标题： 共流体中气泡尺寸预测 显示英文标题

标题： Bubble size prediction in co-flowing streams

摘要： 在本文中，通过共轴微流控装置中气流的破裂形成的气泡大小被推导出来。 被共流液体流包围的气流破裂成单分散的微气泡，气泡的大小由内层气体流的半径和气泡形成频率决定。 我们通过求解低雷诺数流动的纳维-斯托克斯方程以及耗散能量的最小化来获得气体流的半径。 气泡大小的预测仅基于系统的控制参数，即： 内层气体流量$Q_i$，外层液体流量$Q_o$，以及管子半径$R$。 对于非常低的气液流量比（$Q_i / Q_o \rightarrow 0$），气泡半径按$r_b / R \propto \sqrt{Q_i / Q_o}$缩放，与内层与外层粘度比$\eta_i/\eta_o$以及气体中的速度剖面类型无关，速度剖面可以是平顶的或抛物线的，这取决于高分子量表面活性剂是否覆盖气液界面。 然而，在气体速度剖面为抛物线且粘度比足够低的情况下，即 $\eta_i/\eta_o \ll 1$，气泡直径按$r_b \propto (Q_i/Q_o)^\beta$缩放，其中$\beta$小于 1/2。 显示英文摘要

摘要： In this paper, the size of bubbles formed through the breakup of a gaseous jet in a co-axial microfluidic device is derived. The gaseous jet surrounded by a co-flowing liquid stream breaks up into monodisperse microbubbles and the size of the bubbles is determined by the radius of the inner gas jet and the bubble formation frequency. We obtain the radius of the gas jet by solving the Navier-Stokes equations for low Reynolds number flows and by minimization of the dissipation energy. The prediction of the bubble size is based on the system's control parameters only, i.e. the inner gas flow rate $Q_i$, the outer liquid flow rate $Q_o$, and the tube radius $R$. For a very low gas-to-liquid flow rate ratio ($Q_i / Q_o \rightarrow 0$) the bubble radius scales as $r_b / R \propto \sqrt{Q_i / Q_o}$, independently of the inner to outer viscosity ratio $\eta_i/\eta_o$ and of the type of the velocity profile in the gas, which can be either flat or parabolic, depending on whether high-molecular-weight surfactants cover the gas-liquid interface or not. However, in the case in which the gas velocity profiles are parabolic and the viscosity ratio is sufficiently low, i.e. $\eta_i/\eta_o \ll 1$, the bubble diameter scales as $r_b \propto (Q_i/Q_o)^\beta$, with $\beta$ smaller than 1/2.