Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
Concept

Porosity — where it appears

The fraction of a porous medium's bulk volume that is void rather than solid, so that a porosity of 0.3 means three tenths of the block is fluid. It is a volume ratio and carries no length in it, which is why it cannot on its own say how readily the medium passes fluid.

Named by 4 essays across one field — each of them below, with the objects they name alongside it.

Two velocities, 2.50 apart, and only one of them is anybody's. The velocity in Darcy's law is the flow rate divided by the whole cross-section, solid included: a speed no fluid particle ever has, since the fluid occupies only the fraction ε of that area. The speed the fluid actually averages is larger by exactly 1/ε — 2.50 times here — and it is the one that belongs in a residence time, in a pore Reynolds number and in any statement about when a tracer arrives. The grains are drawn to say that the pore-scale flow is not computed here: nothing above resolves it.

A velocity nobody has

The velocity in Darcy's law is the flow rate divided by the whole cross-section, solid included — a speed no fluid particle in the bed ever has. Averaging buys a linear law and charges for it in exactly this coin, and the constant that comes with it is an area of about a square micron.

applied · Porous Two different moments of one distribution. The permeability and the specific surface of a log-normal bundle, against the width of its pore-size distribution at a fixed median. The permeability rises by five orders because it is a fourth moment and the widest tubes dominate it; the surface falls because it is a first moment and the narrowest tubes dominate that.

A permeability that is only the geometry

Kozeny–Carman says that a porous medium's permeability follows from its porosity and its specific surface. Both are real, both are exactly measurable, and they do not determine the answer: forty-nine tube bundles built with identical values of each span a factor of eighty-two in permeability.

applied · Porous Time per litre rises in a straight line with the litres already filtered. The elapsed time divided by the filtrate collected, against the filtrate, for a constant-pressure filtration of a silica slurry through a cloth: integrated step by step, and Ruth's closed form. The line's slope is the cake's resistance, which grows with every litre, and its intercept is the cloth's, which does not. After a quarter of a cubic metre the cake is already the larger.

A filter is slowed by what it has caught

Push a slurry through a cloth and within minutes the cloth no longer matters: the particles it has caught form a cake, the cake is a packed bed, and every litre filtered makes the bed thicker for the next. The filtrate grows only as the square root of time. And if the cake is soft, it packs tighter against the cloth the harder it is pushed, until more pressure buys almost nothing.

applied · Porous A washed filter's best cycle is shorter, and still has one. The filtrate a batch filter produces per hour, averaged over filtering, washing and twenty minutes of emptying and refilling, against the filtrate collected in each cycle, for a slurry of 400 kilograms of silica per cubic metre and wash ratios of 0, 1, 2 and 5 pore volumes. Each curve has a best cycle, marked, and the wash both lowers it and moves it to a thinner cake: from 0.307 to 0.217 m³ per m² of cloth.

A washed filter works as long as it rests

A batch filter that has to be emptied between runs has a best cycle, and the rule for it is exact: the time the cake is responsible for equals the time the filter stands idle. Washing the cake does not break the rule, because a wash through a finished cake costs time in proportion to the square of its thickness, just as filtering it did. What a wash changes is the price, and the price is set by the slurry's concentration and by how far the wash front smears, not by the cake's softness.

applied · Porous

Named alongside it

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

Darcy's lawPacked bedPermeabilityScalingCompressibilityMeasurementModel limitAveragingConserved quantityCorrelationCreeping flowDispersion

All concepts