Osmotic flow of water across membrane

Classical Mechanics Level 4

Given an osmotic pressure across a semipermeable membrane, water will cross the membrane with a particular rate of volume transport (mL/s).

membrane picture

membrane picture

The flux per unit area, \(J_w\), of water across a membrane is proportional to the difference in pressure between the two sides, \(\Delta p_{osm}\). There is also an empirically determined parameter, \(L_p\), called the hydraulic conductivity, a measure of how permeable a given membrane material is to flows.

\[\displaystyle J_w=\Delta p_{osm}L_p\]

Assuming that the pressure difference between the water-filled xylem and sap-filled phloem is dominated by the osmotic pressure, what will be the overall rate of water flow from xylem to phloem (in mL/s)?


  • The xylem and phloem are packed such that the entire surface of the phloem is adjacent to neighboring phloem surface and vice versa.
  • The osmotic pressure is \(\Delta p_{osm} =10^6\) Pa.
  • The length of the phloem is given by \(l_p\) = 1 cm, and the radius of the phloem is \(r_p = 20 \mu\)m.
  • The value of the hydraulic permeability is \(L_p=5 \times 10^{-14}\) m/s/Pa

Illustration by Maxicat Rhododendron


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