Worked example · Bridgman technique

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 quartz-wall mesh), not an illustration.

Engine-linked. The animation replays a precomputed transient solve (111 field frames, 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 (actual node temperatures): 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.

speed

A — centerline cluster (breadboard config)

B — corner probes, UV-adhesive mounted

Axial cross-section sweep (right panel): 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. The four corner probes print warm lobes into the section while their sheaths bridge hot-zone heat; watch how far the lobe effect reaches toward the center as each tip approaches and is engulfed. 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 ≈ 14.9 W/m·K vs DMSO’s 0.25) shifts the front about 0.5–0.7 mm. 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 peaks near 0.9 mm as the SLI sweeps the tip span.

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. The SLI shown is the conduction-model isotherm from the real solver, not a CFD melt front.

Explore next: see the microstructure this front leaves behind in the 3D lamellar-growth viewer (sweep the transverse and axial cross-sections), or read how the number is proven — mesh-independence gating, the mushy-zone enthalpy method, and result provenance.