Illustrated Physics
physics, drawn
Concept

Suspension — where it appears

A mixture of solid particles dispersed through a liquid, too large to dissolve and small enough to stay spread for a time. Its flow depends on how closely the particles are packed and on what happens where they touch, which can make it thicken, jam or stiffen under a field.

Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.

A field strings a suspension into chains. 48 identical polarisable spheres, two radii apart at least, scattered at random through a periodic cell twenty radii square — 38 per cent of its area — and the same spheres after the field (vertical) has been on long enough for the viscous liquid to let them move. Each moves in proportion to the dipolar force from all the others and is stopped only by contact. At the start no two are touching; at the end 45 are bonded end to end along the field and 48 of the 48 spheres belong to chains, lying along the field lines and kept apart sideways because side-by-side dipoles repel. Chains that reach from one electrode to the other are what make the liquid resist shear, and they form in the milliseconds it takes a sphere to travel its own diameter.

The liquid a field turns solid

Stir fine starch or glass beads into silicone oil and the result pours like cream. Put a few kilovolts across it and within milliseconds it holds its shape and will not flow until it is pushed hard. Nothing in it is charged. Each particle becomes a dipole in the field, dipoles pull on each other end to end and push apart side by side, and so the particles string themselves into chains from one electrode to the other — a solid made of forces that exist only while the voltage is on.

electromagnetism · Dielectrics Flow curves that bend back, and one that stops. Shear stress against shear rate, both on logarithmic axes, for volume fractions 0.5, 0.55, 0.565, 0.575, 0.6, from the same model: stress in units of σ, rate in units of σ over the liquid's viscosity. Below φ = 0.569 every curve rises steadily — the suspension thickens but continuously. Above it and below the frictional jamming point 0.58 the curve bends back into an S: over a range of stress, more stress gives less flow, and a suspension driven at a fixed rate must jump between branches. At φ = 0.6 the curve returns to zero rate at 2.47 σ*: pushed that hard, the suspension stops flowing altogether and holds the stress like a solid.

The suspension that seizes when pushed hard

Cornflour stirred into half its volume of water runs off a spoon like cream, and a fist driven into it bounces off as if it had hit a floor. The particles have not changed and neither has the water. What changes, above a threshold stress, is the kind of contact between neighbouring grains: lubricated, they slide past one another and the suspension can pack to 64 per cent before it locks; pressed into frictional contact, they lock at 58. A suspension sitting between those two numbers is a liquid when handled gently and a solid when handled hard.

fluids · Rheology Blood's viscosity, measured in tubes of different sizes. The viscosity of blood at a haematocrit of 45 per cent, as a multiple of the plasma's, measured in glass tubes of each diameter (the fit of Pries and colleagues to many experiments), against the diameter on a logarithmic axis, with the two-layer model of a core inside a cell-free sleeve 2.5 μm thick, the core 4 times as viscous as plasma (dashed). In wide tubes blood is 3.20 times as viscous as plasma. From about half a millimetre down it gets steadily thinner, to 1.25 times at 6.8 μm — about the size of one red cell — and then climbs steeply, to 5.5 at 3 μm, where cells must fold to get through at all. Which viscosity blood has depends on the tube it is in.

The viscosity that belongs to the tube

Measure the viscosity of blood in a wide glass tube and it is about three times that of the plasma it is made from. Measure it in a tube a tenth of a millimetre across and it is lower; in one a hundredth of a millimetre across, lower still, barely more than plasma's. Then, below about six micrometres, it shoots up. The blood has not changed. The red cells push themselves away from the wall and leave a sleeve of plain plasma a few micrometres thick for the rest to slide in, and in a narrow tube that sleeve is a large part of the flow. A viscosity that depends on the pipe is no longer a property of the fluid alone.

fluids · Rheology A rod in a shear flow turns in fits and starts. The angle between a rigid rod's axis and the flow direction, unwrapped, against the strain of a steady shear flow (shear rate times time), for spheroids of aspect ratio 1, 5, 20 lying in the plane of the shear, each starting along the flow. A sphere (r = 1) turns steadily at half the shear rate. A rod spends most of its time nearly aligned with the flow, turning slowly, and then flips through half a turn quickly; at r = 5 it is within 10° of the flow direction 46 per cent of the time, at r = 20, 82 per cent. Each flip is half of Jeffery's period, π(r + 1/r) units of strain.

The rod that tumbles for ever in a stream

Drop a short rod into honey being sheared between two plates and it does not settle into line with the flow. It lies nearly along the stream for a long time, then flips end over end in a moment, then lies along it again, and it keeps doing that for as long as the shear lasts. George Jeffery worked out the motion in 1922: every orientation belongs to a closed orbit, every orbit takes the same time, and the flow has no way to choose between them — so a suspension of rods never reaches a steady state, and its thickness rises and falls in time with the tumbling.

fluids · Viscosity The force to pull a foot out of packed sand. The suction that resists pulling a foot (a sole of 250 cm², 10 cm long) straight up out of sand, as water is drawn through the sand into the space the foot leaves — Darcy's law with a Kozeny–Carman permeability — against the pulling speed, on logarithmic axes, for compacted sand (fraction 0.6) of three grain sizes and for loose sand (0.41) of 0.1 mm; the dotted line is a 70 kg person's weight. The force is proportional to the speed and inversely to the square of the grain size. Pulled at a centimetre a second from compacted 0.1 mm sand, a foot resists with 2.5 kN, 4 times the person's weight; the speed at which the suction equals that weight is 2.71 mm/s. In the loose sand before it compacted, the same pull would need 15 per cent of the force; with clay filling the pores of the compacted sand, as in natural quicksand, a thousand times more, and the speed a body's weight can pull at falls to microns a second.

The sand that lets a body in and will not let it out

Quicksand cannot swallow anyone: liquefied, it is nearly twice as dense as water, and a person in it floats with their chest clear. What makes it dangerous is the opposite asymmetry. Going in is easy, because a step breaks the gel holding the grains apart and the sand turns liquid. Coming out is hard, because the sand settles and packs around whatever sank, and a trapped foot can only rise as fast as water can seep through the packed grains to fill the space it leaves. Pulling harder barely helps; letting water in does.

fluids · Rheology

Named alongside it

The objects these essays reach for when they reach for this one.

ViscosityRheologyYield stressApparent viscosityArchimedes principleAspect ratioBloodBuoyancyClausius mossottiDipoleElectrorheological fluidFahraeus lindqvist effect

All concepts