14. Characterization of Heat Transport and Diffusion Processes During Metal Melt Filtration

In this chapter the experimental procedure to determine the bulk thermal conductivity (BTC) of pure alumina is explained and the main results are presented. The BTC was determined by measuring the thermal diffusivity α, the specific heat capacity c_p and the density ρ (\({\lambda }_{B}=\rho *\alpha *{c}_{p})\) in the range between 20 and 1500 °C. Corresponding to the sintering temperature, the used bulk alumina samples had a certain residual porosity. Since it was aimed to determine the BTC at 0% porosity, measurement results of five different sintering temperatures (1200–1750 °C, porosity ≈ 8–24%) were extrapolated at each measurement temperature. The processed data from [1] are shown in Fig. 14.1.

A scatterplot for the thermal conductivity of alumina versus temperature. The alumina samples are experimented on at different temperatures, ranging from 1200 degrees Celsius to 1750 degrees Celsius. A decreasing trend is plotted for all samples.

The BTC of pure alumina strongly decreases with increasing temperature from >30 W/(mK) at 20 °C to approx. 5 W/(mK) at 1500 °C which agrees well with several literature values. The results were applied for the determination of the ETC of alumina open-cell foams, commonly used as high-temperature insulating materials, catalyst carriers or in the foundry for metal melt filtration, using two-phase models.

As for the industry, carbon-bonded alumina refractories are very promising materials, their thermophysical properties were intensively investigated in Goetze et al. 2013 [2]. Besides the density and the porosity, the thermal expansion, the thermal diffusivity as well as the specific heat capacity for temperatures up to 800 °C were measured. Samples were produced either by isostatic pressing, uniaxial pressing or slip casting. Furthermore, the content of the coal-tar resin Carbores^®P (binding agent) was varied (10, 15, 20%) keeping the general composition (approx. 66% alumina and 34% carbon) nearly constant by adding a corresponding amount of two further carbon modifications (carbon black powder, graphite). The bulk thermal conductivity was calculated as for the alumina samples before. Since the microstructure of the material is affected by the composition as well as by the manufacturing process, an effect of these parameters on several thermophysical properties was detected.

The technical coefficient of thermal expansion α_techn generally increases with increasing temperature because of the increasing lattice energy and distance between the atoms. As expected, lower thermal expansion coefficients than for pure alumina were measured. Since the thermal expansion strongly depends on the carbon modification used, differences in the curves of α_techn between the different contents of the Carbores^®P can be seen and, similarly, the manufacturing procedure also influences the expansion. The specific heat capacity of the carbon-bonded alumina increases with increasing temperature due to enhanced lattice vibrations. The carbon composition or the manufacturing procedure does not significantly affect the measurement results, since heat capacity mainly depends on the chemical composition than on the microstructure. Finally, as expected for solid, crystalline ceramic materials, it was found that the thermal conductivity decreases with increasing temperature. Lower thermal conductivity occurred for higher binding content of Carbores^®P traced back to the microstructure and the smaller grain size of the carbon particles. Furthermore, an influence of the manufacturing process as well as an anisotropic behavior for the uniaxial pressed samples were found.

The TPS technique proposed by Gustafsson 1991 [3] is a transient measurement method to determine simultaneously the thermal conductivity λ, the thermal diffusivity a and the specific heat capacity c_p. The advantages of this measurement method are mentioned to be the large variety of materials (solid as bulk or thin film, liquid, paste, porous/granular) as well as the wide range of thermal conductivity (0.005–500 W/(mK)) that can be measured, the variable sample size and form and low effort for sample preparation [4, 5].

The sensor consists of an insulated bifilar nickel spiral acting as a heater and a temperature sensor (in form of a resistance thermometer) at the same time. [3‐6] The measurements presented below were performed with a Hot Disk TPS 2500 S from the company HotDisk AB. Depending on the temperature range to be investigated sensors with Kapton (RT-250 °C) or Mica (200–750 °C) insulation are used. Furthermore, different sensor diameters (1–59 mm) are available, which are selected according to the structure and thermal conductivity of the sample. The measured, time-dependent resistance change \(R\left(t\right)\) at the sensor can be described by Eq. (14.1) [3‐6].

A key parameter is the Temperature Coefficient of Resistance (TCR), which is further investigated in the context of high-temperature measurements. To deduce the thermal properties, the experimentally determined temperature increase \(\Delta T\left(\tau \right)\) is compared with the approximate numerical solution for the temperature increase of a ring source (Eq. (14.2)) [3‐6].

