6.021/Notes/2006-09-18

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Contents

Water Transport

  • Cells specific for water transport
  • ~15 pounds of water secreted and reabsorbed daily
  • hydraulic pressure: blood
  • osmosis: cells

Osmosis

  • Transport of solvent due to differences in solute concentration
  • described by Dutrochet (early 1800s)
    • developed 1st osmometer
  • Wilhelm Pfeffer
    • osmosis can be stopped by hydraulic pressure
    • pressure proportional to concentration of solute
  • isotonic: concentration at which cells don't change in size
  • osmosis is colligative
    • depends on molar concentration not chemical properties of solute


Van't Hoff

  • Found relationship identical to ideal gas law
  • π(x,t) = RTCΣ(x,t)
  • Also works for salts if count ions of salt
  • CΣ(x,t) is called osmolarity in units of (osmol/volume)
  • 1 osmol is the same as 1 mol
  • π: units of pressure (Pa)
  • ocean about 1000 osmol/m^3, \pi\approx 25\cdot 10^5{\rm Pa}\approx 25{\rm atm}

Model

  • No one really understands osmosis
  • requires semipermeable membrane
  • solute collides and bounces off membrane
  • membrane exerts force due to changing momentum of solute
  • solute transfers momentum to solvent
  • change in solvent momentum is equivalent to hydraulic pressure
  • change in hydraulic pressure is change in osmotic pressure
  • momentum of solvent increase away from membrane due to solute bouncing back off membrane

Darcy's Law

  • flow through porous medium
  • \Phi_V(x,t)= -\kappa\frac{\partial p}{\partial x}
  • solvent flux is proportional to hydraulic pressure gradient
  • continuity: -\frac{\partial}{\partial x}(\rho_m \Phi_V) = \frac{\partial \rho_m}{\partial t}
  • water is incompressible so ρm is constant
  • Therefore, flux gradient is zero so flux is constant and p(x,t) is a linear function of space
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