Experimental study on the dynamic characteristics of an analytical inductively coupled plasma and its tail flame

Abstract

Many numerical simulation models for analytical and industrial ICP sources have been developed; hence, experimental verification is essential. Compared with plasma temperature, the flow velocity profile is a direct and reliable criterion for model verification. In this paper, an experimental study on the dynamic properties of a home-made analytical ICP source and its tail flame is conducted using a high-speed colour camera and a high-speed fibre-optic spectrometer, and the spatially resolved pulsation frequency and flow velocity are presented. The pulsation frequencies of the plasma area and emission intensity were experimentally determined, respectively. The spatially resolved pulsation frequency indicates that pulsation of the normal analytical zone (NAZ) is very stable and synchronous, and the tail flame fluctuates due to ambient air entrainment. The flow velocity in the coolant gas was characterised by tracking the trajectories of injected alumina powder particles. After correcting for the velocity difference between the powder particle with high inertia and the surrounding flow, a plausible range of axial (V_z) and radial (V_r) velocity at the outer edge of the coolant gas is proposed. The flow velocity on the axis downstream of the NAZ was experimentally determined by tracking and interpolating the velocity of discrete erbium ion clouds originating from individual erbia suspension particles. By comparing the simulated profile of axial velocity with the experimental profile, the power coupling efficiency of the present ICP facility is estimated to be around 80%. A linear expression is presented to describe the variation of V_z with the axial position (z) in the range of 0 ≤ z ≤ 50 mm. Because erbium ion clouds were not distinguishable from the very bright emission background within the NAZ, a novel method is proposed to determine the flow velocity in the NAZ by combining the dependence of the audio frequency of plasma pulsation on the flow velocity profile, the simulated profile of axial velocity, and the experimental value of pulsation frequency. The determined value of axial velocity at the torch outlet axis operating at an r.f. power of 1200 W is in good agreement with the fitted value. This work presents complete experimental data on flow velocity in a single ICP facility and experimentally verifies the previously developed 2D numerical model.

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1 Introduction

As an excellent excitation and ionisation source, Inductively-Coupled-Plasma (ICP) is used not only in analytical instruments such as ICP-MS and ICP-OES,^1,2 but also for studies on gas-phase chemical reactions and nanoparticle formation.^3,4 Numerous computational models of ICP have been developed for fundamental studies, instrumentation and technique development.⁵ Compared to two-dimensional models,^5–16 three-dimensional models were proposed to describe ICP torch asymmetry, flow turbulence and air entrainment.^8,17–27 These 2D and 3D numerical models were usually verified by comparing the simulated plasma parameters with the measured values, i.e., temperature, electron number density^16,28–31 and velocity.^16,19,32 Only one or two temperatures are introduced in the simulation. Several temperatures (excitation temperature, gas kinetic temperature, electron temperature and ionisation temperature) are needed to describe various processes in the plasma.³³ The four temperature values differ when the plasma deviates from the local thermal equilibrium state (i.e., the tail flame). Moreover, the accuracy and spatial resolution of the diagnosed temperature and electron number density in ICP are relatively poor.^28–31 Therefore, compared with plasma temperature, plasma flow velocity would be a direct and reliable criterion for verification of the ICP numerical model.

Previous researchers utilised high-speed cameras,^34–37 particle image velocimetry (PIV),^19,32 and time-resolved emission^16,38–41 and mass spectrometry⁴² signals to measure the flow velocity inside the ICP torch and in the normal analytical zone (NAZ). High-speed photographic studies of the yttrium ion cloud by Houk and co-workers reported only one experimental data point in each of their papers.^34–37 A PIV study of intact, spherical mesophase graphite powder particles by Mostaghimi and co-workers presented the experimental and simulated profiles of flow velocity both inside the torch and in the NAZ.¹⁹ The flow velocity in the NAZ was found to depend on the operating conditions, i.e., r.f. power, torch injector diameter (sample gas flow rate), intermediate gas flow rate,¹⁹ and coolant gas flow rate.⁴¹ To our knowledge, the experimental data of the flow velocity downstream of the NAZ (>20 mm above the load coil) are scarce. Therefore, there is a lack of complete experimental data on the flow velocity in a single ICP facility, which is not conducive to comprehensive validation of ICP numerical models.