Further, detailed information on the measurement principle can be found in Gustafsson 1991 [3] or He 2005 [4].

The applicability and conditions of application of the TPS method for ceramic open-cell foams at room temperature were intensively investigated by Goetze et al. [7] studying the influence of several key parameters on the ETC. Numerous measurements with pure alumina foams of different pore sizes (10–60 ppi (pores per inch)) using Kapton-insulated sensors with varying sensor sizes were performed. Most importantly, it was found that an appropriate surface preparation, i.e., increasing the contact area between the foam and the sensor by grinding and polishing the samples is inevitable to obtain trustworthy, reproducible data. However, this might a challenging task because of easily breaking struts of the foams with smaller pore sizes. Furthermore, the influence of the measurement time, the heating power and the mechanical load have been found to be as negligible as the anisotropy studied on 10 and 30 ppi foams with vertically and horizontally oriented cells, since differences were only within the measurement uncertainty. Concerning the sensor size, the sensor diameter should be commonly 10 times larger than the mean cell size. With an appropriate sensor (d = 59 mm) for 10 ppi foams, it was not possible to set measurement parameters in order to reach an acceptable characteristic time and penetration depth at the same time due to the relatively high thermal diffusivity of the samples. To achieve reliable measurement results with this sensor by reaching a higher penetrations depth, an elongated sensor connection in combination with bigger samples would be necessary. Measuring 10 and 60 ppi foams the most reliable results were each obtained with a sensor of d = 29 mm. An even smaller sensor (d = 13 mm) leads to higher scattering of measured values.

Additional measurements were performed with commercial alumina foams (10–50 ppi) of adequate sample size using the same three sensor diameters, however, partially with an elongated connection brought to market by the manufacturer in the meantime to ensure sufficient penetration depth. Comparing the standard deviations, it was found that the sensor with d = 30 mm leads to acceptable results while strongly reducing the required sample dimensions from approx. 180 × 180 × 60 mm³ to 90 × 90 × 30 mm³ in contrast to the bigger sensor with d = 59 mm. An even smaller sensor would strongly increase measurement uncertainty. For foams ≥30 ppi sensors with d = 12 mm or d = 30 mm can be recommended.

Investigating the performance of the TPS method at temperatures up to 750 °C, Goetze et al. [8] found deviations up to 35% between the reference values [9] and the measured effective thermal conductivity of the material Silcal 1100 with an increasing deviation with increasing temperature. Particular high deviations were found around the Nickel Curie temperature, why the range between 350 and 420 °C is excluded from the measurements by the manufacturer.

Numerical simulations indicated that an inhomogeneous temperature field in the furnace does not affect the temperature rise in the sensor and is therefore not responsible for the observed deviations. In contrast, a redefinition of the TCR nearly directly influencing the thermal conductivity has led to a significant reduction of the deviations. A new set of TCR based on measurements with three different materials (Silcal 1100, OM 100 and stainless steel 1.4841) in the range of 20–750 °C was suggested by Goetze et al. [8] by recording the resistance and temperature for different sensor insulations and designs. As a result, deviations from the reference values with the material Silcal 1100 were reduced to ±7%, except in a narrow range around the Nickel Curie temperature.

Further investigations were performed to confirm the TCR proposed by Goetze et al. [8] in comparison to manufacturer values, to enhance the accuracy of high-temperature measurements and to investigate the TCR around the Curie point more in detail. Measurements with four different reference materials (Silcal 1100, Pyroceram, Inconel 600 and Stainless Steel 304) were used to further improve the TCR, achieving deviations from the respective references of max. 6%, mainly below 4% for all four reference materials. By adding additional values, the TCR curve, particularly in the Curie range, was refined. However, a determination of the thermal conductivity at temperatures between 370 °C and 380 °C should be still excluded since deviations in this range strongly increase due to the strong temperature-dependent TCR and a required very accurate temperature measurement in the sample. Figure 14.2 summarizes the original TCR given by the manufacturer in comparison to the values modified by Goetze et al. [8] and the newly optimized TCR.

A line graph of T C R versus temperature in Celsius for the original manufacturer, Goetze e t a l 2017 and optimized. A decreasing trend is plotted for all the lines.

With the corrected TCR, measurements with several alumina open-cell foams of different porosities and pore sizes (Fig. 14.3a) and with 10 ppi ceramic open-cell foams made of different materials (Fig. 14.3b) in the temperature range between 25 and 700 °C were conducted. With increasing porosity (65–90%), the effective thermal conductivity of the alumina foams strongly decreases, especially for temperatures <400 °C due to the reduction of solid mass fraction and the conductive heat transfer. While for foams with a porosity of 65 and 80% the thermal conductivity decreases continuously with increasing temperature, at higher porosity (90%).

