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Tri Tuladhar

Next Generation Ink Jet Technology & Polymer Foaming

Whilst he was a member of the Polymer Fluids Group, Dr Tuladhar worked on two projects: "The Next Generation of Inkjet Technology" and "Polymer Foaming"

Next Generation Ink Ject Technology

This work was part of the "Next Generation Inkjet Technology" consortium. For further details of the project see the main Ink Jet Technology page.

Polymer Foaming

This work involved detailed experimental investigations into the foaming of a commercial expandable polystyrene (EPS) and PS-CO2 in real time using in-house developed Multipass Rheometer (MPR). Both rheology changes and in-situ microstructure evolution were followed during the foaming of a molten polystyrene that was supersaturated with pentane. A bubble growth model incorporating gas diffusion from the surrounding melt was developed to fit the experimental data and provided insight into the early growth stage.

Pentane, CO2 and N2 are used as physical blowing agents in the manufacture of polymer foam and as plasticisers to reduce melt viscosity during processing. The dissolved gas concentration and pressure influence the rheological behaviour of melt and the microstructure of the product during growth and its final foamed product.

Tri studied the foaming of polystyrene (PS) melt under closely controlled pressure, volume and temperature using the Multipass Rheometer (MPR). This allowed online observation of micro-bubble evolution and growth. The effect of blowing agents and their concentration on the melt rheology and bubble growth kinetics of PS foams were studied. Viscoelastic behaviour of the PS foamed samples was also investigated using the MPR and compared with pure PS and homogeneous melt of PS and dissolved gas. In addition, the effect of processing parameters such as pressure release rate, temperature and shear on the bubble growth kinetics and final foamed product was also examined. A bubble growth model was also developed to fit experimental data which gave insight into an early stage of bubble growth.

Systematic foaming experiments were carried out by decompression of PS melt saturated with either CO2 or pentane in the MPR. The movie in figure 1 (not in real time) shows evolution of CO2 bubbles and their growth from a homogeneous melt of PS and CO2 during decompression from 90 bar to 10 bar under isothermal condition of 140°C in the MPR. The pressure was reduced by increasing the MPR chamber volume by moving both top and bottom pistons apart at a speed of 1 mm/s. After a very short lag period, many small nuclei were optically visible. Nucleation appeared to occur randomly leading to subsequent bubble growth from these sites. With time, more bubbles nucleated and grew; the bubbles initially appeared to be circular. As more bubbles formed and grew in close proximity, theirs shape were influenced by the surrounding neighbours leading to polygonal shaped bubbles towards the end. Most of the growth takes place within the first 10 seconds.

The foaming of polystyrene using carbon dioxide 
Figure 1 - The foaming of polystyrene using carbon dioxide

The foam microstructure and bubble size also depended on the homogeneous mixing of polymer and gas in the compressed state and the pressure release rate during decompression.

The figure below follows the time evolution of some bubbles (obtained from above movie) during decompression. The bubble size is represented as an equivalent bubble radius. The figure also shows the effect of change in the overall melt pressure of the system, leading to subsequent bubble formation and growth. There was a lag period of one to two seconds before the bubble became optically visible. The smallest microscopic drops optically visible in these experiments were of ca. 0.5 µm radius and rapid bubble growth occurred from these small nuclei. In the following few seconds, the bubble reached its maximum size after which there was little growth. Though the lag time varied between the bubbles, once the nucleation process initiated, bubble formation and growth was fast. The final bubbles were found to be uniform having an equivalent radius of ca. 70-100 µm.

The growth of foam bubbles within polystyrene
Figure 2 - The variation of bubble radius with time for polystyrene foamed with carbon dioxide

Tri also studied the rheology of such samples consisting of a polymer melt with dissolved gas/bubbles using the MPR. Figure 3 below compares the apparent viscosity of pure PS, PS-pentane single phase and PS-pentane foam at 150°C. The pure PS follows a classic shear thinning flow curve. The addition of pentane at high pressure in the melt phase resulted in ~ 80% reduction in viscosity at low shear rate with some reduction at higher shear rate. The rheology of PS-pentane at low pressure (foamed sample) had a further reduction in viscosity counter to normal expectation in relation to filled systems. The effect of temperature on PS and PS-pentane shows a general trend where the apparent viscosity of the melt decreases with increasing temperature and each flow curve obtained lies below the previous ones (Tuladhar and Mackley, 2004).

