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

OSMOSIS Important Quantities and their units position C1(X, concentration of solute i mo ce/x, t) olarity osmole mole volume osmotic flux sec·n hydraulic permeability P hydraulic conductivity hydraulic pressure IPal osmotic pressure [Pa] R molar gas constant 8. mo1K temperature General Equations cs=>nc,(where the ith solute dissociates into n, particles)Definition of Osmolarity RTO t Hoffs l d,(x,1) Darcy's law at 2-Compartment Model ( water incompressible so always at Ss) d V2() Ca(t d Definition of volumetric flux Hydraulic conductivity d Φ,=Ln(B1-丌1)-(P2-丌2) c(O)(O)+cO(O=c(()+e(O)2()=c(o)1(∞)+e(o)(o)conservationofsoluecosed 1(0)+2(0)=1(D)+12(D)=V1(∞)+12( ervation of solvent system only

OSMOSIS Important Quantities and their units: x position [m] t time [sec] ci(x,t) concentration of solute i [ 3 m mole ] ce(x,t) osmolarity [ 3 3 m mole m osmole = ] rm density [ 3 m kg ] V volume [m3 ] F osmotic flux [ sec m sec m m 2 3 = � ] k hydraulic permeability [ Pa sec m2 � ] Lv hydraulic conductivity [ Pa sec m � ] p hydraulic pressure [Pa] p osmotic pressure [Pa] R molar gas constant 8.314 mol K N m � � T temperature [K] General Equations: cS = � ni ci (where the i th solute dissociates into ni particles) Definition of Osmolarity i p = RTcS van’t Hoff’s Law F v ( x, t) = -k ¶ ( p -p ) Darcy’s Law ¶x - ¶ (r m �F v ) = - ¶ r m Continuity equation ¶x ¶t 2-Compartment Model (water incompressible so always at SS): V1(t) Fv V2(t) c1(t) c2(t) A=cross-section area d 1 d F = - � V Definition of volumetric flux v 1 A dt k L = Hydraulic conductivity v d Fv = Lv ((p1 -p1) - (p 2 -p 2 )) Darcy’s Law 1 2 1 2 1 2 cS (0)V1(0) +cS (0)V2(0) = cS (t)V1(t) + cS (t)V2(t) = cS (¥)V1(¥) + cS (¥)V2(¥) conservation of solute closed V1(0) + V2 (0) = V1(t) + V2 (t) = V1(¥) + V2 (¥) conservation of solvent only system