This manuscript presents an experimental study on the dynamic characteristics of a home-made analytical ICP source. The spatially resolved pulsation frequency and flow velocity were measured using independent techniques. For comparison and interpretation, the flow field was also predicted using a previously developed 2D numerical model.⁹ First, under varying sample introduction conditions, the pulsation frequencies of the plasma area and emission intensity were spatially determined using a high-speed colour camera and a high-speed fibre-optic spectrometer, respectively. Secondly, after continuously injecting alumina powder particles into the coolant gas and tracking their trajectories inside the torch using the high-speed colour camera, the particle velocity was calculated by the time-of-flight (TOF) method. A plausible range of flow velocity was proposed, considering the difference in velocity between the particles and the surrounding gas due to particle inertia. Thirdly, a dilute erbia suspension was nebulised into ICP, and discrete erbium ion clouds were distinguishable downstream of the NAZ. These ion clouds were tracked using the camera, and their velocity was determined using the TOF method. By accumulating and interpolating a sufficient amount of ion cloud velocity, the flow velocity on the plasma axis was retrieved and compared with the simulated value. However, the method is not applicable in the NAZ because the ion clouds were indistinguishable from the bright emission background. Finally, by combining the dependence of the audio frequency of plasma pulsation on the flow velocity profile,⁹ the simulated profile of axial velocity, and the experimental value of pulsation frequency, a novel method was proposed to determine the flow velocity in the NAZ.

2 Experimental

2.1 Experimental setup

The analytical ICP facility without an interface is the same as described in previous work.⁹ Hence, only a brief introduction is presented. The facility consists mainly of an r.f. power generator (Model RSG2000, Changzhou Rishige Electronics Technology Co., Ltd), an impedance matching network (Model PSG-IIIA, Changzhou Rishige Electronics Technology Co., Ltd), a Fassel-type quartz torch (Nu Company), a home-made four-turn copper load coil, a microconcentric nebuliser and a cyclone chamber (Glass Expansion Company). The flow rates of the coolant gas (Q_cool), auxiliary gas (Q_aux), and sample gas (Q_sam) are precisely controlled using three mass flow controllers (MFC) (Model D07-19B, Beijing Sevenstar Co., Ltd), respectively. The operating conditions are as follows: r.f. power = 1200 W, Q_cool = 13 L min⁻¹, Q_aux = 1 L min⁻¹, and Q_sam = 1 L min⁻¹ (99.999% Ar), if not specified. After ignition, the platinum shielding plate around the torch is connected to the grounded housing of the impedance matching network to sustain a shielded ICP. The plasma can develop freely and fully, mix with and dissipate in the surrounding air, as shown in Fig. 1.

Fig. 1 Schematic diagram of measurement of flow velocity and pulsation frequency in the ICP: (1) argon gas cylinder, (2)–(4) MFC for coolant gas, auxiliary gas, and sample gas, (5) nebuliser and cyclone chamber, (6) torch, (7) r.f. power generator and impedance matching network, (8) plasma, (9) exhaust pipe, (10) standard solution or suspension, (11) waste solution, (12) powder injector, (13) high-speed colour camera, (14) high-speed fibre-optic spectrometer, and (15) computer. The powder injector was connected to the tube only when injecting alumina powder particles into the coolant gas.

