Osmosis from the bottom up

Osmosis Bounce Box

Small blue balls are water and slip through the membrane. Large orange balls are solute and bounce off it. Start with one bounce in slow motion. Then watch thousands of bounces in the box below draw water into the solution, until the solution's back-pressure stops the flow.

Close-up: one bounce, slowed down

A magnified patch of membrane, like the dashed box in the arena below. It opens with every ball in random thermal motion, then zooms in and slows the water so you can follow one solute ball from its bounce to the water it draws in. Fewer balls are drawn than in the box below.

Close-up speed
step 1 of 7
Water pressure at the membrane, schematic
pure side
normal solution side
normal
water crossed in 0 · out 0 · net into solution 0

The opening is real thermal motion. After the zoom the water is frozen, a gentle drag between neighboring balls stands in for water's viscosity, and a few scripted nudges stand in for the pressure-driven flow that carries pure water through. The close-up also exaggerates one event: in the full box, each bounce moves only a fraction of a water ball on average.

Pure waterwater 1830
net water flow
Solutionwater 1049 · solute 450
water, passes the membrane solute, bounces off solute rebounding from the membrane water dragged by a rebounding solute pressure deficit behind a rebounding solute membrane, gaps scale with water permeability
Starting condition
Speed

Water flowing into the solution

The chain of cause, measured live

Pressures are in percent of P₀, the starting pressure of the pure-water side.

  1. 1

    A fence only solute can feel

    Water balls cross the membrane in both directions. Solute balls never get through.

    water crossing 0/s → · 0/s ← · solute crossing 0
  2. 2

    Solute bounces back off the membrane

    Every solute ball that reaches the membrane bounces back toward the solution at the same speed. Each bounce reverses its momentum: a small push on the solution.

    solute bounces 0/s
    push
    0.0
  3. 3

    The solute drags water along

    A rebounding solute ball plows into nearby water and carries it away from the membrane. With highlighting on, dragged water turns dark and a pressure deficit trails the solute.

    water balls dragged away from the membrane 0/s
  4. 4

    A pressure deficit forms at the membrane

    Fewer water balls hit the membrane from the solution side than from the pure side, so water pressure there is lower.

    pure side
    0/s solution side
    0/s
    water-pressure deficit at membrane 0.0
  5. 5

    Water flows in to fill it

    More water crosses into the solution than comes back out.

    net flow 0 water/s · moved so far 0
  6. 6

    Back-pressure rises until it cancels the push

    The added water raises the solution's pressure. Flow stops when that back-pressure matches the push: van 't Hoff's Π = c·kBT.

    back-pressure
    0.0
    back-pressure / push 0% · van 't Hoff c·kBT 0.0

Pressure at the membrane

Percent of P₀, smoothed over a few seconds. Hover for values.

push from solute bounces back-pressure (solution − pure) water-pressure deficit at membrane van 't Hoff c·kBT

Water moved into the solution

Net count of water balls that crossed from the pure side. Negative means water left the solution.

What the numbers mean

The balls
Hard disks in two dimensions that collide elastically. Solute balls are about twice as wide and three times as heavy as water balls. Each compartment is held at constant temperature, as living tissue is.
The membrane
It turns back every solute ball. Each water ball that reaches it slips through with the chance set by the permeability slider. Permeability sets how fast osmosis runs, not where it ends. At 100% the membrane ignores water entirely, exactly as in step 1.
Push
Momentum reversed by solute bounces, per unit length of membrane per unit time. It is the pressure the solute exerts on the membrane, and the equal push the membrane returns to the solution.
Where the energy comes from
The membrane is rigid, so a bounce changes the solute's direction, not its speed. It adds no energy. The solute's speed is thermal energy picked up from collisions with water, and that thermal motion is what ultimately drives osmosis.
Back-pressure
Pressure on the solution side minus pressure on the pure side. Each comes from the balls' motion plus the forces of their collisions, averaged over the compartment.
Water-pressure deficit
Momentum delivered by water balls arriving at the membrane from the pure side, minus the same from the solution side. It tracks push minus back-pressure, and it is what drives the flow.
van 't Hoff
c·kBT, with c the solute balls per unit area and kBT taken from the balls' speeds. In 2D, pressure is force per unit length, so P₀ serves as the yardstick.
Why the push beats van 't Hoff
The box is crowded, so solute balls reach the membrane more often than in a dilute solution. The push runs about 25% above c·kBT. Concentrated real solutions show the same kind of excess, called an osmotic coefficient above 1. Back-pressure still settles on the measured push.
The wobble
With a few thousand balls, pressures jitter by a few percent of P₀ even at balance. That jitter is real molecular noise, not error. Raise the speed to watch long-run averages settle.
Starting conditions
Equal pressure starts both sides at P₀. Pre-balanced loads the solution with extra water so it starts at its osmotic pressure. Squeezed starts it at about twice that, which drives water out: reverse osmosis.