6.021/Notes/2006-09-20

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Osmosis

  • pressure given by van't Hoff law (prev lecture)
  • π(x,t) = RTCΣ(x,t)
  • semipermeable membrane reflects solutes \Delta\pi \rightarrow \Delta p
  • osmotic pressure exactly the same as hydraulic pressure except opposite in sign
  • only have to consider p − π
  • ΦV = LV((pi − πi) − (po − πo))
  • Note that the volume flux of Φ is different from the normal flux φ in its units. Φ has units of m/s whereas φ has units of mol/(m^2 s). As we are considering a volume of incompressible fluid (water), we can convert one to the other using a conversion factor (e.g. 55 mol/L for water).

Osmosis in cells

  • only water crosses membrane
  • pi = po
  • \frac{dV^i}{dt} = -A(t)\Phi_V = -A(t)RTL_V(C^o_\Sigma(t)-C^i_\Sigma(t))
  • equilibrium: \frac{dV^i}{dt} = 0 \rightarrow (C^o_\Sigma(\infty)=C^i_\Sigma(\infty))
    • solution is v_c(\infty) = v_c' + \frac{N^i_\Sigma}{C^o_\Sigma} (perfect osmometer)
    • non-linear relationship between C^o_\Sigma and volume of cell
  • Experimental data for many types of cells agrees with this equation
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