Electroosmotic Micro Thrusters of Phan-Thien-Tanner (PTT) Fluid at High Zeta Potential
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摘要: 在高的壁面zeta电势下, 考查了Phan-Thien-Tanner(PTT)黏弹性流体在平行板微通道中的电渗推进器问题. 在没有考虑Debye-Hückel线性近似的条件下, 求解了非线性Poisson-Boltzmann方程, 得到了高zeta电势下电势的解析解. 通过求解PTT流体满足的Cauchy动量方程, 获得了Navier滑移条件下微推进器速度的数值解. 进而通过数值积分得到了电渗微推进器的性能分布, 包括比冲、推力、效率和推力-功率比. 最后, 详细分析了黏弹性参数、壁面zeta电势、滑移系数和双电层厚度对速度分布及推进器性能的影响. 结果表明, 与Newton流体相比, PTT流体作为推进剂有利于推进器性能的提高, 比如, 流体速度随着黏弹性参数的增大而增大, 导致推进器性能也呈增大的趋势. 此外, 当前推进器比冲为800~1 000 ms时，推力可达0~250 μN, 效率为6%~12%, 推力-功率比为0~20 mN/W.Abstract: Electroosmotic micro thrusters filled with Phan-Thien-Tanner (PTT) viscoelastic fluid between 2 parallel plates were investigated at high wall zeta potential. The nonlinear Poisson-Boltzmann equation was solved without the Debye-Hückel linear approximation, to obtain the analytical electric potential at the high zeta potential. The numerical velocity of the micro thruster was given under the Navier slip condition in solution of the Cauchy momentum equation satisfied by the PTT fluid. Performances of the micro thrusters, including the specific impulse, the thrust, the efficiency, and the thrust-to-power ratio, were obtained through numerical integration. Finally, effects of the viscoelastic parameters, the wall zeta potential, the slip coefficient, and the double electric layer thickness on the velocity distributions and propeller performances, were discussed. The results show that, compared with the Newtonian fluid, the PTT fluid as a propellant is conducive to the improvement of propeller performances. For example, the fluid velocity increases with the viscoelastic parameters, resulting in an increasing trend of propeller performances. The present thruster delivers a thrust about 0~250 μN with a specific impulse of 800~1 000 ms, achieving an efficiency of 6%~12% and a thrust-power ratio of 0~20 mN/W.
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Key words:
- high zeta potential /
- electroosmotic flow /
- micro-thruster /
- thruster performance
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图 1 平行板微管道中黏弹性流体的纯电渗流
Figure 1. The pure electroosmotic flow of the viscoelastic fluid in a parallel plate microchannel
图 3 对于不同的εDe2, 电渗微推进器的速度分布
Figure 3. The velocity distributions of the electroosmotic microthruster for different values of εDe2
图 4 对于不同的εDe2值, 推进器性能随κ的变化情况
Figure 4. The thruster performance changes with κ for different values of εDe2
图 5 在不同的zeta电势下, 电渗微推进器的速度分布
Figure 5. The velocity distributions of the electroosmotic microthruster for different zeta values
图 6 在不同zeta电势下, 推进器性能随κ的变化情况
Figure 6. The thruster performance changes with κ for different zeta values
图 7 当滑移系数knl取不同值时, 电渗微推进器的速度分布
Figure 7. The velocity distributions of the electroosmotic microthruster for different slip coefficients
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