Elsevier

Fluid Phase Equilibria

Volume 490, 30 June 2019, Pages 92-100
Fluid Phase Equilibria

Development of a method to measure the thermal conductivity of pressurised solutions containing dense gases using 11000 g/mol polydimethylsiloxane and carbon dioxide as example fluid

https://doi.org/10.1016/j.fluid.2019.03.005Get rights and content

Highlights

  • The thermal conductivity of mixtures of carbon dioxide and a linear polydimethylsiloxane was measured.

  • Two different sensors for measuring thermal conductivity under high pressure were designed, tested and compared.

  • The repeatability of the results of the needle sensor was found to be better than 0.7%.

  • The short hot wire delivered the more reliable results under pressure.

  • The maximum pressure investigated was 16 MPa.

Abstract

The development of a method to measure the thermal conductivity of mixtures containing pressurised gases is presented. As example fluid, we use carbon dioxide mixed with a linear polydimethylsiloxane (PDMS) with a molecular weight of 11000 g/mol. Experiments were carried out at 25 °C, 40 °C and 60 °C in a pressure range of up to 16 MPa. Thermal conductivity was measured in a high-pressure view cell using two different sensors: a cylindrical needle sensor and a short hot wire. Both sensors are based on the principle of a transient linear heat source. Their applicability was compared and evaluated. Rather low molecular weight polydimethylsiloxane was chosen as model substance to close the data gap regarding the thermal conductivity of gas saturated solutions, pressurised with carbon dioxide. All experiments were carried out under isothermal conditions. It was the aim of the present work to develop and to test an adequate measuring instrument; this involves the selection and implementation of appropriate auxiliary equipment, too.

Introduction

Polymers play an important role in various processes, and a lot of products could not be made without them. Consequently, there is a wide range of highly developed, reliable treatments like injection moulding or calendering. In addition to these rather classical processes, new techniques using dense gases as solvents or reaction media have been devised and refined during the last few decades. However, the understanding of these pressurised solutions, e.g. with carbon dioxide, is not as advanced as the understanding of mixtures containing organic solvents [1]. In particular, there is a knowledge gap concerning heat transport and its interaction with applied pressures and gas content. While research into the rheology and diffusion properties of such solutions has been carried out, investigations into their thermal conductivity are rare.

Heat transfer plays a role in a multitude of different processes and is thus of importance for process design and optimisation. Due to ongoing research, a broad range of data is available for all kinds of fluids, liquids and gases, at atmospheric and under pressurised conditions. In contrast to this, relatively few measurements have been carried out with pressurised mixtures or solutions. Data may only be found for specific systems of high commercial interest, for example rocket propellants and diesel fluids [2,3] or refrigerant mixtures [[4], [5], [6]].

Pressurised solutions containing a dense gas, the topic of the present work, are used for several processing purposes. An example of a broad area of research and application which uses such solutions is the treatment of polymers. Recently, results of the mutual solubility of carbon dioxide and different linear polymerdimethylsiloxanes (PDMS) have been presented by our group [7]. Nevertheless, a review of the use of carbon dioxide for polymer processing found that there have been no data reported for the measurement of heat transfer coefficients in gas-saturated polymer melts [8]. To the best of our knowledge, this has not changed until now. This contribution is intended to fill this gap.

In general, heat conduction only takes place, if a temperature gradient is present. Therefore, most measurement methods are based on the generation of such a gradient and the subsequent analysis of its effects. Whenever fluid flow must be considered, heat is transported by convection, due to fluid movements. This effect can cause superposition and thereby affect the precision of thermal conductivity measurements. Therefore, natural convection should always be negligibly small, regardless of the measurement method, as it cannot be quantified in data evaluation. The fact that the medium is always slightly disturbed from its equilibrium state during the measurement procedure should also be considered. Any experimental method must fulfil these two crucial criteria [9].

As the thermal conductivity is derived primarily from measured quantities, either from temperature evolution or a constant temperature difference, it is important to obtain this data with high accuracy. This can be done with stationary or transient measurements. A rotationally symmetric temperature field for measurements of thermal conductivity can be created in the gap between two concentric cylinders when one of them is heated or cooled. This concentric, or coaxial, cylinder method is typical for stationary measurements [10]. A gap between a sphere and a similarly shaped surrounding object can be used in the same way, but this has been done only rarely [[11], [12], [13], [14], [15]]. Plate-plate apparatuses are another frequently used type of equipment. They involve the development of a planar temperature gradient. The stationary parallel-plate method is especially common for measurements of pure fluids close to the critical point, within three degrees of the critical temperature [10].

