Python code for flows at very small scales, where viscosity wins: beating cilia, protein brushes on cells, swimming algae, and flow through porous material. It is written to be read and taught from, in the spirit of IB2d.
For a cell or a cilium, swimming in water is like a person swimming in honey while moving no faster than a few centimetres a minute: the moment it stops pushing, it stops. Inertia does not matter, so the flow obeys the Stokes equations, which are linear: the flow made by many small forces is the sum of the flows made by each one.
A regularized Stokeslet is the flow made by one small force, smoothed over a tiny blob so that nothing blows up. Fluidlets puts these forces on the surface of a body, solves for the forces that make the body move the way it should, and adds up their flows. There is no mesh of the fluid, so complicated, moving shapes are easy to set up.
Each example runs with one command and explains the physics in plain language. Each one is checked against a published result or against the code Fluidlets grew from.
The cell beats its two flagella, and Fluidlets works out how it must move so that the total force and torque on it are zero. The result matches the swimming speed in Gallagher & Smith (2018) once the flagellum is built the same way as in the authors' own code. Tracer particles in the movie show how the flagella sweep the water.
Cells often swim, crawl, or roll near surfaces. A wall changes the flow a lot: fluid cannot slip along it, so it holds back the fluid under the body and raises the drag. Fluidlets builds the no-slip wall into the flow of each force with an exact image system, so no points are needed on the wall. The drag matches the tables of Ainley et al. (2008).
Much of the fluid in and around cells is threaded with fibers: mucus, biofilms, the glycocalyx on blood vessel walls. Averaged over the fibers, this is a Brinkman medium. The mesh screens the flow, so a moving body disturbs only the fluid close to it, and the fluid to its sides flows backward. Drag, torque, and flow agree with Cortez, Cummins, Leiderman & Varela (2010) to within a few percent.
Protein towers standing on a wall in a shear flow. This reproduces the original UNC code that Fluidlets grew from, to about one part in ten million (the old code's rounding).
glycocalyx_towersDrag and torque on a sphere, the standard check of any regularized Stokeslet code, against Cortez, Fauci & Medovikov (2005).
translating_sphereJupyter notebooks that teach the method step by step, with the math next to the code. Each one ends with exercises, runs in under a minute on a laptop, and can also be opened on Colab.
Derive the regularized Stokeslet from the blob and compare it with the singular one.
Open the notebookHow big the blob should be, and how its error trades off against the spacing of the points.
Open the notebookForces in, velocities out, and the reverse; walls; and a cell that swims by changing its shape.
Open the notebookScreening, backflow, and the drag on a sphere in a porous medium.
Open the notebookFluidlets was the software goal of the NSF Focused Research Group Advanced Algorithms and Software for Problems in Computational Bio-Fluid Dynamics (DMS-0854961, 2009–2013) at UNC Chapel Hill, with Michael Minion, Jan Prins, and Jingfang Huang. It starts from the regularized Stokeslet code written for the group's glycocalyx project. That code is kept unchanged alongside the new one, and the new code was checked against it.
Fluidlets needs Python 3.10 or later, NumPy, SciPy, and Numba. Clone the repository and run pip install -e . to install it. Developed by Laura A. Miller and collaborators. BSD 3-Clause License.