Life in Moving Fluids (continued)

Yesterday, I quoted excerpts from Steven Vogel’s book Life in Moving Fluids about the Reynolds number. Today, I’ll provide additional quotes from Vogel’s Chapter 15, Flow at Very Low Reynolds Number.

[Low Reynolds number] is the world, as Howard Berg puts it, of a person swimming in asphalt on a summer afternoon—a world ruled by viscosity. It’s the world of a glacier of particles, the world of flowing glass, of laboriously mixing cold molasses (treacle) and corn (maise) syrup. Of more immediate relevance, it’s the everyday world of every microscopic organism that lives in a fluid medium, of fog droplets, of the particulate matter called “marine snow”… “Creeping flow” is the common term in the physical literature; for living systems small size rather than (or as well as) low speed is the more common entry ticket. And it’s a counterintuitive—which is to say unfamiliar—world.

Vogel then lists properties of low Reynolds number flow.

At very low Reynolds number, flows are typically reversible: a curious temporal symmetry sets in, and the flow may move matter around but in doing so doesn’t leave much disorder in its wake. Concomitantly, mixing is exceedingly difficulty…

Inertia is negligible compared to drag: when propulsion ceases, motion ceases…

Separation behind bluff bodies is unknown…

Boundary layers are thick because velocity gradients are gentle, and the formal definition of a boundary layer has little or no utility…

Nor can one create appreciable circulation around an airfoil… Turbulence, of course, is unimaginable…

While this queer and counterintuitive range is of some technological interest, its biological importance is enormous… since the vast majority of organisms are tiny, they live in this world of low Reynolds number. Flow at very low Reynolds number may seem bizarre to us, but the range of flow phenomena that we commonly contend would undoubtedly seem even stranger to someone whose whole experience was at Reynolds number well below unity.

Ha! Try explaining turbulence to Covid-19.

Vogel then discusses Edward Purcell’s classic paper “Life at Low Reynolds Number.” He notes

But while these slow, small-scale flows may seem peculiar, they’re orderly (Purcell calls them “majestic”) and far more amenable to theoretical treatment than the flows we’ve previously considered.

You can find an example of the theoretical analysis of low-Reynolds number flow in Homework Problem 46 in Chapter 1 of Intermediate Physics for Medicine and Biology, which discusses creeping flow around a sphere.

As you can probably tell, Vogel is a master writer. If you are suffering from boredom during this coronavirus pandemic, order a copy of Life in Moving Fluids from Amazon. I own the Second Edition, Revised and Expanded. It’s the perfect read for anyone interested in biological fluid dynamics.