The performance of two types of static mixers of 6 mm diameter, manufactured by 3D metal printing, have been investigated with respect to
Residence time distribution.
Pressure drop is in line with bigger diameter static mixers. Mixing performance is not only depending on viscosity ratio, but also on flow rate and density difference of the liquids to be mixed. Heat transfer outperforms static mixers manufactured traditionally. The residence time distribution is characterised by a constant value of the dimensionless radial dispersion coefficient (Fourier number).
Although some authors claim the first static mixers were already used at the end of the 19th century, most scientists and engineers agree that static mixers were used from the 70s of last century in process industries. The helical type design, which is known widespread under the name Kenics, was patented in 1965. Later other designs were introduced, leading to the multitude of static mixers currently available on the market[i].
Static mixers are nowadays used mainly for the effective mixing of liquids. In extruders they are used to equalise temperature differences in the polymer flow leaving the extruder screw.
The first patent describing the production of a polymer in a static mixer was filed in 1976 by DuPont. In this patent the polyamide production in a static mixer was claimed. The production of polystyrene in a static mixer was reported in 1985[ii].
Due to the favourable surface to volume ratio, tubular reactors have advantages when processing fast, highly exothermic reactions. Despite the advantageous thermal control in a tubular reactor, only few polymerisations are carried out in such a device on commercial scale. Partly, this is due to the inability of tubular reactors to process poly‑condensation satisfactorily as it requires the withdrawal of volatiles in course of the polymerisation, but also due to the fact that polymer chemistry is still developed in a glass flask mainly for specialty polymers. In the scale‑up procedure for such new polymers, change of manufacturing technology is generally not considered.
For the development of new polymer grades and formulations small scale equipment is attractive as the amount of material necessary for experimentation is limited and the equipment should fit into a fume hood. Recent developments in pump manufacturing, flow measurement and 3D printing of metals, makes it possible to manufacture such continuous flow equipment that suits the requirements of low volume, small size set‑ups for new polymer grade development. The behaviour of such equipment however, lies outside the scopes of any investigation published in literature.
To investigate the mentioned performances, for each of the two static mixer designs (helical tape and X-bar), two experimental setups were built: one for measuring pressure drop and heat transfer and one for mixing performance and residence time distribution. All measurements were carried out with water and glycerol, or mixtures thereof on tubes of 6 mm diameter. Determining the heat transfer coefficient at low flow rates poses a challenge when doing so the “classical” way utilising a double pipe. Not only have two partial heat transfer coefficients to be considered, for low flow rates the temperature difference at the tube outlet diminishes. Both problems have been tackled by applying electrical heating and using the mixer tube itself as the heating element. The mixing performance and residence time distribution have been assessed by colorimetry using a cyan dye. The effluent of mixing tubes of different length was spread between two glass windows and the mixing pattern was acquired by digital photography. The mixing quality was determined by the pixel to pixel difference of extinction of red light relative to blue and green light. The residence time distribution was determined analogous by use of digital video. Both photographs and videos were evaluated using Matlab scripts.
Pressure drops were measured using the heat transfer tubes without heating at variable flow. Both types of mixers were used of two different lengths: 10D and 35D. The results are in agreement with results obtained for larger diameter measurements, not manufactured by 3D printing.
Heat transfer turned out to be higher compared to published data in literature. The increase can be attributed to the different manufacturing technique. Traditionally, static mixers are inserts into tubes and there is no good contact to the tube wall. In the 3D printed tubes, the mixers and tubes are one piece of metal resulting in maximum possible thermal conductance from tube into the mixing element, enlarging the effective heat transfer area. Measuring for two different lengths, 10D and 35D, revealed no dependence of the Nusselt number on L/D of the tube.
In public literature, mixing performance has been published up to a viscosity ratio of 1:100. In practical use, mixing performance for viscosity ratios starting at 1:100 and up to 1:5000 are of interest. Therefore the mixing performance at viscosity ratios 1:100 and 1:1000 have been investigated. The result is a significant worse mixing performance at a viscosity ratio of 1:1000 as compared to a viscosity ratio of 1:100. Moreover, since the liquids that were used also showed a high density difference of over 200 kg/m3, flow velocity effects were also observed. At low velocity, pooling was observed that gradually gets less when the flow velocity is increased. At last, the mixing arrangement, high viscous into low viscous or the other way round, that yields best results depends on both viscosity ratio and dosing ratio applied.
The residence time distribution was derived from the response curves achieved by frame to frame analysis of the digital video footage. Residence time distribution in a tubular system is generally quantified as an axial dispersion coefficient superimposed onto plug flow. To our opinion, this approach is not suited for laminar flow systems like polymerisation reactors since the extreme at indefinite high axial dispersion coefficient yields the solution for a CSTR and not for a laminar tube flow model. We have the RTD quantified using a radial dispersion coefficient superimposed onto a laminar tube flow model[iii]. This approach yields the correct solution at both the extreme values for the dispersion coefficient. When analysing the value of the radial dispersion coefficient (D), a linear relationship with velocity is observed, resulting in a constant value for its dimensionless form, the Fourier number (Fo = D*tav/R2).
[i] Ghanem, A., Lemenand, T., Della Valle, D., Perhossaini, H.: Static Mixers: Mechanisms, Applications, and Characterization Methods - A Review, Chemical Engineering Research and Design, 92 (2014), 205 - 228
[ii] Tien, N.K., Flaschel, E., Renken, A.: Bulk Polymerisation of Styrene in a Static Mixer, Chemical Engineering Communications, 36 (1985),
[iii] Naumann, E. Bruce: Chemical reactor design, optimization, and scaleup (MGH, 2002), Chapter 8.
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