Directional solidification: watch the freezing front pass four sensors
A quartz cuvette of liquid DMSO translates from a hot zone to a cold zone at 5 µm/s.
The solid–liquid interface (SLI, the 18.5 °C isotherm) sweeps the bore and crosses the four
centerline sheathed thermocouples in succession — each sensor traces the classic S-curve as the gradient zone
passes over it. A fifth trace follows a bare, uninstrumented melt node so you can see the natural DMSO response
undistorted by sensor hardware. Every frame is output of the refined, breadboard-matched NovaThermal solve
(0.1 mm mesh, refined to 0.05 mm across the central 1 mm of the bore for the centerline bundle), not an illustration.
Engine-linked. The animation replays a precomputed transient solve (110 field frames for variant A and 108 for variant B, 1.5 h of process time).
The parameter panel redraws the geometry live; to re-solve with your own values, open the console.
Close-up, top-down across the bore (solved node temperatures on a 0.1 mm grid, refined to 0.05 mm across the central 1 mm for variant A; interpolated for display, “Show node cells” shows the raw nodes):
while a tip is near the front, its sheath bridges heat down from the hot zone, locally delaying freezing — the
front carries a divot (indenting cold-ward) at the sensor cells, the distortion seen
in the breadboard video as each tip is engulfed. Late in the pull the relationship inverts
(cold zone over the sheath span → cold fingers). Two mounting variants play together below;
real breadboard traces (Samples 2–4) overlay variant A’s chart, aligned at each
sensor’s Tm crossing.
Centerline bundle packing:
A: centerline bundle, square, S1+S2 adjacent
Bundle cross-section (left): the four 0.25 mm sheaths drawn at true size and
position, packed as a touching 2x2 square.
A sheath exists only from its tip to the hot end, so the bundle grows from one sheath to four as the plane moves hot-ward past
the tips; watch the warm or cool footprint of the bundle widen as each sheath joins. The second close-up above
runs through the sheaths the first one misses. The grid is 0.05 mm across the central 1 mm of the bore and 0.1 mm elsewhere.
B — corner probes, UV-adhesive mounted
Axial cross-section sweep (cross-section plot): looking down the long axis at the
3×3 mm bore, sampled at the plane where the bore-average temperature equals Tm — the plane rides the front as it
translates. A probe exists only from its tip to the hot end, so it is drawn only once the plane has reached its tip. The
corner cells run slightly cool in every plane, with or without a probe: that is the square bore’s own two-wall
coupling to the furnace. Once the plane reaches a tip, that probe’s sheath bridges hot-zone heat and prints a warm
lobe at its corner; in this solve the lobe holds the front back by a median of about 0.46 mm at the tip
(0.30–0.67 mm across frames), and its reach ahead of the tip fades to a median of about 0.05 mm at 4 mm and about 0.01 mm around 6 mm. The
orthogonal view above is the same close-up clocked 90°: the far wall row, where S2 and S4 live.
Edit the geometry
These fields map 1:1 to the solver template. Changing them redraws the drawing so you can stage your own case;
the animation above stays the solved reference case. Run your edited case in the console →
What the model showed
Perturbation
A thermocouple is a thermal short
A 0.25 mm sheathed probe (effective axial k ≈ 14.6 W/m·K vs DMSO’s 0.25)
shifts the front 0.3–0.7 mm at its tip (corner probes, range across frames of this solve). The sign depends on which zone the sheath bridges.
Planarity
Symmetry governs front shape
Equal-length probes (center or corners) keep the front flat. A rake of differing lengths tilts it —
warp across the displayed row peaks near 0.87 mm for the corner probes (variant B) and 0.93 mm along the centerline row through S1 (variant A, every packing) as the SLI sweeps the tip span.
Bundle
The pucker grows with each sheath
Over the centerline bundle the front forms a local pucker that deepens as the front reaches more sheaths. Median depths, measured against the
bore-scale front shape, are about 0.14–0.18 mm with one sheath reached, 0.23–0.27 with two, 0.33–0.35 with three and 0.41–0.42 mm with all four,
and the median width grows from about 0.45–0.6 to 0.75 mm. Individual frames scatter around these medians, most near a tip. Packing and
sheath order change the median depth by up to about 0.04 mm.
Verification
Steady == transient to ~1%
At 5 µm/s the Péclet number is tiny: the conduction field is quasi-static and the
isotherm lands mid gradient-gap at the measured 1.5–2.1 K/mm.
Honest limits. Lumped conduction omits 1-g buoyant melt convection (the microgravity flight case is near-exact);
DMSO solid properties are literature values. Conductivity is temperature-dependent for fused quartz (Kaye & Higgins 1926 slope) and the
thermocouples (Inconel 600 sheath, chromel and alumel wires, from manufacturer and published data); DMSO uses its solid and liquid values at
the melt point with provisional small slopes. The SLI shown is the conduction-model isotherm from the real solver, not a CFD melt front.
Model update (29 September 2026): cells occupied by a thermocouple sheath no longer carry DMSO latent heat, which had given them about 50 times
the sheath’s own heat capacity near Tm; touching sheaths keep a thin DMSO-film contact conductance. For the corner probes this moved the
front by at most 0.07 mm.