The aerodynamic levitation system consists of an aerodynamic levitator, a gas flow controller (KOFLOC EX250SC), and a 2D optical micrometer (Keyence TM-3000). Located in the center of the levitator is a conical converging-diverging nozzle to levitate a sample sphere of 2–3 mm in diameter. The argon gas stored in a high-pressure gas tank is depressurized to about 200 KPa and reaches the nozzle for sample levitation. The gas flow controller enables fine regulations of argon gas flowrate. To monitor and improve the sample levitation stability, a 2D optical micrometer is placed on the horizontal side of the sample sphere to measure the levitation height. The argon gas flowrate can be accordingly adjusted to improve the stability.

The laser heating system consists of two CO₂ laser devices (Synrad ti-100HS) and their laser-beam delivery optics. The two 100 W CO₂ laser devices controlled by a laser controller (Synrad UC 2000) are placed as such that they heat both the lower and the upper sides of the sample (see Figure 1). Each device emits a laser beam with a wavelength of 10.6 μm and a diameter of 2 mm. Two laser beams are guided to the sample via flat mirrors and focusing lenses. Since the lower laser beam passes through the gas channel, a ZnSe window transparent to the 10.6 μm laser beam is installed under the levitator.

High stability (2%) of the laser output power is necessary to the fine temperature regulations, and the heating efficiency is as high as practically achievable. The laser beam with the wavelength of 10.6 μm is favorable to absorption of oxidic materials. Two waveplates are inserted into the optical paths to convert linearly polarized beams into circularly polarized beams.

The image recording system consists of a high-speed camera (Phantom VEO440L), a zoom lens (Movetem MAZ12.0×LZ), a backlighting laser (CNI MGL-III-532) and a narrow-band filter. The high-speed camera equipped with the zoom lens has a magnification of 14 and a working distance of 85 mm, which makes full use of camera pixels.

The backlighting laser is employed in a shadow photography system in which the backlighting laser with a beam expander is positioned on the opposite side of the high-speed camera with the narrow-band filter installed in front of the camera lens. The shutter speed of the camera is therefore independent of temperature of the sample, and sharp edges of the sample can be obtained from the images.

Since the shadow photography system has not been ready yet, the present study uses conventional photography in which the direct images of the incandescent sample at high temperatures are recorded. The higher the temperature, the brighter the sample. This means the shutter speed of the camera has to be adjusted to obtain reasonable images at different temperatures.

The sample temperature is measured with two bichromatic pyrometers (Sensortherm H311), one with the measuring range of 1173–2073 K (0.75–0.93 μm and 0.93–1.1 μm), and the other 1873–3573 K (0.78 and 0.99 μm) with the measurement uncertainty of 0.5%. A programmable temperature controller (Sensortherm Regulus RD) integrates the temperature ranges of these two pyrometers and is connected to the laser controller, achieving fast temperature measurement and control. When the molten sample is heated by lasers which are indirectly controlled by the temperature controller, the temperature fluctuation is below 10 K. The pyrometers measure the spectral radiance of the sample at two selected wavelengths (signals are collected by two separate channels, respectively) and calculate the ratio. The influence of the argon gas around the sample is negligible since the ratio is almost unchanged even though both the two signals are changed.

The acoustic excitation system consists of a waveform generator and a group of loudspeakers. The waveform generator generates sinusoidal voltages of various frequencies which are transmitted to the loudspeakers. The loudspeakers are coupled to the argon gas pipeline. Therefore, the sound wave generated from the loudspeakers can be imposed on the molten sample through the argon gas. The molten sample is excited by the sound wave and the surface begins to vibrate. The resonance frequency can be found by measuring the vibration amplitude of the molten sample at different frequencies, and then the surface tension can be derived. Viscosity is finally calculated from the decay constant when loudspeakers working at the resonance frequency stop and the damped oscillations of the molten sample start. The acoustic excitation system is under installation and intended for measurements of surface tension and viscosity.

The density is the ratio of mass to volume of the sample. The mass of the sample is measured with an electronic balance and the volume is obtained from the images recorded by the high-speed camera. In the beginning, a sample is levitated above the conical nozzle and heated by the upper laser. Then the sample melts into a liquid drop. The images of the sample are recorded by the camera, and image processing is performed frame by frame with a software program written in MATLAB. The surface profile of the drop is determined through an image edge detection technique. Since the drop appears ellipsoidal, its center as well as semi-major axis and semi-minor axis are determined by an ellipse fitting algorithm. Based on these data, the density is calculated with the following equation: ρ = 3 M 4 π r a 2 r b (1) where ρ is the sample density, M the sample mass, r a the semi-major axis, and r b the semi-minor axis.

