SWIMMING WHERE VISCOSITY WINS
Swimming without inertia, from Purcell’s scallop to pairs of swimmers
A bacterium lives where viscosity wins and inertia is negligible, so it stops the moment it stops pushing. Start with why a back-and-forth stroke goes nowhere, then build a three-sphere swimmer and take it to a wall and to a partner.
One swimmer in open water · Chapters 1–5
Why a stroke has to trace a loop
See why a microbe stops the moment it stops pushing, prove the scallop theorem, then build the three-sphere swimmer and measure its step as an area.
Start with a microbe that cannot coast →Walls, tails and pairs · Chapters 6–9
What changes beside a wall or a neighbour
Follow a swimmer beside a wall, see how flexible tails and corkscrews escape the theorem, time two swimmers against each other and read the original paper.
Start beside a wall →Nine chapters, with examples and experiments
01 L1
A microbe stops the moment it stops pushing
What changes when a swimmer is so small that it cannot coast?
Read and try →02 L2
Stokes flow answers every push at once
Which equations govern the water around a microswimmer, and what do they predict for a single sphere?
Read and try →03 L2
Opening and closing a shell gets you nowhere
Why does any back-and-forth stroke bring a microswimmer exactly back to where it started?
Read and try →04 L2
Three beads, two arms and a mobility matrix
How do you find how fast three spheres on a line move when you prescribe only how their arms change?
Read and try →05 L3
Distance per stroke is an area in shape space
Why does a small stroke loop carry the swimmer a distance proportional to the area it encloses in the plane of arm lengths?
Read and try →06 L3
A wall slows each sphere and turns the swimmer
How does a nearby wall change the mobility of each sphere, and what paths does a three-sphere swimmer follow beside it?
Read and try →07 L3
Flexible tails and turning corkscrews escape the scallop theorem
How do real microorganisms make strokes that never retrace themselves, and how fast do those strokes push them?
Read and try →08 L4
Two swimmers feel each other through the timing of their strokes
When two three-sphere swimmers stroke near each other on fixed clocks, how does the phase between their strokes decide whether they attract, repel or oscillate?
Read and try →09 L4
Reading Najafi and Golestanian’s three-sphere paper
What does the 2004 paper show, which of its numbers can you reproduce, and where do later papers correct or extend it?
Read and try →