s8.3 Diffusion and mass transfer , o/(扩散和单 within single phase 向传质) 8.3.1 Molecular diffusion in binary mixtures Diffusion (P Features a hatsdiffusioni3 Diffusion is the movement, under the infiuence of a physical stimulus(物理驱动)oam individual component(单独的组份 through a mixture
一.Diffusion（P511） Features: 1. ～ What’s diffusion ？ Diffusion is the movement, under the influence of a physical stimulus（物理驱动）, of an individual component（单独的组份） through a mixture. 8.3.1 Molecular diffusion in binary mixtures （扩散和单 向传质） §8.3 Diffusion and mass transfer within single phase
s8.3 Diffusion and mass transfer , o/(扩散和单 within single phase 向传质) 8.3.1 Molecular diffusion in binary mixtures Diffusion (pu 2 Why reason? The most cause of diffusion is a concentration gradient of the diffusing component. 3. Purpose? A concentration gradient(浓度梯度) tends to move the component in such a direction as to equalize concentration and destroy the gradient
一.Diffusion（P511） 2. ～ Why reason? The most cause of diffusion is a concentration gradient of the diffusing component. 3. ～ Purpose? A concentration gradient（浓度梯度） tends to move the component in such a direction as to equalize concentration and destroy the gradient. 8.3.1 Molecular diffusion in binary mixtures （扩散和单 向传质） §8.3 Diffusion and mass transfer within single phase
8.3.1 Molecular diffusion in binary mixtures Diffusion (Pai) 4 ≈ Steady- state flux When the gradient is maintained by constantly supplying the diffusing component to the high- concentration end of the gradient and removing it at the low-concentration end. there is a steady-state flux of the diffusing component This is characteristic of many mass-transfer operations
一.Diffusion（P511） 4. ～ Steady-state flux When the gradient is maintained by constantly supplying the diffusing component to the highconcentration end of the gradient and removing it at the low-concentration end, there is a steady-state flux of the diffusing component. This is characteristic of many mass-transfer operations. 8.3.1 Molecular diffusion in binary mixtures
83.I Molecular diffusion in binary mixtures 5 Although the usual cause of diffusion is a concentration gradient, diffusion can also be aals ed by an activity gradient(能动梯度) as in reverse osmosis(反渗透),bya pressure gradient, by a temperature gradient, or by the application of an external force field (外场力), as in a centrifuge(离心力场)
5. ～ Other reasons Although the usual cause of diffusion is a concentration gradient, diffusion can also be caused by an activity gradient（能动梯度）, as in reverse osmosis（反渗透）, by a pressure gradient, by a temperature gradient, or by the application of an external force field （外场力）, as in a centrifuge（离心力场）. 8.3.1 Molecular diffusion in binary mixtures
8.3.1 Molecular diffusion in binary mixtures 6.< What's thermal diffusion?热扩散 Molecular diffusion induced by temperature gradient is thermal diffusion. 7。 What's the force diffusion?强制扩散 Molecular diffusion induced by the application of a force from an external filed is forced diffusion
6. What’s thermal diffusion?热扩散 Molecular diffusion induced by temperature gradient is thermal diffusion. 7. What’s the force diffusion? 强制扩散 Molecular diffusion induced by the application of a force from an external filed is forced diffusion. 8.3.1 Molecular diffusion in binary mixtures
8.3.1 Molecular diffusion in binary mixtures 8< Diffusion in a direction扩散方向 Diffusion in a direction is perpendicular to the interface between the phases and at a definite location in the equipment 9 Steady state Steady state is assumed, and the concentrations at any point do not change with time
8. Diffusion in a direction 扩散方向 Diffusion in a direction is perpendicular to the interface between the phases and at a definite location in the equipment. 9. Steady state Steady state is assumed, and the concentrations at any point do not change with time. 8.3.1 Molecular diffusion in binary mixtures
c8.3. 1 Molecular diffusion in binary mixtures Fick's first law of diffusion for a binary mixture (P51)(双组份扩散时的费克第一定律) 1 What's Fick's first law ∵分子扩散的实质是分子的微观随机运动。 对于一定温度和压力下的一维定态扩散,其统计 规律可用宏观的方式表达。这就是费克定律: d =-D △B (8-9) Where: Ja the diffusion flux of component A IA moles/per unit area per unit time IA moles/ms
二. Fick’s first law of diffusion for a binary mixture (P514)（双组份扩散时的费克第一定律） 1. What’s Fick’s first law ? ∵分子扩散的实质是分子的微观随机运动。 ∴对于一定温度和压力下的一维定态扩散，其统计 规律可用宏观的方式表达。这就是费克定律： Where: JA= the diffusion flux of component A; [A moles/per unit area per unit time] ～ [A moles/m2·s] 8.3.1 Molecular diffusion in binary mixtures ( ) A A AB dC = - 8 - 9 J D dZ
8.3.1 Molecular diffusion in binary mixtures dca/dF the concentration gradient of component a diffusing in a direction, [(mol/m )/ml DAR=Diffusivity of component A in component B, m/s I Reference to(8-9), a similar equation for component B: do JB- DBa dz B(8-1) For binary mixture DAB=DBA-D Then J=-J B (8-13)
dCA/dz= the concentration gradient of component A diffusing in a direction， [(mol/m3 )/m] DAB=Diffusivity of component A in component B，[m2 /s ] Reference to（8-9）, a similar equation for component B: ∵ For binary mixture DAB=DBA=D Then JA=－JB （8-13） 8.3.1 Molecular diffusion in binary mixtures ( ) B B BA dC = - 8 -11 dZ J D
8.3.1 Molecular diffusion in binary mixtures 2.“现象定律 That's phenomena law. 上学期已经学过两个基本定律: 牛顿粘性定律: 气 Newton's la aw ot viscos Molecular momentum transport 傅立叶定律:a cFourier's law of heat conduction c Molecular energy transport Comparison to those three formulas ()传递的物理量:动量,热量,质量 momentum, energy, and mass
2. “现象定律” ～ That’s phenomena law. 上学期已经学过两个基本定律： 牛顿粘性定律: ～Newton’s law of viscosity ～ Molecular momentum transport 傅立叶定律: ～Fourier’s law of heat conduction ～ Molecular energy transport Comparison to those three formulas: ⑴ 传递的物理量：动量，热量，质量 ～momentum, energy, and mass 8.3.1 Molecular diffusion in binary mixtures du τ μ ＝－ dy dt q = k － dy
18.3.1 Molecular diffusion in binary mixtures (2)均为传递通量:(传递的物理量)/m2s 大小( Magnitudes):与对应强度因素梯度成正比。 方向( Directions):沿着浓度减小的方向传递。 (3)各式中的系数仅为状态函数,即是TP和组成的函 数,而于流动无关。 又统一称这三个定律为 “现象定律”~That' s phenomena law 大家在学习质量传递时,完全可以与前面所学过的动 量、热量传递进行类比
⑵ 均为传递通量：（传递的物理量）/m2·s 大小 (Magnitudes) : 与对应强度因素梯 度成正比。 方向（Directions) : 沿着浓度减小的方向传递。 ⑶ 各式中的系数仅为状态函数，即是T,P和组成的函 数，而于流动无关。 ∴又统一称这三个定律为 “现象定律” ～ That’s phenomena law. ∴大家在学习质量传递时，完全可以与前面所学过的动 量、热量传递进行类比。 8.3.1 Molecular diffusion in binary mixtures