Melt Thermal

You have a web of a given thickness and material, film, paper or board, at a given temperature and travelling at a given speed. A blob or stream of hot-melt material at a given temperature and of a given thickness arrives at t=0 and after an "open" time to reach the next process (governed by web speed and distance), the temperatures will have shifted.

It is often stated, correctly, that the app isn't needed - the temperature of melt and web reach the average of the two very quickly. Here we can see if that's the case for our system.

Traditionally the average would be computed from thickness, density, ρ, and heat capacity, Cp and the timescale would depend on the thermal conductivity, K. But here we are using the "thermal diffusivity" values, D, in m²/s for the two materials where `D=K/(Cp.ρ)`.

The advantage of using D is that we use 1 parameter instead of 3, and values of D are commonly available. Here's an informal list of D values for polymers, all followed by 10^-7

ABS : 0.12; PA : 0.13; PBT : 0.1; PC : 0.15; PE : 0.11; PEEK : 0.14; PEI : 0.08; PET : 0.16; PMMA : 0.1; POM : 0.11; PP : 0.09; PPS : 0.1; PS : 0.11; PVC : 0.14;

Paper/board tends to be ~ 0.7 though you can make it a bit more precise if you know the density, ρ, in g/cc: `D=0.6+0.9(1-ρ)`

The plot shows the temperature (x-axis) versus height from the top. The time steps are rainbow colour-coded from short (blue) to long (red) giving a feeling for the timescales involved. Moving the mouse provides the T, h, distance and t values at any point.

Using the temperature

If you are coating onto a film, the temperature/time profile lets you be alert to potential damage to the web or will let you think through whether there is enough time to get adhesion via entanglement between the two polymers.

If you are coating onto a paper or non-woven, your question is whether the temperature of the system is large enough for the viscosity to be low enough to flow in (by capillary pressure or applied pressure in a nip) to the fibres and achieve an acceptable level of interlocking. That's a calculation for the Inflow app.