Previous studies have shown that the Canny edge detection algorithm generally performs better than other operators such as Sobel, Robert, Prewitt, Laplacian, and Laplace of Gaussian (Maini and Aggarwal, 2009). A common Canny edge detection algorithm includes the following four steps: 1) a Gaussian filter is used to smooth the original image which eliminates the noise; 2) the edges including gradient intensity and gradient direction of the image are calculated by the first-order difference method with the Canny operator; 3) the Non-Maxima Suppression is performed so that only the points with the largest local gradient are retained; and 4) the double threshold algorithm is used to detect and connect the edges. The edge function using the Canny operator in MATLAB is preferred because it improves the Canny operator and threshold value.

In this paper, least-squares fitting based on algebraic distances is performed using the pseudo inverse technique (Zhang, 1997). A 2-D elliptic equation can be described as follows: Q ( x , y ) = A x 2 + 2 B x y + C y 2 + 2 D x + 2 E y + F = 0 (2) A common practice is to minimize the algebraic distance, which means to minimize the following function: ψ = ∑ i = 1 n Q 2 ( x i , y i ) (3) When the normalization of A + C = 1 is considered, the elliptic equation becomes: Q ( x , y ) = A ( x 2 − y 2 ) + 2 B x y + 2 D x + 2 E y + F + y 2 = 0 (4) Therefore, the elliptic equation can be described by a vector p: p = [ A , B , D , E , F ] T (5) For a point ( x i , y i )   on the ellipse, the following vectors are constructed: a i = [ x i 2 − y i 2 , 2 x i y i , 2 x i , 2 y i , 1 ] T (6) b i = − y i 2 (7) Then, the elliptic equation becomes: Q ( x i , y i ) = a i T p − b i = 0 (8) Given n points, the following matrix yields: M = [ a 1 , a 2 , … . a n ] T (9) q = [ b 1 , b 2 , … . b n ] T (10) The function to minimize becomes: ψ ( p ) = ( Mp − q ) T ( Mp − q ) (11) Obtaining its partial derivative with respect to p and setting it to zero yield: 2 M T ( Mp − q ) = 0 (12) The solution is: p = ( M T M ) − 1 M T q (13) Therefore, elliptical parameters including A, B, C, D, E, and F are all known. Finally, the semi-major and semi-minor axes are determined as follows: r a = 2 ( A E 2 + C D 2 + F B 2 − 2 B D E − A C F ) ( B 2 − A C ) [ ( A − C ) 2 + 4 B 2 − ( A + C ) ] (14) r b = 2 ( A E 2 + C D 2 + F B 2 − 2 B D E − A C F ) ( B 2 − A C ) [ − ( A − C ) 2 + 4 B 2 − ( A + C ) ] (15)

The measurement uncertainty of density mainly comes from uncertainties of the sample mass and volume according to Eq. 1. Mass is determined by the electronic balance which has the uncertainty of 0.05 mg for a sample of 19.69 mg. Since the semi-major and semi-minor axes of the ellipsoidal sample are obtained from image processing of the sample images, the measurement uncertainties of the semi-major and semi-minor axes can be considered, which are about 4.4 pixels within 690 pixels and 3.5 pixels within 670 pixels. According to Eq. 1, the accuracy of density measurement is 1.40%.

Some uncertainties in the measurement are not quantifiable such as the distortion of the photography of an incandescent object and the departure from the ellipsoidal assumption. The first influencing factor can be resolved through the shadowgraphy which will be implemented. However, caution must be paid to the possible deviation from an ellipsoidal shape, since the ellipsoidal shape may be affected not only by the joint forces of gravity and argon gas flow, but also by the temperature gradient inside the sample.

Powders or irregular objects can be melted into a nearly spherical sample by laser heating in a device called the laser hearth melter. The laser hearth melter is made of copper and the structure is shown in Figure 2. Oxide samples with a diameter of 2–3 mm can be made by the laser hearth melter. According to previous studies, the induced impurities are negligible (Richard Weber et al., 1996).

About 20 mg of alumina (99.9% purity) was put in the concave of the laser hearth melter and was heated into a liquid drop by the upper laser. A nearly spherical shape was formed due to surface tension. After the laser was turned off, the sample was solidified and homogenized by turning it over and remelting it. The alumina samples prepared by the laser hearth melter are also shown in Figure 2. When the laser power is gradually reduced to zero, the alumina drop can crystallize to form a transparent bead.

