Fick's FirstLaw ofDiffusionIn1855,AdolfFickderivedtheequationtodescribethediffusion,whichgovernthediffusionofagasacrossafluidmembrane.Fick'slawdescribestherateatwhichonespeciesdiffusethroughtheotherThemassfluxisamountof material flowingthroughaunitcrosssectionofabarrierinunitetime,whichcanexpress asdM(2.9a)J=s.dtAdolfEugenFick(1829-1901)whereJisthemassflux[kg/(m?-s)],Misthemassofthematerialflowing(kg)SisGerman-bornphysiciancrosssectionalareaofflow(m2);tisthetime;andphysiologistDrXinyanHuang.PolyUFire Science
Fire Science Dr Xinyan Huang, PolyU Fick’s First Law of Diffusion In 1855, Adolf Fick derived the equation to describe the diffusion, which govern the diffusion of a gas across a fluid membrane. Fick’s law describes the rate at which one species diffuse through the other. where 𝐽 is the mass flux [kg/(m2 -s)], 𝑀 is the mass of the material flowing (kg) 𝑆 is cross sectional area of flow (m2 ) ; t is the time; Adolf Eugen Fick (1829-1901) German-born physician and physiologist 𝐽 = 𝑑𝑀 𝑆 ∙ 𝑑𝑡 (2.9𝑎) The mass flux is amount of material flowing through a unit cross section of a barrier in unite time, which can express as
Fick'sLawandDiffusionThemassfluxisproportionaltotheconcertationgradientdc/dxdT(2.1)-6qconddxdcS(2.9b)dxdTqconddxpcwhereDisthediffusioncoefficient[m?/s]:Cistheconcentration(kg/m3);xisdistanceThreetransportcoefficients(diffusivities):Thenegativesignofequationsignifiesthatdiffusion1)MassdiffusivityDoccursinadirectionoppositetothatofincreasing.k2)Thermaldiffusivityα=-concentration.pCpThediffusion coefficientD is nota constant,whichis3) Momentum diffusivity =affectedbytheconcentration,temperature,pressure,L(orkinematic viscosity)solventpropertiesetc.Allhavethesameunitofm?/sDrXinyanHuang.PolyUFireScience
Fire Science Dr Xinyan Huang, PolyU Fick’s Law and Diffusion 𝐽 = −𝐷 𝑑𝐶 𝑑𝑥 (2.9𝑏) The mass flux is proportional to the concertation gradient 𝑑𝐶/𝑑𝑥 where 𝐷 is the diffusion coefficient [m2 /s]; 𝐶 is the concentration (kg/m3 ); 𝑥 is distance • The negative sign of equation signifies that diffusion occurs in a direction opposite to that of increasing concentration. • The diffusion coefficient 𝐷 is not a constant, which is affected by the concentration, temperature, pressure, solvent properties etc. Three transport coefficients (diffusivities): 1) Mass diffusivity 𝑫 2) Thermal diffusivity 𝜶 = 𝒌 𝝆𝒄𝒑 3) Momentum diffusivity 𝒗 = 𝝁 𝝆 (or kinematic viscosity) All have the same unit of m2 /s 𝑞ሶ𝑐𝑜𝑛𝑑 ′′ = −𝑘 ቤ 𝑑𝑇 𝑑𝑥 𝑥=0 2.1 𝑞ሶ𝑐𝑜𝑛𝑑 ′′ 𝜌𝑐 = −𝛼 ቤ 𝑑𝑇 𝑑𝑥 𝑥=0