2 dashed line graphs. A. A line graph of thermal conductivity versus temperature in Celsius for different porosities and pore p p i. A decreasing trend is plotted for all porosities and pore p p i. B. A line graph of thermal conductivity versus temperature in Celsius for alumina, non pore, alumina, pure, carbon based alumina, zirconia, and silicon carbide. All lines illustrate an increasing trend.

A minimum in thermal conductivity around 300–400 °C is formed because of the higher void ratio and the resulting increased radiative heat transfer with increasing temperature. The pore size or ppi number has a lower impact on the ETC, both, at room temperature and at higher temperatures. With increasing pore size (decreasing ppi) the thermal conductivity at higher temperatures slightly increases because of increasing radiative heat transfer in the bigger pores. Furthermore, the observed minimum (around 300–400 °C with 10 ppi) shifts to higher temperatures with decreasing pore size.

Besides the porosity, the material of the open-cell foam can significantly affect its thermal conductivity. In contrast to the 10 ppi pure alumina foams, the solid thermal conductivity of the base material of all other investigated foams (carbon-bonded alumina, zirconia, silicon carbide, non-pure alumina) material increases with temperature, hence, the curves do not show a minimum of the thermal conductivity.

In addition to the experimental determination, a model-based description of the heat transport processes in the foams to numerically calculate the ETC was performed in cooperation with subproject B02 of the CRC 920. The main results are summarized by Mendes et al. [10] by comparing TPS measurements of alumina open-cell foams (10 ppi, porosity 89%) with a numerical 1D homogeneous model considering coupled conductive and radiative heat transfer. Previously the applicability of this model was confirmed by Mendes et al. [11] by comparing different detailed, 3D heterogeneous and simplified, 1D homogeneous models to determine the ETC at high temperatures. It was shown that the homogeneous models can yield errors of less than 10% with strongly reduced computational time and effort. Further validation was demonstrated in Mendes et al. [12] using open-cell metal foams.

To describe the geometry of the foams, 3D CT scans were carried out, which on the one hand enabled an exact structural characterization and on the other hand, after binarization, directly served to create the geometric model for the simulation. Important model parameters, such as the proportion of pure heat conduction through solid and gas phase and the extinction coefficient β were derived from the 3D CT scans. The simplified model is based on the homogenization approach considering a coupled conductive and radiative heat transfer. The 1D steady-state energy conservation equation including radiation as a source term is solved using the finite volume method [10].

The results show the potential of a precise prediction of the ETC only with geometric parameters obtained from the structural characterization of the foams using the 3D CT scans. A major advantage of modeling the heat transfer is that the influence of individual parameters can be analyzed with little effort. It was shown that the samples exhibited a certain anisotropy and, in addition to known influencing variables (such as total porosity and temperature), the microporosity in the struts not captured by the 3D CT scans also plays an important role. Taking the anisotropy of the foams into account the TPS measurements at temperatures up to 750 °C revealed good agreement with the simulations. The measured ETC can be interpreted as an averaged thermal conductivity of the room directions obtained from the simulation [10].

As a basis for the experimental determination of the radiative properties, measurements of hemispherical transmission and reflection were performed with a Bruker Vertex 80v FTIR spectrometer (Fig. 14.4). Since the filters are highly inhomogeneous and normally used sample sizes would not produce representative measurement results, the FTIR spectrometer is equipped with an external integrating sphere (Fig. 14.4) with an inner diameter of 150 mm allowing it to cover a measurement area of about 25 mm. Measurements were performed in the Near-Infrared (NIR, λ ≈ 0.9–2.4 µm) and the Mid-Infrared (MIR, λ ≈ 2.0–16 µm) on different commercial filters used for metal melt filtration and made of alumina (Al₂O₃, 10 and 20 ppi), zirconia (ZrO₂), silicon carbide (SiC) or carbon-bonded alumina (Al₂O₃-C, each 10 ppi). Further information on the measurement parameters and samples can be found in Heisig et al. [13].

A photograph of the F T I R spectrometer Bruker Vertex. The device is kept in a glass box.

The radiative behavior (transmission, reflection, absorption) as well as the experimentally determined spectral and Rosseland mean extinction coefficients of several ceramic open-cell foams are presented in detail by Heisig et al. [13]. Besides an influence of the ppi value, significant differences in the radiative behavior between light, oxidized ceramics (Al₂O₃, ZrO₂) and dark, carbon-containing materials (SiC, Al₂O₃-C) were demonstrated (see Fig. 14.5).