The sample diameter determined by the image processing is represented by pixels, so it is necessary to convert pixels to standard length units. Standard stainless-steel spheres with diameters of 2.0 and 2.5 mm were used in the calibration where the standard spheres were loaded on the nozzle and photographed by the camera. To improve measurement accuracy, the camera was set up with the maximum resolution of 2,560 × 1,600 pixels. The calibration for the relationship of pixel with micrometer given in Table 1 is obtained through the comparison of the pixels with accurate diameters of the standard spheres.

An alumina sample was firstly placed on the conical nozzle and levitated by argon gas flow. When the argon gas flowrate was about 0.4 L/min, there formed a gap of about 50 μm between the sample and the nozzle wall at ambient temperature without laser heating. The sample position fluctuation was monitored by the 2-D optical micrometer. When the sample was heated to 3333 K, the sample position fluctuation was determined by image processing results of the images recorded by the high-speed camera since the micrometer couldnot work when the sample was highly luminous. It turned out that the sample position fluctuation was below 10 μm at 298 K and 3333 K, as depicted in Figure 3. Though levitation instability was found when the sample was heated and melting, levitation stability resumed after the sample was entirely molten, i.e., after the formation of a drop at a prescribed temperature. Compared with the position fluctuations of 100 μm in an ESL experiment (Tamaru et al., 2018) and 40 μm in an ADL experiment (Krishnan et al., 1997), levitation stability in the present study is improved with the optimized nozzle.

At ambient temperature, the levitation is stable since the argon gas flow in the conical nozzle is laminar. When the upper laser is turned on for heating, the sample position fluctuation can reach about 200 μm since the thermal conductivity of the solid-state alumina sample is small, resulting in a large asymmetric temperature gradient. Therefore, the argon temperature field around the sample surface is also asymmetric which deteriorated the levitation stability.

During the melting of an alumina sample as shown in Figure 4, the solid and liquid parts coexist. The irregular shape of the melting sample will change the mass center, weakening levitation stability. When the sample starts to melt from the upper part to the lower part, the melting process is potentially stable, since the newly melted liquid part with lower temperature and higher density stays at the solid-liquid interface. If the sample is heated by the lower laser, it will start to melt from the lower part to the upper part, the newly melted liquid part with lower temperature and higher density will move to the bottom. The flow inside the liquid part will deteriorate the stability. Therefore, only the upper laser is used for sample melting to ensure levitation stability.

When an alumina sphere is entirely molten and the temperature is above 2300 K, the levitation of the drop is stable. This can be related to the increase in thermal conductivity and improvement of temperature uniformity. Besides, due to the decrease in density and increase in viscosity of argon gas around the sample, Reynolds number is less than 1/6 of that at ambient temperature which further improves the stability (Paradis et al., 1996).

Density measurement was conducted in the cooling process of the alumina sample after the sample was levitated, heated to 3333 K and stabilized for seconds. The cooling process was induced by the sudden shutdown of the heating laser. The camera was set up to record at 1,000 fps with a resolution of 2,560 × 1,600 pixels. The temperature was synchronously recorded by pyrometers.

The temperature history of the cooling process and sample images at different stages are shown in Figure 5. A sudden temperature rise is found while the recalescence phenomenon is recorded when the sample solidifies. In the sample images, the ellipse edge, major axis and minor axis determined by image processing are all plotted. The whole morphology of the molten drop is difficult to obtain due to the nozzle shielding. Therefore, it is difficult to evaluate the joint effects of gravity and argon gas flow shearing on the drop morphology. Nevertheless, the sample images show that the visible part of the liquid drop agrees well with the ellipsoidal assumption. Therefore, it is reliable to calculate the drop volume based on the ellipsoidal assumption.

The sample mass before and after the experiment is measured to be 19.82 and 19.69 mg. This is because the heating of the sample takes a few minutes, and the highest temperature 3333 K has exceeded the boiling point of alumina (3240 K), resulting in large evaporation and mass loss before the cooling process. On the other hand, since the cooling process takes less than 5 s, the mass loss during this period is negligible. Hence, the mass of 19.69 mg is used to calculate the density.

