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ActiveDrops

Spontaneous symmetry breaking of self-propelled drops.

A planar drop emits a chemical species at its interface. The species diffuses and is advected in the outer phase. The implemented constitutive law is sigma = 1/Ca + 4*cL: positive concentration increases surface tension. Above a critical Péclet number the isotropic state is unstable: a small asymmetry in the concentration field drives a Marangoni flow that reinforces the asymmetry, and the drop self-propels. The code integrates this problem in the Stokes limit with Basilisk using the coupled level-set and volume-of-fluid (CLSVOF) interface method and the integral formulation of surface tension, and provides a bracketed search for the finite-time onset in Pe.

Layout

Requirements

  • A C compiler, make, gawk and curl for the Basilisk install.
  • Python 3 for PeScan.py and the tests (standard library only).
  • Python 3 with numpy, pandas and matplotlib for postProcess/*.py.

Basilisk is pinned per project. From the repository root:

curl -fsSL https://raw.githubusercontent.com/comphy-lab/basilisk-C/v2026-08-30/reset_install_basilisk-ref-locked.sh | bash -s -- --ref=v2026-08-30
source .project_config

This installs the selected comphy-lab/basilisk-C release into basilisk/, records the ref in basilisk/.comphy-lock and writes .project_config, which the runners source. Both paths are ignored by Git. The code was last built and run against release v2026-08-30; it requires a release of August 2026 or later (FILTERED defined with a value, comma-free reductions, no dirty attribute).

Single case

bash runSimulation.sh default.params

The runner creates simulationCases/c<CaseNo>/, copies the parameter and source files there, compiles with -I../../src-local and runs ./dropMove case.params. Snapshots go to intermediate/snapshot-<t> and diagnostics to log.dat with columns i t ke dist xcm ycm volume. The run prints exactly one STATUS line (MOVED, NOT_MOVED or FAILED) and one SUMMARY key=value line. Use --threads N for an OpenMP build and --exec to select another source in simulationCases/.

Parameter file keys

dropMove.c reads these keys (defaults in brackets):

  • CaseNo [1000], must be at least 1000 so case folders sort.
  • Pe [1.6]: Péclet number, species diffusivity 1/Pe.
  • MAXlevel [8], MINlevel [0]: quadtree refinement bounds.
  • Oh [1], Ca [0.1], AcNum [1]: density 4/Oh^2, clean surface tension 1/Ca, interfacial chemical flux.
  • L0 [10]: square domain size in drop radii; walls are no-slip with zero concentration.
  • tmax [50], tsnap [0.1]: observation horizon and snapshot interval.
  • threshold [1]: centroid displacement in drop radii classified as MOVED; a value of zero or less disables the early stop.
  • FErr, VelErr, cErr, KErr [1e-3]: wavelet adaptation tolerances.
  • keLimit [1e3]: kinetic energy classified as FAILED.

Embedded confinement cases

bash runSimulation.sh embed-pipe.params --exec dropMove-embed-pipe.c
bash runSimulation.sh embed-channel.params --exec dropMove-embed-channel.c

wallHalfWidth is the pipe radius or channel half-width, in initial drop radii (default 2.53). A wall exactly aligned with finest-grid faces is rejected because it has no cut-cell fragment for the embedded no-slip flux. The pipe starts a unit sphere on the axis (y=0) and cannot represent transverse migration. The channel starts a planar unit circle at (0,dropOffset); its default offset is 0.5. initialDipole seeds an axial concentration asymmetry and may be set to zero. Both example files disable the displacement early stop with threshold=0.

The embedded sidewalls are no-slip and impermeable to species: cL[embed] = neumann(0). The axial endcaps are no-slip with cL=0, so the finite end distance remains a model parameter. Activity adds the source AcNum*|grad(f)| at the drop interface; it does not create wall flux. Here cL is produced species, not directly a consumed-fuel concentration. Absorbing, reactive or fixed-fuel walls would require a different chemical boundary model.