2 line graphs of transmittance and reflectance versus wavelength for A L 2 O 3 10 P P I, A L 2 O 3 20 P P I, Z R O 2 10 P P I, and S I C 10 P P I. Both line graphs illustrate a decreasing trend.

There are several approaches and methods to determine the radiative properties of porous media which can be either experimentally or numerically based. Furthermore, lots of empirical correlations are proposed in the literature mainly predicting the extinction coefficient.

A simple and often applied way to experimentally determine the extinction coefficient is using Bouguer’s Law. Assuming a homogeneous medium only absorbing or scattering radiation isotropically, the spectral extinction coefficient can be derived only from the measured transmittance and the sample thickness. For comparison and practical application, the wavelength-independent Rosseland mean extinction coefficient averaging the weighted spectral extinction according to Planck's radiation distribution over the relevant wavelength spectrum is commonly used [14]. Besides Bouguer’s Law, the inverse parameter identification technique allows to determine radiative properties of the foams by solving the complete radiative transfer equation (RTE), thus considering also non-isotropic scattering. The comparison of simplified methods determining the extinction coefficient of open-cell foams in contrast to the parameter identification method will be a topic of future investigations.

In the practical application, empirical correlations are often applied, as a fast and simple method to estimate the radiative properties, especially the extinction coefficient avoiding elaborative measurements or numerical simulations. The accuracy and reliability of several predictive correlations were investigated and compared in Heisig et al. [13]. The best agreement with the previously experimentally determined extinction coefficients was achieved with correlations given by Hendricks and Howell [15] as well as Li et al. [16] with a mean deviation of 10 or 16%. Several other considered models lead to significantly higher average deviations up to 43%, since they might be based on limited data and, hence, not universally applicable to all types of ceramic foams. Furthermore, comparing deviations between the different filter materials of all investigated models a significant influence of the specific filter material or certain structural characteristics of the filter type on the extinction coefficient has been detected, not considered in the models so far and further to be investigated. Finally, another disadvantage of the empirical correlations is that in general a wavelength or temperature dependency of the radiative behavior as it occurs for example with the semi-transparent Al₂O₃ foams is not respected in the models.

Besides empirical correlations an image superposition technique proposed by Loretz et al. [17] referred to as projection method in the following offers a simple, fast and more accurate determination of the extinction coefficient. The method is based on Bouguer’s Law as well, however, instead of measurements the transmittance is obtained by processing the images of a 3D micro-computed tomography scan of the foam. The superposition method is also applied by Mendes et al. [10, 11]. Deviations from the experimentally determined extinction coefficients are limited to 18% (12% on average). The extinction coefficient is generally overpredicted, since, in contrast to the measurements, forward scattered radiation is not taken as transmission. Quite constant deviations of each filter material indicate that respecting the definite filter structure with the certain geometric characteristics of the different filter materials by using 3D tomography scans leads to strongly reduced deviations. However, a disadvantage is like with the empirical models, that opaque foams are assumed, i.e. the wavelength dependency of Al₂O₃ or ZrO₂ foams at higher temperatures is not considered.

In Mendes et al. [11] the radiative part of the steady-state heat flux in the foams, in addition to the conductive part, is calculated either by solving the complete RTE using the discrete transfer method or by simply applying Rossel and diffusion approximation. This approximation is quite commonly used in the context of open-cell foams. Quite accurate results for the ETC (deviation to detailed model considered as reference: <6%) can be received using the simplified models including radiative heat transfer solved without the approximation. In contrast, using Rosseland approximation leads to an overprediction of the ETC of 15–23%, possibly because the assumption of optically thick media (optical thickness >10) is either not or only just achieved for the investigated open-cell foams. In Mendes et al. [10], only the more accurate, simplified model solving the RTE is used. Nevertheless, the very easily applicable Rosseland approximation can serve as a rough estimation of the radiative transfer and is especially attractive since only the extinction coefficient is needed as a radiative property.

Besides the extinction coefficient two further radiative properties, namely the scattering coefficient or scattering albedo and the scattering phase function are required for solving the RTE, determined in Mendes et al. [10, 11] from suitable approximations: The scattering albedo ω was set equal to the reflectivity of the foam and the phase function was assumed to be the one for large diffuse spheres. The extinction coefficient into different directions was determined by applying the previously mentioned projection method. A strong decrease of the extinction coefficient for foam thicknesses with less than one mean pore diameter was observed, why this range was excluded from the evaluation in Mendes et al. [10]. Over the remaining sample thickness, β_av, β_min and β_max were determined, whereas it was found that results for the ETC fits best using β_max. In addition, as mentioned before, a combination of different spectroscopic measurements and the parameter identification method would offer a possibility to experimentally determine all the three radiative properties.

