | dimensionless velocity in vertical direction | |
| umax | = | maximum velocity in horizontal direction at x = 250 μm |
| vmax | = | maximum velocity in vertical direction at y = 50 μm |
| = | velocity of lattice Boltzmann method in test case | |
| = | analytical velocity in test case | |
| Vc | = | characteristic velocity |
| wi | = | weight coefficient in direction i |
| x | = | position vector |
| x | = | horizontal coordinate |
| = | dimensionless horizontal coordinate | |
| y | = | vertical coordinate |
| = | dimensionless vertical coordinate | |
| xmax | = | horizontal coordinate of vmax |
| ymax | = | vertical coordinate of umax |
| α | = | defined as |
| αg | = | lattice diffusivity of Laplace’s equation |
| αh | = | lattice diffusivity of Poisson’s equation |
| β | = | thermal expansion coefficient |
| ΔT | = | characteristic temperature |
| δσ | = | defined as |
| δϵ | = | defined as |
| δt | = | time step |
| δx | = | lattice space |
| ϵ | = | permittivity |
| ϵr | = | reference permittivity at Tr |
| ϕ | = | AC electric potential |
| = | dimensionless AC electric potential | |
| ϕ0 | = | applied potential |
| ϕleft | = | electric potential on left electrode |
| ϕright | = | electric potential on right electrode |
| μ | = | dynamic viscosity |
| θ | = | dimensionless temperature |
| θi | = | direction of lattice speed |
| ρ | = | density |
| = | density in LBM computation | |
| σ | = | conductivity |
| σr | = | reference conductivity at Tr |
| τ | = | charge relaxation time |
| τg | = | dimensionless relaxation time of Laplace’s equation |
| τh | = | dimensionless relaxation time of Poisson’s equation |
| τf | = | dimensionless relaxation time of density |
| υ | = | fluid kinematic viscosity |
| ω | = | AC voltage frequency |