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【求助】Fick扩散定律的公式
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各位虫友，我在看一篇外文文献中看到其对Fick定律的公式书写如下： J=-ρD(dw/dx) 其中，w是vapor fraction？？ 谁能解释一下w的含义，这个公式和传热学书的公式：J=-D(dρ/dy) 是不是一回事啊？ |
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2楼2009-08-19 21:28:27
星竹石
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Consider a binary mixture of ideal gases 1 and 2 at constant T and P. From a momentum balance describing collisions between molecules of species1 and molecules of species 2, we can obtain ▽p1= - f12 y1 y2 (v1 - v2), (yi - mole fraction) where f12 is an empirical parameter like a friction factor or drag coefficient. For convience, we just define an inverse drag coefficient D12 = P/f12, hence we can rewrite the above equation as d1=▽p1/P=- y1 y2 (v1 - v2) / D12 [VERY IMPORTANT STEP] Here d1=▽p1/P=(1/P)▽p1 is the driving force for diffusion of species 1 in a ideal gas mixture at constant T and P. This is the so called Maxwell-Stefan equation(MS equation), D12 is the MS-diffusivity. , when the systme pressure is constant across the diffusion path, the equation can be simplified to ▽y1 = - y1 y2(v1 - v2)/D12. furthermore, with some simple deduction given in many textbooks, we can get, for a binary mixture of ideal gas where the driving force for diffusion is the mole fraction gradient, the flux will be J1=-c D12 d1 = - c D12 ▽y1 At about the same time when Maxwell and Stefan were developing their ideas of diffusion in multicomponent mixtures , Fick and others uncovered the basic diffusion equations through a large amoutnt of experimental studies , the result of his work is the first Fick's law: for a binary mixture in a isothermal , isobaric system, the rate equation is J1=-c D12 ▽x1 (xi - mass fraction) where D12 is Fick diffusivity D12=D12 Γ where Γ is a thermodynamic factor which has some relationship with activity coefficients. you can find the details about it in phsical chemistry or thermodynamics text books, but for the ideal system Γ = 1 [ Last edited by 星竹石 on 2009-8-20 at 09:14 ] |
3楼2009-08-20 09:12:29
4楼2009-08-22 12:28:35
5楼2009-08-29 12:50:08