Since Vijay et al. [19] found that when performing steady-state experiments thermal dispersion cannot be neglected and the dispersion conductivity k_d is in addition to h_v a second unknown parameter. Therefore, transient experiments using the single-blow method presented in Vijay et al. [18] should serve to determine h_v separately in advance. In a self-built wind tunnel, an air stream provided by a side channel blower was heated by a coil heater and passed through a flow straightener before streaming through an insulated section with the inserted foam. Furthermore, the measurement section is equipped with a thermal mass flow sensor as well as nine thermocouples at the inlet and outlet of the foam. After having a steady-state isothermal flow field in the test section, the inlet temperature was increased to the target temperature and recorded together with the outlet temperature for 20–60 s until thermal equilibrium was nearly reached.

Concerning the numerical evaluation, first, the flow field was determined using a modified Darcy-Forchheimer-Brinkman equation. Subsequently, the 1D energy equations (local thermal non-equilibrium) were solved using a simple implicit scheme. By calculating the instantaneous energy terms of each type of heat transfer in relation to the convection, it was shown that with transient experiments simplifications like neglecting dispersion lead to an error of less than 5%. This proved that the interstitial convection is the dominant mode of heat transfer and neglecting dispersion is permissible. Finally, h_v in dependence of the inlet superficial velocity was presented and compared to the literature for verification of the determined values. For increasing inlet superficial velocities from 1 to 10 m/s h_v increases from ≈7 to 22 W/(m³K) for the 10 ppi foam and from ≈16 to 51 W/(m³K) for the 30 ppi foam. It can be concluded from the results that smaller pore size (higher ppi number) as well as lower porosity leads to an increased h_v. Partially good agreement with literature values as well as reasons for inconsistencies were given.

In general, the experiments with a metal melt are to be carried out in the same way, also using the single-blow method, but with an appropriate adjustment of the experimental setup and the evaluation. A first attempt to create a suitable test rig was presented by Goetze et al. [20]. Using gravity casting the measurement section is a sand mold in which the aluminum is first redirected to flow through the inserted commercial alumina filters from bottom to top to achieve a more stable fluid flow. Between the filter mineral-insulated thermocouples are placed. A cast of the measurement section is shown in Fig. 14.6a.

2 illustrations. A. A photograph of a measurement set up for gravity casting has the following labeled parts. Melt inlet, 5 filters, and thermocouple. B. An illustration of an improved measurement section with 3 filters and steel pipe with insulation labeled.

A rough estimation of the average h_v was given and an average Nu-Re-Correlation was set up using the overall energy balance and assuming the whole process as a set of quasi-steady-state processes. Furthermore, several other, not realistic assumptions like adiabatic walls of the sand mold and hence, a 1D heat transfer, had to be made. For 10 and 30 ppi alumina filters with an achieved fluid velocity of 0.06–0.09 m/s (Re ≈ 500…1200) average h_v between 780 and 2371 W/(m³K) and average Nu between 0.85 and 2.37 were calculated. It was concluded that Nu increases with increasing flow velocity and with increasing ppi.

Since with the performed measurements, several problems and inaccuracies, like the varying pouring temperature, the melt flow rate that is not constant or adjustable or the low date acquisition rate appeared, general improvements and modifications in the design of the test section were made. Instead of performing gravity casting with a sand mold a steel pipe (see Fig. 14.6b) is placed on a low-pressure furnace, which enables to achieve a more constant casting temperature, a targeted adjustment of the melt velocity via the pressure and a uniform oncoming flow to the filters. Furthermore, the data acquisition rate can theoretically reach 10.000 Hz. Besides the thermocouples, an additional measurement of the melt velocity via an anode–cathode reaction was implemented. Furthermore, to estimate the heat losses of the measurement section as well as the flow profile, before and behind each filter three thermocouples with different distances to the edge were placed. The typical temperature curves at these measurement points are shown in Fig. 14.7 and the position of each thermocouple (TC) can be found in Fig. 14.6b.

A dashed line graph of temperature in Celsius versus time in m s for several aluminum experiments illustrates a sharp increasing trend before stabilizing and fluctuating.

