Osmotic Microcapsule

What is modelled

A capsule with a membrane that passes water but not solute sits in a bath. If the inside is more concentrated, water enters, the capsule swells and the elastic shell pushes back. The swelling stops when the osmotic pressure difference equals the elastic pressure, or the shell breaks if the strain reaches its limit.

Equations

• Van t Hoff Π = R T (cin − cout) with cin = n / V.
• Shell pressure Pel = K (r / r0 − 1).
• Water flux dV/dt = Lp A (ΔΠ − Pel).
• Rupture when r / r0 − 1 reaches the set strain.

Checks run in the page

• Van t Hoff pressure from the set concentrations.
• Bisection equilibrium against time integration.
• Conservation of the impermeant solute.
• Free-swelling limit V = V0 c_in / c_out.

Honest simplifications

The shell is a linear radial spring, the solute is ideal and impermeant and the membrane has a fixed permeability. Real polymer capsules and cells stiffen non-linearly and leak solute. This is a teaching model, not a calibrated drug-delivery or cell model.

• Press Hypotonic bath: the soft, permeable capsule A swells quickly while the stiff capsule B swells less.
• Press Pure water shock to watch the shells reach their rupture strain.
• Press Isotonic bath and see that nothing moves.