Detection of mixing ratio of binary-mixture particles based on a principle of magnetic separation conducted in a microgravity area

A method to detect magnetic susceptibility χ of a single weak-magnetic (i.e. diamagnetic and paramagnetic) particle was recently proposed, and its efficiency was confirmed by observing the translation of the particle in an area of monotonically decreasing field that was located in an area of microgravity (μ).¹ Furthermore, separation and material identification of ordinary solid particles was realized in μ condition² as well as in terrestrial gravity condition³ using a small magnetic circuit composed of Nd-magnetic plates. Previously, field-induced dynamic motions were considered to occur only on substances that contain ferro- or ferri-magnetic moments, and ultra-strong field generators were required to induce such motion in the weak-magnetic materials (e.g., Maret, G. 1989;⁴ Rosen, H et al. 2005;⁵ Beaunion et al.⁶ 1991; Uyeda et al., 1991⁷).

Based on the abovementioned principle of magnetic separation and identification on weak magnetic solids, the χ values of binary-mixture particles were successfully measured; here the experiment was performed on particles composed of ice (Ih) and graphite.⁸ Mixing ratio f of the particles were estimated from its χ values without consuming sample particle. Solid particles that are collected in a field exploration (as well as in the process of material synthesis) are often composed of binary-mixture materials. For example, the icy particles of the Saturn rings were formerly considered to contain significant amount of rock-forming silicates. However, recent observations suggest that the solid particles are mainly composed of ice (Ih) with high purity.^9,10 Hence, for future missions orientated to the Saturn rings, a new method is required to speedily investigate the minor silicate compositions that are included in the abovementioned icy particles.

In the present report, we show that χ values of CO₂-graphite mixture particles are successfully measured by observing their field-induced translations at a reduced temperature condition of T= 195 K with various mixing ratios. Based on the experimental data obtained by the compact magnetic circuit, the merit of performing a quick analysis on the particle ensemble collected in various on-site missions is discussed.

In order to efficiently conduct the experiments of this study, the design of the apparatus used in a previous study^2,8 was reformed as follows. Firstly, the experimental setup was enclosed in a Pyrex insulating-container, and was filled with solid CO₂ blocks to maintain the experimental temperature at T=195 ± 1 K (see Fig. 1). The container was attached inside a drop box, together with a hi-vision camera (CASIO EX-F1) to observe the translation of samples from outside of the container. The camera could observe the motion of the samples by 0.033 fps from the [-y] direction of the figure with a spatial resolution of 0.004 cm. The relationships between sample velocity and field intensity in the translating area were determined from the sample images (see Fig. 2) taken by the hi-vision camera. The short μg-condition (duration< 0.5 s) required in the experiment was produced in a drop shaft with a height of 180 cm.^1,2,8

Secondly, field intensity and field gradient in the translating area was considerably increased to induce a smooth release of sample; the incensement was realized by introducing a new magnetic circuit composed of a pair of Nd magnetic plates. In a microgravity experiment, the release of a small particle in a diffuse area was often prevented by the various attractive forces between the samples and the sample stage, i.e. adhesions due to small contaminating particles as well as the Coulomb force caused by surface charges. Indeed, using the apparatus assembled in the previous studies, the experiment of field-induced translation was often prevented because the field-gradient force was not strong enough to promote a normal release of particles from sample holder. The sample pieces would be spontaneously released in the area of monotonically decreasing field by the enhanced repulsive force. The field center inside the gap of the magnetic plates was defined as the origin of the coordinates. Magnetic line of force was produced along the [+z]-axis, i.e. between the N pole and the S pole of the circuit.

The numerical data of the binary mixture samples composed of graphite and solid CO₂ are listed in Table I. Note that fraction f of graphite is different between individual samples. The graphite chips were cut from synthetic blocks with high purities (>99.99%); mass of the chip was measured by an electronic balance. Solid CO₂ block was separated into small sample pieces with diameters less than 1 mm, and the graphite chip was placed on top of the CO₂ piece which was maintained on an aluminum stage that was cooled at T= 196±1 K. Small amount of H₂O ice frost was collected by a thin bamboo spoon, and the frost was used as a binder to attach the graphite chip to the CO₂ piece.

The χ_DIA value (per unit mass) of the graphite block was examined by a vibrating sample magnetization (the VSM method), and the measured value was consistent with the published values. Graphite is known to have the largest absolute value of χ_DIA among popular solid materials, and its value is more than ten times larger compared to that of solid CO₂. According to a data book of diamagnetism,¹¹ most of published χ_DIA values of solid materials distribute between the above two values.