In contrast to the previous evaluation of the measurement data, a more detailed simulation should serve to determine h_v. Since preliminary calculations have shown that the heat losses through the test section to the ambient have a considerable influence on the results, a 2D evaluation of the experiments, i.e. taking into account the radial heat transfer, is aimed. For conductive heat transport, the previously measured, temperature-dependent ETC is used (see Sect. 14.2.3). Using the same 10 and 30 ppi foams as with previous experiments, the first simplified simulations suggest h_v of 10⁴ to 4·10⁵ W/(m³K) and Nu of 0.5–16, which is significantly higher than the values obtained by Goetze et al. [20]. However, the same dependencies were found: With increasing velocity (Re), Nu increases. Furthermore, Re using the 10 ppi samples (Re ≈ 525–790) are clearly higher because of increased permeability compared to the 30 ppi filters (Re ≈ 180–490).

For the experimental determination of hydrogen solubility in aluminum melts, various measurement devices based on indirect or volumetric measuring methods were developed from 1922 until the end of the 1990s. For the volumetric measuring methods, quantities such as the measurement cell volume, dead volume and sample respectively melt volume have to be determined in advance to be able to infer the dissolved hydrogen quantity from the resulting pressure at constant volume or volume change at constant pressure. Most of the reported values of hydrogen solubility in liquid pure aluminum have been determined according to this measurement principle, in particular by means of the so-called “Sieverts’ direct absorption method” [23]. Other techniques obtain solubility data from isothermal degassing processes of hydrogen-saturated samples or by measuring the gas content of previously solidified samples. Here, besides the possible loss of gas, the sudden change in hydrogen solubility during the liquidus-solidus transition must also be taken into account.

In general, the indirect determination of solubility data from the previously mentioned measured quantities is associated with numerous sources of error. This causes, together with further uncertainties of the respective method, widely diverging results in the literature [24]. Even at the melting temperature and a hydrogen pressure of 1 atm reported hydrogen solubility in liquid pure aluminum ranges from 0.43 cm³/100 g [22] to 0.918 cm³/100 g [21], with discrepancies increasing with increasing temperatures. This in turn leads to significant discrepancies in the results of mathematical models and calculations on melt treatment processes and porosity formation in aluminum products [23].

A very precise measurement principle for sorption investigations, in particular for long equilibrium times, is the gravimetric one, but up to now, this has not been used for the determination of gas solubility in metal melts. A reason for this is certainly that the measuring accuracy of balances in the middle of the twentieth century, when the majority of the experimental investigations were carried out, was comparatively low and thus the small mass of dissolved hydrogen was hardly detectable gravimetrically. Meanwhile, there has been significant progress in the field of weighing technology. Between 1965 and 1995, highly sensitive balances with electromagnetic force compensation were developed for commercial distribution. Using these, the first gravimetric measurements of gas adsorption were already possible for non-corrosive gases at pressures up to a maximum of 15 MPa, but only at temperatures below 175 °C [25]. In order to extend the application range and protect highly sensitive components, a technology was then developed that completely decouples the balance mechanically from the measurement cell. For this purpose, the sample load is transmitted from the measurement cell to an analytical balance placed under ambient conditions by means of a magnetic suspension system. In the sorption analysis, the use of these so-called magnetic suspension balances (MSB) is now well established for precise investigations under demanding conditions and hence intended to be applied to the measurement issue within the collaborative research center. Due to the direct recording of the sorption-related mass changes with the aid of a high-precision microbalance, the main sources of error and uncertainties of the previously used methods are avoided.

Since at the beginning of the subproject no commercial sorption analyzer with MSB was available for the required temperature range, it was decided to use the thermogravimetric system DynTherm MP-HTIII (instrument type: TGA510), hereafter referred to as TGA, from TA Instruments. The TGA was modified according to the requirements of the measurement task and the instrumental setup was extended by the necessary systems for measurement and control. The adaptations include various aspects such as data acquisition, gas dosing and pressure control, the development of appropriate sample containers and sample preparation, as well as the minimization of environmental influences and explosion protection measures.

In the following, the basic principle of MSB is explained and the technical specifications of the apparatus used are described. For clarification, the schematic structure of the main device is shown in Fig. 14.8.

An illustration of the construction of the applied magnetic suspension balance T G A has the following parts labeled. Electromagnet, permanent magnet, coupling housing, gas inlet, sensor coil, sensor core, water cooled casing, gas outlet, and others.