The temperature-dependent density measured in the present study is depicted in Figure 6, where the data measured by the ADL and ESL methods (Glorieux et al., 1999; Paradis et al., 2004; Langstaff et al., 2013; Tamaru et al., 2018; Kondo et al., 2019) are also plotted for comparison. More related data measured by various contact and contactless methods are given in Table 2. The relationship between density and temperature for the temperature range of 2300 K < T < 3000 K obtained in the present study can be fitted by the following equation: ρ = − ( 2.421 ± 0.089 ) × 10 − 4 × T + ( 3.493 ± 0.023 )   ( g / cm 3 ) (16)

Large fluctuations in the density measurement are found at the beginning of the cooling process. This is because the rapid thermal transient upon the shutdown of the laser results in a sudden position change as shown in Figure 7. The sample is positioned well in the horizontal direction, but moves down about 40 μm in 15 ms since the sample volume decreases with reducing temperature. The argon gas flow induced velocity and pressure changes quickly, producing disturbance of the sample surfaces as shown in Figure 8. The downward displacement may firstly elongate and then flatten the alumina drop, resulting in the decrease and then increase of the semi-major axis. The disturbance gradually disappears when a stable levitation is successfully re-established. Therefore, measured data between 3000 and 3333 K is not used due to poor accuracy.

When the temperature is lower, alumina density is overestimated with a fixed shutter time of the camera, which is a common phenomenon for the conventional photography of an incandescent object. In the image edge detection code, the edge of the liquid drop is determined by the gradient of gray value in the sample images. A threshold is set in the Canny algorithm to recognize the edge. When the gradient is greater than the threshold, it is considered as the edge. During the cooling process. the lightness of the liquid drop decreases before solidification (see Figure 5). The gradient is then smaller overall at lower temperatures. However, the threshold does not change, causing the detected edge moves towards the inside of the sample. Hence, the drop volume is underestimated and the density is overestimated. The edge movement is related to the temperature of the sample and the shutter time of the camera. Therefore, the detected edge movement accounts for the higher temperature coefficient of density in the present study. Besides, results may be different with different shutter times due to this common phenomenon. Shadowgraphy will be implemented to eliminate the effects of image brightness changes in future work. The background will be bright and the liquid drop will be black in sample images when a backlighting laser and a narrow-band filter are used. The brightness of the images is then independent of temperature during the cooling process. Nevertheless, conventional photography is still of great value and permits to visualize both the presence of impurities and the surface conditions, which can be used to investigate the solidification after undercooling.

In addition to the accuracy of the instruments, there are still multiple factors that affect the measurement accuracy. In the present study, the sample top side is heated by a single laser while the bottom side is not heated. Temperature gradient of a few hundred Kelvin is expected and may lead to a density gradient within the sample. The joint effect of gravity and argon gas flow shearing on drop morphology is still hard to estimate since lower part of the sample is hidden by the conical nozzle. The sample volume calculated by image processing of the visible portion based on 2-D ellipse fitting will also be affected. Besides, the pyrometers focus on the top side of the sample, which overestimate the sample temperature.

As shown in Table 2, a large density disparity exists between results obtained by contact methods. For example, the density at 2327 K of alumina, is 3.06 g/cm³ in (Ikemiya et al., 1993) and 2.55 g/cm³ in (Wartenburg et al., 1936). These contact measurements are quite old and are greatly affected by sample contamination. This may also account for the large disparity between the contact and contactless methods. Among the contactless methods, the density measured by Glorieux et al. (1999) is significantly lower. The reason may be that the sample is imaged from the top and assumed to be spherical, while the liquid alumina is closer to the ellipsoid under gravity and gas flow shearing. For example, the semi-major axis is about 3.4% longer than the semi-minor axis for the alumina drop at 3333 K (see Figure 8). Ignoring the influence of asphericity may overestimate the volume and underestimate the density of the sample. The density measured by Paradis et al. (2004) is higher instead. The reason may be the high-vacuum conditions. The liquid drop may become unstable due to sample evaporation. Another reason may be the low camera resolution. Work by Tamaru et al. (2018) is done under microgravity. Voids may form within the sample and are difficult to be removed, which may cause errors. Considering the 1.40% error bar of density (calculated based on mass and radius uncertainties) in the present study, good agreement is found with previously reported data measured by the ADL and ESL methods.

The liquid drop may rotate when levitated by argon gas flow. The higher the flow rate, the faster the rotation speed. When the levitation is well controlled, the deviation of the rotation axis from the vertical direction is small. However, when the temperature is close to the boiling point, or some large disturbance is introduced externally, the levitation becomes less stable and the deviation angle becomes larger. The destruction of flow field symmetry will lead to large measurement errors. Therefore, when a large deviation angle from the vertical direction during the cooling process occurs, another experiment is suggested for more accurate results. If the drop accidentally sticks to the nozzle wall during the measurement, the experiment needs to be terminated and restarted after cleaning the nozzle.