AI 中文总结
研究轴对称通道中盐溶液因浓度和压力降引起的流动，提出相关理论，计算通道\(\Delta p (Q)\)曲线，引入圆柱体近似，推导离子通量与流体总流速关系方程，为解释数据和设计微纳流体装置提供框架。
AI 中文摘要
我们提出了一种关于长轴对称通道中盐溶液流动的理论，该流动由通道两端的浓度和压力降引起。考虑限于与局部半径相比薄的静电扩散层，即使浓度降很大时该理论仍有效。我们表明圆柱体中扩散渗透流体流速\(Q_{DO}\)与直径厚度相等的狭缝中的相同，但可变横截面通道可能会根据其几何形状减缓或增强它。施加压力降\(\Delta p \neq 0\)会对流体总流速\(Q\)产生额外贡献\(Q_{P}\)，但不影响\(Q_{DO}\)。我们计算了几个轴对称通道的\(\Delta p (Q)\)曲线并得出它们近似线性且对形状斜率敏感。这导致可以引入简单但相当准确的圆柱体近似，其中虚圆柱体半径与实际通道的流体动力电阻率相关且若已知其几何形状则可轻松确定。我们还推导了一个将离子通量与流体总流速相关联的方程，并证明通过使用适当的通道形状可以调整离子通量的符号和大小。我们的分析为解释实验和数值数据提供了框架，也可能指导微纳流体装置的设计。
英文摘要
We present a theory of a flow of salt solutions in long axisymmetric channels induced by concentration and pressure drops between their ends. The consideration is restricted to thin, compared to the local radius, electrostatic diffuse layers, but remains valid even when the concentration drop is quite large. We show that the magnitude of the diffusio-osmotic fluid flow rate $Q_{DO}$ in the cylinder is the same as in the slit of equal to its diameter thickness, but channels of variable cross-sections could either retard or enhance it, depending on their geometry. The application of the pressure drop $Δp \neq 0$ results in an extra contribution $Q_{P}$ to the total flow rate of fluid $Q$, but does not affect $Q_{DO}$. We calculate the curves $Δp (Q)$ for several axisymmetric channels and conclude that they are nearly linear, with the sensitive to the shape slopes. This leads to the possibility of introducing a simple, but rather accurate, cylinder approximation, where the radius of the imaginary cylinder is related to a hydrodynamic resistivity of the real channel and can be easily determined, if its geometry is known. We also derive an equation relating the ionic flux with the total flow rate of fluid and demonstrate that both the sign and magnitude of ionic flux could be tuned by using the appropriate channel shape. Our analysis provides a framework for interpreting experimental and numerical data, as well as may guide the design of micro- and nanofluidic devices.