In principle, any of the described methods could be used under pressure, although the technical effort involved might vary between methods. However, most systems involving carbon dioxide show a mutual solubility. If the thermal conductivity of the saturated dense phase of such a system was measured with a stationary method, the temperature gradient applied over a long period of time would lead to supersaturation and de-mixing. Stationary methods were therefore excluded from further considerations.

In contrast, transient measurement methods are worth looking at. They are often chosen for the investigation of fluids, because they consume less experimental time: There is no need to wait for the temperature gradient to equilibrate. However, when a temperature gradient is present, there is also a density gradient, which may lead to convection. Since transient measurements are done comparably quickly, the development of convection and de-mixing is less likely.

Probably the most common sensor in transient heat conductivity measurements, the so-called hot wire, generates an axisymmetric temperature field in its surrounding. The sensor consists of an electrically heated wire with a large length/diameter (l/d) ratio. It can thus be taken as infinitely long and thin in mathematical considerations. In modern equipment, the wire serves not only as a heat source, but is also used as resistance thermometer at the same time. Actual arrangements commonly contain two wires of different lengths, allowing compensation for end effects. Modifications of this equipment are the needle sensor and the short hot wire. The needle sensor is thicker than the hot wire and can thus be seen as a cylindrical heat source. Polymer melts [16] and ionic liquids [17] are examples of the application of the needle sensor in fluids under ambient pressure. The needle sensor has also been used at elevated pressures on several foods [18,19]. In 1971, Davis et al. presented a 6.2 μm diameter wire as short as 1.3 cm, which could be considered the first short hot wire [20]. Recently, use of the short hot wire has been proposed for measurements in electrically conducting fluids under micro-gravity conditions, as a shorter wire can be more easily coated with an insulating layer [21]. Other uses are the determination of the thermal conductivity of polymers (50 μm in diameter and 10 mm in length) and nanofluids (20 μm in diameter and 14.5 mm in length) [3]. Both sensors, the needle sensor and the short hot wire, were used for the investigations presented here. Thus, polydimethylsiloxane as polymer with a known good miscibility with the solvent carbon dioxide has been chosen. PDMS in general are well-used substances to extend theoretical knowledge. In addition, applications like welding of immiscible polymers, impregnation purposes and drug release have been documented in literature [[22], [23], [24]]. The aim of this contribution was the development of an adequate method to measure the thermal conductivity of gas saturated, pressurised solutions, and appropriate auxiliary equipment was selected and implemented.

Section snippets

Materials

Linear polydimethylsiloxane (PDMS) (food grade) without cross-linking and with a molecular weight of 11000 g/mol was provided by Drawin (Ottobrunn/Riemerling, Germany) and used as received. The molecular weight and the polydispersity were measured by GPC analysis (Malvern Instruments, Worcestershire, United Kingdom). The analytic system was a Viscotek GPCmax equipped with a TDA 305 triple detector (refractive index, light scattering and viscosity). Absolute molecular weight was calculated using

Results and discussion

In this section, results of the thermal conductivity measurements of mixtures containing PDMS and CO2 are presented. Both developed sensors, the needle sensor and the short hot wire, were used. Apart from the original data measured with both sensors, a third set of data measured by the company Flucon, a manufacturer of high-precision measuring equipment, is shown [32]. These data were measured with a “Thermal conductivity system LAMBDA” using the same batch of PDMS under the same conditions, in

Summary and conclusions

Two different sensors, both based on the principle of a transiently heated linear source, were designed, tested and applied to different mixtures of PDMS with carbon dioxide under pressure. One of the sensors was a cylindrical needle probe with a length of 6 cm and a diameter of 1.27 mm, the other one was a short hot wire, made of 15 μm platinum wire with a length of 1.5 cm. The development of the set-up involved the selection and implementation of appropriate auxiliary equipment, especially a

Declarations of interest

None.

Acknowledgements

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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