In analyzing the experimental results, we assume a diamagnetic particle with a susceptibility χ_DIA (per unit mass), which is quietly released in an area of static field that monotonically decreases along an x-axis.^1–3 Considering an conservation rule for a sum of kinetic energy and a magnetic potential, particle velocities and field intensities observed at two arbitrary positions x_i and x_j follow a relationship described as

where V_i and V_j denote particle velocities at positions x_i and x_j, respectively. The field intensities observed at x_i and x_j are described as B_i and B_j, respectively. By measuring many sets of [V_i, B_i] values in a single translation, the χ_DIA value of the particle is experimentally obtained from the gradient of a linear relationship between the sets of V_i² - V_j² and B_i² - B_j², which is deduced from eq. (1).

When a magnetic susceptibility χ_AB is experimentally obtained for a binary-mixture particle composed of two end members A and B, its fraction f_A of material A is simply calculated as⁸ 

where χ_A and χ_B denote the diamagnetic susceptibilities of the end members A and B, respectively. Accordingly, the value of f_A is uniquely determined by the experimental χ_AB value, in condition that published values of χ_A and χ_B are given; note that the experimental value of particle mass is unnecessary in obtaining f_A.

Time dependent photographs taken during the field-induced translation are shown in Fig. 2 for two pieces of CO₂-graphite mixtures with different f values. The images confirm that diamagnetic particles are easily accelerated by a field gradient produced by a small Nd magnetic circuit at a low temperature condition at about 200 K. The time-dependent visual data were obtained as well for the other samples that are listed in Table I. The numerical values of particle velocity and field intensity were determined from the sample positions recorded in the images. Accordingly, χ_AB of the particle is obtained by inserting the abovementioned values in eq. (1).

The relationship between χ_AB and f_A of the solid CO₂-graphite mixtures were experimentally obtained in the above manner, and the result is shown in Table I as well as in Fig. 3. The experimental data shown in solid circles in the figure are consistent with the theoretically expected relationship deduced from eq. (2) which is shown by a solid line in the figure. The errors of experimental χ values mainly derive from the uncertainty of the sample velocity obtained from the time dependent images, while the errors of f values originate from the ambiguity of sample sizes determined from the above-mentioned images. As is obvious from Fig. 3, the accuracy in determining the f value is not high enough to resolve the variance of the mixing rations required in a practical analysis, and further improvement of the measuring system is necessary.

The experimental results of Fig. 3 show that the energy conservation law described in eq. (1), assumed for the field-induced translation of weak magnetic particles in general, is effective at a reduced temperature condition of T∼200 K. The effectiveness is confirmed because the range of published χ_DIA values reported for weak magnetic materials; i.e. –1x10^-7 to −52x10^-7emu/g (Gupta¹¹ 1982), almost overlap with the observed χ values described in the figure. The effectiveness of the conservation law was previously confirmed only at room temperature (Hisayoshi et al.,² 2016, Uyeda et al.,³ 2019). Note that the majority of the solid particles observed in the outer solar system are volatile solids such as carbon mono-oxide, ethane, methane and nitrogen; their melting points range between T=100 K and 50 K. The setup shown in Fig. 1 provides a technical basis to examine the effectiveness of the energy conservation rule, because the experiments of field-induced translation are realized in these materials by changing the cooling medium from solid CO₂ to solid nitrogen. By conducting the abovementioned experiments, the conservation rule can be approved for most solids particles that exist in nature.

As mentioned before, the conventional analytical techniques adopted in on-site missions are not capable in speedily obtaining a histogram of f for binary-mixture particles. For example, in the case of an infrared spectrometer, it is difficult to detect the heterogeneous material buried inside the particles when diameter of the particle exceeds a sum-millimeter level. A mass spectrometer provides a more or less indirect data in obtaining the f value, because the method only provides the total elemental abundance of individual particles. Moreover, the particles included in the ensemble should be measured one by one to obtain the histogram, which requires a considerable time to complete the analysis.

For a future task, binary-mixture particles can be magnetically separated by the variance of χ_mix values by improving the setup shown in Fig. 1, and the histogram of f is directly obtained from the population of the separated particles. Note that the system is compact, rigid and easy to operate; also the time required for analysis is considerably short compared to the conventional analyzers. The improved system may provide a basis in designing an apparatus to analyze the volatile solid particles in various on-site missions.