Forming lab

Glassblowing is limited by viscosity, which rises as the glass cools. A gather fresh from the furnace is runny enough to drip off the pipe in a couple of seconds; a minute later its skin is past the working point. Everything a blower does, turning, reheating, blowing in puffs, swinging, is a way of steering three slow flows while the glass cools. The simulator below computes them.

time
skin
core
size
wall
blows like
sag
emissivity
heat

A model: a hollow sphere of NBS 710 soda-lime glass in 24 shells of equal mass, each at its own temperature and viscosity; blowing, sagging and stretching from the textbook viscous solutions for that shape; heat by conduction between shells and radiation in three wavelength bands. Drawn in section. Hold the button (or the space bar) to blow.

Things to try

Stop turning. Set the turn to zero and the gather sags off the pipe within a few seconds. Turn it again and look at the end-on view: the far end no longer falls; it circles a point off to one side. Turning does not stop the glass from flowing. It reverses the direction of the flow every half turn, so the sag cancels itself instead of adding up.

Blow and hold. The first bubble is the hard part. At the tip of the pipe it is a few millimeters across, and the glass around a small bubble must stretch hard to let it grow, so a gather that has cooled for half a minute hardly moves. Once it starts, it runs away: a thinner wall is easier to stretch, so the same breath stretches it faster, until your breath rather than the glass sets the pace. Keep holding and the wall thins until it chills and sets as a thin, oversized bubble. Blowers start the bubble while the gather is hot, then blow in short puffs with reheats between, so the wall never gets ahead of them.

Swing. Point the pipe down and the gather stretches under its own weight; point it up and it settles back, shorter and fatter. Swinging the pipe is how a blower makes length.

Reheat. In the glory hole a gather takes heat back by the same bands it loses heat by. Watch the clear one: near the chamber's own temperature it all but disappears against the walls, the same law that makes it glow dimly in the dark shop (see the glory hole).

The three flows

Viscosity sets the pace of every flow, and for soda-lime glass it changes about 27,000-fold between the furnace at a typical 1150 °C (about 150 Pa·s on this curve; the furnace figure is unverified) and the softening point at 724 °C, where a hanging fiber stretches under its own weight. The simulator takes it from one measured glass, NBS Standard Glass No. 710, through the Fulcher fit Napolitano and Hawkins made for it in 1964, the same curve as the site's stage 00. The gather is cut into 24 shells of equal mass, each with its own temperature and so its own viscosity, and each flow is the textbook result for a viscous body of that shape.

Blowing: a hollow sphere

Glass is incompressible, so when the bubble grows every shell must move outward with velocity u = C/r², whatever its temperature. That fixes the flow, and the pressure it needs follows exactly: Δp = ∫ 12 η(r) C / r⁴ dr across the wall. Two consequences follow. The 1/r⁴ weight puts almost all the stretching in the glass next to the bubble, so in a thick gather the core's heat, not the skin's, decides whether it will blow. And for a thin wall the rate becomes da/dt = Δp a² / 12 η h: it grows as the bubble grows and the wall thins, which is the runaway. Surface tension on both faces pulls back by 2γ/r each, which matters only for the smallest bubbles.

Sagging: a viscous cantilever

The part of the gather beyond the pipe's tip is a short beam under its own weight. Slow viscous flow obeys the same equations as elastic deformation, with velocities in place of displacements and 3η in place of Young's modulus (the Stokes–Rayleigh analogy, exact for incompressible material, after Stokes in 1845 and Rayleigh's Theory of Sound, as Teichman and Mahadevan attribute it). So the elastic tip deflection wL⁴/8EI becomes a deflection rate. Its stiffness weights each shell by r³, the opposite of blowing: the skin carries the bending. In the model, this is how a blower keeps control: let the skin chill and it holds the gather straight while the core is still hot enough to blow.

Turning the pipe at ω carries the sag round with the glass. In the shop's frame the far end obeys d′ = ω × d + v ĝ, and the solution circles the point v/ω to one side of the pipe with radius v/ω. For a fresh gather turned once a second, the far end strays less than a centimeter; stopped, the same glass falls two or three centimeters a second (both from the model).

Swinging: stretching under weight

Along the pipe, the weight of the glass pulls the gather into a longer spheroid at a strain rate σ/3η, where 3η is the extensional viscosity Frederick Trouton measured for pitch and other very viscous liquids in 1906.

Cooling, in three bands

Out of the fire the gather loses heat mainly as radiation, and glass is not a simple radiator. Liu, Kitamura, Xia and Pilon measured soda-lime melts in 2016 and described their absorption in two bands. Below 2.8 µm the glass is nearly transparent: clear glass absorbs about 43 per meter there, so light crosses centimeters of it, while green bottle glass, with six times the iron, absorbs about 179 per meter. From 2.8 to 5 µm every soda-lime glass absorbs about 460 per meter, and beyond 5 µm it is opaque. At 1100 °C a black body sends about 45% of its power into the first band, 35% into the second and 20% into the opaque one (computed from Planck's law).

So each band leaves from a different depth. The opaque band leaves from the skin, the second from the outer few millimeters, and the first from deep inside a clear gather. Each shell here emits each band in proportion to how much of it can reach the surface, by the exact result for a non-scattering slab (the kernel 2κE₂(κd), whose total is the slab's emissivity, 1 − 2E₃(κh)). Two things follow that the simulator shows. A thin blown wall is a poorer emitter than the solid gather, because thin glass is transparent to its own first band, the point Robert Gardon made in 1956. And it cools much faster anyway, because the same glass now has three or four times the surface. Heat moves between shells by conduction, with the conductivity Liu and colleagues measured.

The glow is computed the way the glory hole computes it: Planck's law times the glass's own visible emissivity, one minus its transmission along a line of sight through the wall (Kirchhoff, 1860). Each shell is drawn at its own temperature, so a chilled skin shows as a dimmer rim around a brighter core.

What the model leaves out

Sources

← back to the glory hole