These cases require the pinned Basilisk v2026-08-30 and reconstruct the stationary embedded geometry after mesh adaptation. No contact-angle or wetting model is supplied: a liquid-containing cell entering a three-finest-cell wall/endcap band stops with FAILED. In the pipe, volume and ke omit the common 2*pi factor; ycm is the mean radius, and dist measures axial displacement. Existing planar post-processing readers must not be used to infer pipe volume or transverse motion.

Software checks for geometry and species wall conditions are available via bash testCases/run-embed-tests.sh. These are implementation checks; convergence and physical wall attraction or repulsion require separate study.

Parameter sweep

bash runParameterSweep.sh sweep.params --dry-run
bash runParameterSweep.sh sweep.params --parallel 2

SWEEP_* lists in the sweep file form a Cartesian product; each case gets a deterministic CaseNo from CASE_START. Set CASE_END to assert the expected number of cases.

Onset scan

python3 PeScan.py 1.0 0.5 --tmax 50 --max-level 9 --tol 0.005 --tag level9

PeScan.py runs one case per sample through runSimulation.sh (case numbers from --case-start, default 2000), first bracketing the transition with one stationary and one moving endpoint, then bisecting until the bracket is narrower than --tol, then taking one verification sample on each side. Results, including every sampled run and the classification convention, are written to simulationCases/pescan-<tag>/results.json. Outcomes are:

  • bracketed: interval [pe_lo, pe_hi] with pe_lo stationary and pe_hi moving;
  • undetermined: no bracket inside [--pe-min, --pe-max] (all runs moved, or none did within tmax);
  • failed: a run stopped on a numerical failure and is not classifiable;
  • nonmonotone: a verification sample contradicts a single threshold.

The exit status is 0 only for a bracket converged to tolerance.

Diagnostics and classification convention

The drop centroid, drop volume and kinetic energy are integrated with the cell volume, f*dv(). On the adaptive mesh the cell count is not a measure of area, so a count-weighted centroid is biased towards refined regions; testCases/centroid-check.c places a circle on a mesh whose right half is refined two levels deeper and shows a count-weighted centroid error of about two coarse cells against below one percent of a coarse cell for the volume-weighted centroid. Displacement is measured from the centroid at the first step.

MOVED means the centroid moved by more than threshold before tmax. This is a finite-time, finite-displacement convention: near onset the displacement grows slowly and can be censored by the observation window, so a reported interval depends on tmax, threshold and MAXlevel, all of which are recorded in every SUMMARY line and in results.json. Near the transition, lengthen tmax, lower threshold and increase MAXlevel until the interval stops moving, and inspect the growth of dist in log.dat before quoting a value.

Tests

bash testCases/run-tests.sh

Both tests are software tests: the first exercises the scan logic with synthetic classifiers (monotone threshold, all moving, all stationary, non-monotone window, numerical failure, run cap); the second checks the centroid diagnostic against the exact centroid of a circle on an asymmetrically refined quadtree and needs qcc. Neither is a verification of convergence nor a validation against independent data; no such case exists in this repository yet.

Post-processing

cd postProcess
python3 contour.py --caseToProcess ../simulationCases/c1000 --tSnap 0.1 --cpus 4

contour.py compiles getFacets and getData once with qcc, then renders one frame per snapshot in parallel (--cpus, alias --CPUs; --max-frames bounds the number of snapshots). vectors.py is a legacy serial script with hard-coded paths kept for reference. The readers compile individually with

qcc -O2 -Wall -disable-dimensions getCM.c -o getCM -lm
./getCM ../simulationCases/c1000/intermediate/snapshot-10.0000

Documentation site

bash .github/scripts/build.sh
bash .github/scripts/deploy.sh

The generator renders the literate C and Python sources under src-local/, simulationCases/, postProcess/ and testCases/ into .github/docs/, which is committed; the GitHub Pages workflow deploys it from main.

Licence

GPL-3.0; see LICENSE.

Generated Documentation

Root Directory

postProcess

simulationCases

src-local

testCases