麻省理工学院：《电气工程与计算机科学》学习资料_diffusionequations

Delphines handy dandy units and formula sheet DIFFUSION Important Quantities and their units position me concentration diffusive flux k partitioning coefficient Furitless] P permeability steady state time constant equilibrium time constant General equations p(x,1)=-D(c(x,1) Fick's first law p(x,)=(c(x,) Continuity Equation combine to get c(, o=D if you have a partition coefficient, k, then stick k with d in the above equations 2-Compartment Model 2 ) P Membrane permeability T Steady State Time Constant Equilibrium Time Constant if tss<<tEo(thin membrane)and at steady state then o=P(c(1-cn)) Fick's law for membranes

Delphine’s handy dandy units and formula sheet DIFFUSION Important Quantities and their units: x position [cm] t time [sec] c(x,t) concentration [ 3 cm mole ] f diffusive flux [ 2 sec cm mole � ] D diffusivity [ sec cm2 ] k partitioning coefficient [unitless] P permeability [ sec cm ] tSS steady state time constant [sec] tEQ equilibrium time constant [sec] General Equations: f (x, t) = -D ¶ (c(x, t)) Fick’s First Law ¶x - ¶ f ( x, t) = ¶ (c(x, t)) Continuity Equation ¶x ¶t combine to get: ¶ ¶ t (c( x, t)) = D ¶ ¶ x 2 2 (c(x, t)) Diffusion Equation if you have a partition coefficient, k, then stick k with D in the above equations. 2-Compartment Model: V1 V2 c1(t) d c2(t) kD P = d Membrane Permeability d 2 t SS = 2 Steady State Time Constant p D 1 t EQ = Equilibrium Time Constant � 1 1 � AP� � Ł V1 + V2 ł � � if tSS<<tEQ (thin membrane) and at steady state then: f = P(c1 (t) - c 2 t)) Fick’s Law for membranes