# Ink jet and flilament stretch

In the 2000s a Cambridge based project on the science and technology of ink jet printing provided a welcome ten year period of funding and in the Chemical Engineering Department our role was to characterise the complex and delicate behaviour of ink jet fluid rheology and formulation. From this work we developed our “Trimaster” family of filament stretching devices in order to capture the high speed extensional deformation and breakup behaviour of low viscosity fluids.

Below is a brief summary of some of our** publications** followed by a **2009 review powerpoint presentation** and then more recent **2018 and 2019 presentations** on the stretch and breakup of viscous and yield stress fluids.

Ink jet processing is very sensitive to the formulation of the ink jet fluid and in particular the rheology. Normally ink jet fluids have a viscosity below 5 mPas, close to that of normal solvents and water. Ink jet processing usually involves high jet speeds, typically 6 m/s and this results in high strain rate deformation with dominant extensional behaviour during drop formation outside the jet nozzle. Strain rates in excess of 1000 s-1 are often achieved. Ink jet fluids whilst generally being Newtonian in steady shear can be viscoelastic where the relaxation times involved can be very short, typically a millisecond or less. This takes rheology into an area of “extreme rheology” needing to characterise the viscoelasticity of “watery” fluids with short relaxation times. In addition nonlinear extensional behaviour of these low viscosity, viscoelastic fluids can be important.

Our own work on ink jet fluids started with measurements of high shear rate apparent viscosity and we soon discovered that ink jet formulations were essentially Newtonian even at shear rates in excess of 1000 s-1. Tuladhar, T.R. and Mackley, M.R. Filament stretching rheometry and break-up of low viscosity polymer solutions and inkjet fluids* Journal of Non-Newtonia*n Fluid Mechanics, 148 97-108. (2008). In this paper we also described the filament stretching behaviour of ink jet formulations using the Multipass Rheometer (MPR) as a non linear filament stretching device. We now call this apparatus the Mk1. Cambridge Trimaster. Subsequently we built a Mk2 Cambridge Trimaster filament stretch apparatus that used a simple stepper motor drive, rather than the more complex MPR servo hydraulics. D.C.Vadillo, T.Tuladhar, A.C. Mulji, S. Jung, S.D. Hoath,and M.R. Mackley Evaluation of the inkjet fluid’s performance using the “Cambridge Trimaster” filament stretch and break-up device Journal of Rheology 54, 2 .261-282 (2010)

In order to characterise the high frequency linear viscoelastic response of ink jet fluids a Piazo Axial Vibrator (PAV) that had been pioneered by the late Prof Pechold from the University of Ulm was used. This is a brilliant and delicate apparatus that is capable of exploring linear viscoelasticity at high frquencies. D.C. Vadillo, T.R. Tuladhar, A.C. Mulji and M.R. Mackley The rheological characterization of linear viscoelasticity for ink jet fluids using piezo axial vibrator and torsion resonator rheometers. Journal of Rheology, 54, 4. 781-795 (2010 )

The link between ink jet performance and ink jet rheology is given in, S. Hoath, I. M.Hutchings, G.D. Martin, T.R.Tuladhar, M.R.Mackley and D. Vadillo * Links Between Ink Rheology, Drop-on-Demand Jet Formation, and Printability *Journal of Imaging Science and Technology 53, 4, pp. 041208-(1-8) (2009).

The way in which Trimaster filament stretch, thinning and breakup can be modelled is told in a number of further papers. M. Tembely, D. Vadillo, M. R. Mackley and A. Soucemarianadin The matching of a “one-dimensional” numerical simulation and experiment results for low viscosity Newtonian and non-Newtonian fluids during fast filament stretching and subsequent break-up* *J. Rheology. 56, 159- 184 (2012).

D. C. Vadillo, M. Tembely, N.F. Morrison, O. G. Harlen, and M. R. Mackley The matching of polymer solution fast filament stretching, relaxation, and break up experimental results with 1D and 2D numerical viscoelastic simulation. J. Rheology . 56, 1491-1516 (2012)

**2009 Monash Review presentation.**

A summary of the ink jet rheology story is given below from a 2009 Seminar presentation at Monash University, Australia (Unfortunately some of the photographs and graphs have not come out in the reproduction).

**2018 Cambridge seminar. Fast filament stretching.**

Over the past few years Dr Simon Butler and I have been working with a French Group (CEMEF) at Sophia Antipolis who have carried out impressive modelling that provides insight on how viscosity, surface tension and yield stress influence high speed deformation and breakup of filaments and this presentation is a summary of that work.

**Droplet deformation and breakup** – a recent presentation.

**2019 University College London (UCL) seminar. Fast filament stretching.**

This presentation is a concise follow up of the 2018 Cambridge seminar. Some movie clips are missing however hopefully the presentation conveys a simple message for the conditions required to form drops, threads and for “yield stress fluids”, a cusped conical section. There has also been much debate in the literature that “Carbopol” systems are the best preferred model yield stress fluid. This presentation shows that Nivea Cream gives a much sharper and cleaner Yield stress transition!

**Papers relevant to Ink Jet Rheology and Processing**

- Tuladhar, T.R. and Mackley, M.R. Filament stretching rheometry and break-up of low viscosity polymer solutions and inkjet fluids
*Journal of Non-Newtonia*n Fluid Mechanics, 148 97-108. (2008) - S. Hoath, I. M.Hutchings, G.D. Martin, T.R.Tuladhar, M.R.Mackley and D. Vadillo
*Links Between Ink Rheology, Drop-on-Demand Jet Formation, and Printability*Journal of Imaging Science and Technology 53, 4, pp. 041208-(1-8) (2009) - D.C.Vadillo, T.Tuladhar, A.C. Mulji, S. Jung, S.D. Hoath,and M.R. Mackley Evaluation of the inkjet fluid’s performance using the “Cambridge Trimaster” filament stretch and break-up device Journal of Rheology 54, 2 .261-282 (2010)
- D.C. Vadillo, T.R. Tuladhar, A.C. Mulji and M.R. Mackley The rheological characterization of linear viscoelasticity for ink jet fluids using piezo axial vibrator and torsion resonator rheometers. Journal of Rheology, 54, 4. 781-795 (2010 )
- M. Tembely, D. Vadillo, M. R. Mackley and A. Soucemarianadin The matching of a “one-dimensional” numerical simulation and experiment results for low viscosity Newtonian and non-Newtonian fluids during fast filament stretching and subsequent break-up
- D. C. Vadillo, M. Tembely, N.F. Morrison, O. G. Harlen, and M. R. Mackley

The matching of polymer solution fast filament stretching, relaxation, and break up experimental results with 1D and 2D numerical viscoelastic simulation. J. Rheology . 56, 1491-1516 (2012)