An electromagnet is mounted on the under-floor weighing attachment of the microbalance. This keeps the permanent magnet located in the upper area of the magnetically neutral coupling housing in a suspended state via a corresponding control device [26]. The permanent magnet is in turn connected to the sample container via a two-part rod. On the upper part of the linkage, between the permanent magnet and the measuring load coupling, there is a sensor core whose vertical position is measured via the inductance of an externally mounted sensor coil. Using a PID controller, the current applied to the electromagnet is adjusted to keep the position of the permanent magnet stable [27]. In this way, the weight force of the sample is transmitted contactlessly to the microbalance in the form of the required magnetic force. In addition, the position of the permanent magnet can be varied with the aid of a superimposed set point controller. This makes it possible to temporarily decouple the measuring load consisting of the sample in the sample container and the lower part of the linkage, which represents the zero point position [27]. In order to record the zero drift of the balance, the permanent magnet is periodically moved from the measuring point position to the zero point position while the measurement is in progress.

Besides the advantages of a magnetic suspension balance resulting from the separation of the measurement cell and the weighing instrument, the temperature control system is of particular importance for the measurement task. It has to thermally decouple the magnetic coupling from the measurement cell and at the same time ensure a precise control of the sample temperature. To achieve this, an electrical high-temperature heating element allows sample temperatures of 50 °C up to 1650 °C to be realized and kept constant inside the Al₂O₃ measurement cell. On the outside, the measurement cell has a thermal insulation and a water-cooled casing, so that heat losses to the environment are minimized and a precise regulation of the furnace temperature with defined cooling rates is ensured. The tempering of the magnetic suspension coupling is carried out separately via a liquid-tempered double casing, since in the area of the magnetic force transmission temperatures of max. 258 °C may occur and temperature constancy is of enormous importance.

As the accuracy of the recorded weight contributes significantly to the quality of the measurement results, the TGA was combined with the 66S high-load microbalance of the Sartorius Cubis series, with a resolution of 0.001 mg. In addition, a computer-controlled gas dosing and pressure control unit (GDU) ensures precise pressure regulation and exact reproducibility of the conditions in the measurement cell. As Fig. 14.8 shows, the measurement apparatus has a separate gas inlet and outlet so that a dynamic pressure control can be implemented. By continuously supplying a defined gas flow rate (using thermal mass flow controllers) and regulating the desired pressure in the measurement cell, the conditions remain consistent throughout the entire measurement duration. Whereas with the previously used measurement methods already the loss of the slightest amount of hydrogen due to leakage or diffusion from the individual measurement apparatus led in some cases to significant errors in the calculated hydrogen solubilities, this does not affect the measurement accuracy of the new measurement apparatus.

Figure 14.9 illustrates the experimental setup, including gas dosing, magnetic suspension and furnace, as well as several other components to ensure the proper functioning and control of the measurement apparatus.

An illustration of a set up with 12 labeled components. Some of the components are the argon cylinder, hydrogen cylinder, vacuum pump, magnetic suspension coupling, recirculating chiller, gas dosing, and others.

The presented measurement apparatus enables fully automated long-term measurements in the pressure range of medium vacuum to a maximum of 160 kPa. Besides the time-resolved recording of temperature, pressure and sample weight in a controlled atmosphere, the zero drift of the balance is also recorded for an appropriate correction of the measurement data. This significantly increases the accuracy of the data. The electronic and controller rack ensures that the different positions of the permanent magnet are alternated periodically and that the temperature is regulated according to the previously generated temperature profile during measurements.

Depending on the target value, different sample containers, also called crucibles, are used to investigate the maximum gas solubility and diffusion coefficients of dissolved gases in metal melts. Since the crucibles are manufactured entirely from high-purity alumina (99.9%) using the additive LCM method, they are suitable for measurement temperatures of up to 1650 °C. This enables a wide measuring range for the determination of temperature-dependent sorption properties so that in addition to aluminum melts, molten iron alloys can also be investigated later on.

The crucibles are gas-impermeable, so only the top layer of the melt is accessible to the sorptive gas. In accordance with this, a high ratio of free surface to volume of the metal melt is required for the investigation of the maximum solubility to minimize the measurement time. A sample container system of four flat crucibles stacked above one another at defined distances was developed aiming to increase the sample quantity measured at the same time and thus the measurement sensitivity. Figure 14.10a shows a model of the developed multi-layer sample crucible and Fig. 14.10b illustrates the mounted condition on the measuring apparatus with a photo.

3 illustrations. A. An illustration of a multi layer crucible model for the measurement of gases. B. A photograph of a multi layer crucible, along with a measuring apparatus. C. A 3 D illustration of a bucket like container.

