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Water Transport

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


  • 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
  • [math]\displaystyle{ \pi(x,t)= RTC_\Sigma(x,t) }[/math]
  • Also works for salts if count ions of salt
  • [math]\displaystyle{ C_\Sigma(x,t) }[/math] is called osmolarity in units of (osmol/volume)
  • 1 osmol is the same as 1 mol
  • [math]\displaystyle{ \pi }[/math]: units of pressure (Pa)
  • ocean about 1000 osmol/m^3, [math]\displaystyle{ \pi\approx 25\cdot 10^5{\rm Pa}\approx 25{\rm atm} }[/math]


  • 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
  • [math]\displaystyle{ \Phi_V(x,t)= -\kappa\frac{\partial p}{\partial x} }[/math]
  • solvent flux is proportional to hydraulic pressure gradient
  • continuity: [math]\displaystyle{ -\frac{\partial}{\partial x}(\rho_m \Phi_V) = \frac{\partial \rho_m}{\partial t} }[/math]
  • water is incompressible so [math]\displaystyle{ \rho_m }[/math] is constant
  • Therefore, flux gradient is zero so flux is constant and [math]\displaystyle{ p(x,t) }[/math] is a linear function of space