The column a dissolved thing holds up

At its defaults it draws the column a dissolved thing holds up. Two arms of one vessel, joined below by a membrane that passes water and not solute. On the right is 10 mol/m³ of dissolved particles at 25 °C; on the left, pure water. Water crosses into the solution until the extra weight of the right-hand column has raised its pressure by the osmotic pressure — 24.8 kPa, which is 2.53 m of water, drawn here to scale. Nothing is pulling. The solvent is at a lower chemical potential where it is mixed, so it moves that way, and it stops when mechanical pressure has made up the difference. A solute a thousand times more dilute than seawater lifts a column taller than a person.

osmotic-cell is one function in lib/figures/fluids.js — matter that will not hold a shape, and the forces in it. Everything below came out of it during this build, at parameters taken from the essays rather than invented for this page. A figure here is the figure a reader meets in an essay, and if the generator changes, this page changes with it.

Two arms of one vessel, joined below by a membrane that passes water and not solute. On the right is 10 mol/m³ of dissolved particles at 25 °C; on the left, pure water. Water crosses into the solution until the extra weight of the right-hand column has raised its pressure by the osmotic pressure — 24.8 kPa, which is 2.53 m of water, drawn here to scale. Nothing is pulling. The solvent is at a lower chemical potential where it is mixed, so it moves that way, and it stops when mechanical pressure has made up the difference. A solute a thousand times more dilute than seawater lifts a column taller than a person.

The volume of a red cell of 90 fL against the salt concentration of the solution round it, in per cent sodium chloride by weight, with 0.9 per cent isotonic. By the Boyle–van 't Hoff law the water inside follows the outside's tonicity: the cell's volume is an inactive part, 40 per cent of the normal volume in haemoglobin and other solids, plus a part inversely proportional to the concentration. Its membrane's 135 μm² can enclose at most 147.5 fL, as a sphere (dashed). The swelling curve reaches that at 0.44 per cent salt: below it the cell has no more shape to give up and bursts. In a 1.5 per cent solution the same cell shrinks to 68 fL and crenates, with membrane to spare.

A red blood cell in section, drawn from the profile Evans and Fung measured in 1972: a disc 7.8 μm across, 2.6 μm thick at the rim and 0.8 μm at the centre, enclosing 94 femtolitres inside 134 square micrometres of membrane. Beside it, the sphere with the same area: 6.56 μm across, holding 146 femtolitres. The disc uses 64 per cent of the volume its membrane could enclose. Every shape between the two has the same area, and the membrane can pass between them almost freely; it cannot become larger than the sphere's surface by more than about two per cent without tearing. A cell that takes in water therefore has room for about fifty-five per cent more, and then none.

The excess pressure a red cell can hold once it has become a sphere, in kilopascals, against how far its membrane has been stretched beyond its resting area, from Laplace's law, Δp = 2τ/R, with a tension τ = K·strain and an area-expansion modulus K of 450 mN/m. The membrane tears at a tension of about 10 mN/m, a stretch of 2.2 per cent, where the pressure is 6.0 kPa. The osmotic pressure of the cell's contents is about 719 kPa: the membrane can hold back an imbalance of under 0.8 per cent of it. Before the cell is spherical the membrane is slack and holds no pressure at all; after, a further dilution of one per cent bursts it.

The fraction of red cells burst against the salt concentration, for three populations of 4,000 cells whose volumes and membrane areas scatter independently about their means, each cell bursting when its Boyle–van 't Hoff volume reaches the sphere its membrane allows plus two per cent. Half of the normal cells have burst at 0.42 per cent salt. Cells that have lost about an eighth of their membrane, as in hereditary spherocytosis, burst at 0.54 per cent; small, thin cells with membrane to spare, as in iron deficiency or thalassaemia, at 0.34. The clinical test that measures these curves is called a test of fragility, and what it measures is not the strength of the membrane, which is much the same in all three, but the ratio of membrane to contents.

The salt concentration at which a red cell becomes a sphere and bursts, against its membrane area, for cells of 70, 90 and 110 fL, from the Boyle–van 't Hoff law with an inactive fraction of 0.4. A normal 90 fL cell with 135 μm² bursts at 0.44 per cent; with 120 μm² it bursts at 0.55, and below about 97 μm² it would be a sphere already and burst at isotonic salt. A 70 fL cell with the same 135 μm² survives to 0.32 per cent. Each curve rises steeply as the area approaches the smallest sphere that holds the cell, which is why a modest loss of membrane makes cells strikingly fragile.

physicscheck asserts something about osmotic-cell that could fail — it draws it and measures the result against a value reached some other way.

Across the library: 100 interrogated, 2 exercised only, 1 untouched, of 103. Read out of the gate's source by the gate's own two patterns — and the gate's last claim fails the build if that read disagrees with what it was handed while running.