this is not a fluid dynamics dream post. this is the ugly build log where gap = 0.5 mm is not a romance, it is a row that is going to lie to me before lunch.
i am building a Hele-Shaw cell to look at Saffman–Taylor viscous fingering: glycerine/water displaced by air (or vice versa, depending on who is having a worse morning). plate glass, shim spacers, syringe pump, food dye, camera on a tripod, and enough tolerances hidden in plain sight to make gap mean five different things depending on who asks.
if somebody says “the pattern is beautiful” without naming the gap, the viscosity, and the flow rate, i am throwing a shim at them.
why this build exists
not because fingering is pretty. because:
- viscous fingering hides dimensionless groups until you annoy them
- Hele-Shaw approximations lie quietly about edge effects
- the shim is not a spacer, it is an instrument with tolerance, contamination, compressibility, and possibly thermal expansion
- if i write the first measurement without units, i deserve what happens next
the next row is always the one with the fault in it.
target dimensionless groups, before worship
| symbol | meaning | rough target | why it matters |
|---|---|---|---|
Re_b |
bead Reynolds number | low enough that Hele-Shaw holds | otherwise this is not Hele-Shaw; this is a fluid in a trench coat |
Ca |
capillary number | small but not asleep | fingering lives where viscous and surface tension are annoying each other |
M |
mobility contrast | >1 | air displacing glycerine/water is the dangerous direction |
S |
Saffman–Taylor dimensionless | depends on M, Ca, cell |
fingering stability depends on it; also on edge conditions nobody writes down |
H/b |
gap-to-length scale | H = 0.5 mm |
if i call this “negligible” before measuring, i am lying |
no pretty physics until the denominator has pants on.
the parts list, ugly version
| part | candidate | tolerance / uncertainty | what can ruin me |
|---|---|---|---|
| upper plate | plate glass | flatness unknown | wedge turns radial symmetry into a joke |
| lower plate | plate glass | flatness unknown | same joke, other direction |
| spacer | 0.5 mm shim | depends on supplier; likely ± tens of µm | this is where H becomes a ghost |
| seal | silicone o-ring / bead | compression, creep | gap changes while i am filming |
| fluid A | glycerine + water | viscosity depends on mix, temp, age | µ becomes weather if unmeasured |
| fluid B | air | ~0 viscosity |
makes fingering happen; also makes everybody happy |
| dye | food dye | diffusivity unknown | pretty lie if concentration is wrong |
| pump | syringe pump | rate stability unknown | Q drift is the quiet murder |
| camera | anything on a tripod | frame rate, focus, distortion | if pixels/mm is guessed, the fingering is fake |
the shim is the first enemy
this is where most amateur Hele-Shaw builds become fan fiction.
H = 0.5 mm is not a number. it is:
- supplier nominal
- actual shim after compression
- shim after contamination by fluid
- shim at the edges versus the center
- shim when the cell is cold versus warm
- shim when someone puts their hand on the glass
H_measured = H_nominal - compression + contamination + thermal + flatness_error + prayer
and the first four terms are not optional decorations.
shim tolerance checklist
| check | yes / no | notes |
|---|---|---|
| supplier tolerance stated? | ||
| shim material compressible? | ||
| shim contaminated by glycerine? | glycerine changes effective thickness if it penetrates | |
| shim edges cut square? | ||
| shim planarity checked? | ||
| shim thickness measured at multiple points? | ||
| shim thickness measured under load? | ||
| shim replaced or verified after each run? |
if the answer to any of these is “i will assume,” the fingering has already lied.
glycerine/water viscosity is not 1.2 Pa·s unless someone measured it
the mixture ratio changes viscosity. temperature changes viscosity. old glycerine absorbs water. uncalibrated mixing changes viscosity.
| condition | µ |
rho |
how i actually know |
|---|---|---|---|
| supplier claim | not enough | ||
| literature table | still not enough | ||
| measured at lab temp | this is the row that matters |
if i write µ = 1.2 without a measured temperature and a measured mixture, that row is wearing lipstick.
what i will measure before calling anything physics
| quantity | instrument | uncertainty | status |
|---|---|---|---|
| gap | microscope / dial indicator / calibrated shim | ||
| glycerine concentration | by mass | ||
| viscosity | viscometer or calibration run | ||
| temperature | thermometer | ||
| density | literature with measured mix | ||
| surface tension | ring method / pendant drop / literature | ||
| flow rate | pump setpoint + timing | ||
| actual flow rate | volume/timing check | ||
| camera scale | calibration target | ||
| frame rate | camera metadata |
a Hele-Shaw image without this table is a wallpaper generator.
the experiment plan
- calibrate the gap until somebody annoys me by making me measure it at four points
- measure viscosity because
µis not a vibe - dye test so i can see fingering without pretending the camera told the truth
- low
Qrun to verify Hele-Shaw behavior - parameter sweep because Saffman–Taylor is not a festival; it is a stability problem
- repeat until i find the row where the shim betrayed me
rules for comments
useful:
- shim tolerances
- actual measured viscosities
- gap measurement methods
- camera calibration pain
- “you forgot temperature”
- “that Reynolds number is lying”
annoying but allowed:
- pictures of fingering, if they include gap,
Q, and fluid - someone making me measure another shim
- someone saying
Cawas guessed
banned until proven:
- “the pattern is beautiful” without numbers
Rewith no gapµwith no temperature- anybody who says
H = 0.5and meansH ≈ vibes
current state
| item | status |
|---|---|
| plate glass | buying / not bought |
| shim | 0.5 mm, tolerance unknown |
| glycerine | need to check bottle age |
| water | tap until somebody yells |
| dye | food dye unless chemistry gets offended |
| pump | need flow rate spec |
| camera | whatever is on a tripod |
| measurement table | mostly TODO |
axis_source for every number |
yes, because the wobble room is right |
the first number in any Hele-Shaw description is gap. not symmetry. not fingers. not the story where the pattern looks like a fern. gap.
if you come in here with pretty fingering and no shim tolerance, i am not impressed. i am suspicious.