Rheology of foamed and unfoamed polystyrene
Figure 3 - Comparision of the rheology of unfoamed and foamed polystyrene

Having established both the bubble growth kinetics and rheology of the system, a growth model was developed to describe the process. After the onset of nucleation, the pressure of the gas in the bubble (PG) provides the driving force to expand while the viscosity (η) of the polymer and surface tension (σ) of the bubble wall provide resistance to bubble growth. Each bubble is assumed to be spherical with nucleation radius, Ro, and is surrounded by a finite volume of melt with an initial radius S0. Assuming the melt to be Newtonian, the bubble growth equation is represented by three equations based on combined equations of momentum and continuity of the melt surrounding the bubble in radial component (r) of spherical coordinates (eq. 1), mass balance of the gas at the bubble surface (eq. 2) and diffusion of gas in the melt (eq. 3).

Equation 1  eq. 1 
Equation 2  eq. 2 
Equation 3  eq. 3 

where PL is ambient pressure, c is the dissolved gas concentration (wt. fraction) in the melt, D is the diffusion coefficient, ρ is the melt density, T is the temperature and M is the molecular weight of the gas. The concentration at the bubble surface was related to PG by Henry's law.

Figure 4 below compares the model prediction for PS- pentane foaming at 140 and 150°C. In the model, the onset of nucleation is taken as where the time equals zero. Most of the parameter values such as c0, ρ, σ, η, D and T are either provided or experimentally determined. During the growth stage, the concentration of the gas at the bubble surface varies from the initial loading concentration to almost zero towards the end (Tuladhar and Mackley, 2004) suggesting that both η and D are time dependant. Assuming R0, variable parameters S0, η, and D were adjusted to fit the growth data. These values were tested against the experimental data and literature values so that they lie within the estimated range. The model shows a good fit using realistic parameter values. The fittings parameter values are shown in figure. The model shows sensitivity to all these parameters and is consistent with what one would expect with change in gas type and concentration. The values of h is within the experimental zero shear viscosity of PS and PS-gas single phase. The experiment and model also shows sensitivity to change in temperature (Tuladhar and Mackley, 2004).

Model predictions compared with experimental data obtained from foamed polystyrene
Figure 4 -Comparision of model predictions with experimental results for polystryrene foamed with pentene


  1. Tuladhar, T.R. and Mackley, M.R., "Experimental observations and modelling relating to foaming and bubble growth from pentane loaded polystyrene melts", Chemical Engineering Science, 59 (24), 5997-6014, 2004.
  2. Tuladhar, T.R. and Mackley, M.R., "The development of polymer foam microstructure: experimental observations and matching modelling for polystyrene foams using different blowing agents", Conference proceeding at 7th World Congress of Chemical Engineering, Glasgow, Scotland, 10-14 July, 2005.
  3. Tuladhar, T.R. and Mackley, M.R., "Experimental and numerical studies of polymer foaming process", in Cellular Metals and Polymers, edited by R. F. Singer, C. Korner, V. Altstadt, Fragezeichenverlag, Fuerth, Trans Tech Publications, Switzerland, Long ISBN number 0-87849-491-x, pp 239-242, 2005.
  4. Tuladhar, T.R. and Mackley, M.R., "The pressure dependant evolution of rheology and microstructure of pentane loaded molten polystyrene during controlled foaming", Conference proceedings at XIVth International Congress on Rheology, Edited by The Korean Society of Rheology, Seoul, Korea, ISBN 89-950057-5-0, pp Fe10-1- Fe10-3, August 22-27, 2004.

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