Besides the maximum solubility, the kinetics of the sorption processes are of interest. On the basis of time-resolved measurement data, the diffusion coefficients can be determined by the defined reference plane in the form of the melt’s free surface. For this task, a crucible of a larger volume (see Fig. 14.10c) is chosen, so that effects occurring at the surface only influence the kinetics immediately at the beginning. As for liquids, interfacial reactions characteristically proceed faster than the diffusive mass transport of gases in the liquid [28], this method allows the determination of the binary diffusion coefficient.

Aluminum with a purity of 99.999% is used for the investigations so that any influence of alloying elements or impurities is excluded. To determine the maximum solubility, samples with a diameter of 11 mm and a mass of about 1 g are contained by each crucible.

All measurements are performed under defined atmospheres using high purity gases (≥99,999%). Prior to the start of each experiment, the measurement apparatus is evacuated three times and purged with inert gas. Here, argon is chosen as inert and reference gas, since Liu et al. [24] proved helium to be soluble in liquid aluminum. The samples are heated under vacuum or argon atmosphere with a heating rate of 5 K/min from ambient temperature to the desired measurement temperature. Then the atmosphere intended for the investigation as well as the gas flow conditions are set and the sorption measurement itself begins. Afterwards, the recorded data are corrected by baseline subtraction.

Due to the high affinity of molten aluminum to oxygen, the intended measurements on maximum solubility and for determining the diffusion coefficients of hydrogen in aluminum melt had to be deferred. Initial measurements with high-purity aluminum showed an increase in mass when reaching the liquidus temperature, which is attributed to the formation of an oxide layer. A significant impact of the sample temperature was observed, resulting in an increasing mass change ratio with increasing temperature (especially at the beginning of measurements). In contrast, whether the oxide layer formed at ambient conditions was removed or not prior the measurement did not show any significant effect.

These observations revealed the necessity of a lower partial pressure in the vacuum as well as the removal of the oxygen impurities (≤2 ppm mass fraction) from the 5.0 gases used with the aid of special purification cartridges. In this context, the piping system and the sealing of the regularly loosened connections on the furnace were also optimized. Furthermore, a larger inert gas flow rate should ensure that even the slightest oxygen ingress diffusing through existing connections is avoided or removed quickly. If oxide layer formation should occur nevertheless, an O₂-trap based on a material with an even higher affinity to oxygen than aluminum might be installed.

The characteristically slow diffusion in liquids, and thus also in melts, often limits the overall rate of the occurring processes [28]. Hence, it is assumed that the rate of hydrogen dissolution is also limited by diffusion. This enables the study of diffusive mass transport of gases in metal melts based on the kinetics of sorption processes. A mass diffusion model commonly used in the literature for the diffusion of gases in liquids [29‐32] is applied to estimate effective diffusion coefficients for the system hydrogen-aluminum melt on the basis of time-dependent solubility data. Moya et al. [32] even used this model for the estimation of diffusion coefficients out of gravimetrically obtained absorption kinetic curves (of CO₂ in ionic liquids).

In the present work, the mathematical description of the diffusion process is based on the following conditions:

Since the diffusive mass transport j of the hydrogen in the melt is a one-dimensional diffusion process without convection in the same direction, the hydrogen concentration c at position z in the liquid aluminum can be described using Fick's law [28, 34].

Assuming a constant diffusion coefficient D and a constant cross-sectional area over which diffusion occurs, the process can be described using the basic Eq. (14.4) for transient diffusion processes, also referred to as Fick's 2nd law [28, 35].

At the beginning of the measurement, no hydrogen is dissolved in the melt and thus, the entire melt volume has the uniform hydrogen concentration \({c}_{0}\). While this changes over the measurement duration, the hydrogen concentration \({c}_{l}\) at the surface of the melt (z = l) is constant. These results in the following initial and boundary conditions for the gravimetric investigation method applied [30, 31]:

Under the prevailing conditions, Crank [35] specifies the analytical solution for Eq. (14.4) depending on the filling level l of the crucible as follows (Eq. (14.5)):

The equation sets the total amount \({M}_{t}\) of diffusing gas present in the melt at time t in relation to the corresponding amount \({M}_{\infty }\) after infinite time, representing the maximum solubility. According to Crank [35], the solution Eq. (14.5) is accurate to four significant digits for desorption in the range \(\frac{{M}_{t}}{{M}_{\infty }}<\frac{2}{3}\). In addition, the analytical solution (Eq. (14.5)) can be solved graphically for \(\frac{Dt}{{l}^{2}}\) by appropriate representation based on the relative mass change \(\frac{{M}_{t}}{{M}_{\infty }}\) as a function of sorption time t, and thus the diffusion coefficient can be determined out of the gradient of the plotted sorption data [35].