2.2 Measurement of the pulsation frequency

2.2.1 Observation using a high-speed colour camera. The photograph of pure argon ICP with no sample introduction was recorded as a blank using a high-speed colour camera (MEMRECAM ACS-3 model, NAC, Japan). The camera's frame rate and frame size were set at 16 000 fps and 1280 × 800 pixels, respectively. Then, twenty-two single-element standard solutions (Ag, Al, Au, Be, Ca, Cd, Ce, Cs, Cu, Er, Eu, Fe, Li, Mg, Na, Nd, Pb, Sb, Sr, Ti, W, and Y, 1000 μg ml⁻¹, NCS Testing Technology Co., Ltd) were nebulised sequentially. The corresponding photographs were recorded using the same method. As shown in Fig. 2, the plasma pulsation begins to smooth out when more than 100 frames (corresponding to a time duration of 1/160 s) are averaged. The blue, pink and red lights in the plasma originate from Y⁺, Y, and YO emission spectra,^35,36 respectively, and the distributions reflect the evolution of the nebulised yttrium.

Fig. 2 Photograph of ICP when nebulising a yttrium nitrate standard solution. (a) 1 frame, (b) 10 frames averaged, (c) 100 frames averaged, and (d) 1000 frames averaged.

The plasma pulsation frequency was determined by calculating the periodic variation of the plasma total area as follows: (i) convert every colourful image to a grey image, (ii) calculate the plasma total area in each frame using a code written in Matlab^®, (iii) perform Fast Fourier Transform (FFT) to obtain the power spectrum, and (iv) retrieve the discrete peak value as the pulsation frequency of the plasma total area. To further investigate spatial heterogeneity in plasma pulsation, the plasma image was sliced equally with a thickness of 2 mm. The pulsation of the plasma area slice, enclosed by two vertical lines with a space of 2 mm and the plasma outer edge, would represent local pulsation. Thus, the pulsation frequency was spatially resolved by calculating the periodic variation of the plasma area slice.

2.2.2 Observation using a high-speed fibre-optic spectrometer. For further comparison, the emission spectra of pure Ar ICP, Al ICP and Fe ICP at different axial positions were recorded using a high-speed fibre-optic spectrometer. The spectrometer is mainly composed of an optical spectrometer (Model Omni-λ5008i, Beijing Zolix Co., Ltd), an sCMOS camera (Model ZYLA5.5 USB3.5, Andor Co., Ltd) and an optical fibre. The frame rate of the sCMOS camera was optimised to obtain a good signal-to-noise ratio. The observation conditions are listed in Table 1. The peak area of the characteristic emission line in each frame was calculated, and then an FFT was performed. The peak position of the discrete characteristic peak in the power spectrum was retrieved as the pulsation frequency of the emission intensity.

Table 1 Observation conditions for the pulsation frequency of the plasma emission spectrum

Introduction	Wavelength/nm	Frame rate/Hz
No sample	Ar I 811.53, Ar I 810.37	600 to 5000
Fe solution	Ar I 811.53, Fe I 373.49	1100 to 8300
Al solution	Al I 396.15	500 to 7200

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2.3 Measurement of the flow velocity

In the Fassel-type torch, both the sample gas and the auxiliary gas are introduced axially, while the coolant gas with a large flow rate is introduced tangentially. Hence, a spiral flow is formed inside the torch.⁴³ Under typical operating conditions, the acoustic frequency of plasma pulsation increases with increasing r.f. power, Q_sam and Q_cool, and is independent of Q_aux.^9,44,45 In this work, we conducted two experiments in which two types of particles were introduced differently to trace the flow streamlines. In one experiment, alumina powder particles (a density of 3.99 g cm⁻³, a melting point of 2054 °C,⁴⁶ and a size of around 40 μm observed by optical microscopy) were injected into the coolant gas. In the other experiment, a suspension containing erbia particles (a density of 8.64 g cm⁻³, a melting point of 2344 °C,⁴⁶ a size of around 10 μm observed by optical microscopy) was nebulised and introduced into the sample gas.

2.3.1 Tracking alumina powder particles injected into the coolant gas. Due to the high melting point and large size, alumina powder particles could remain intact upstream of the NAZ and be visible to the high-speed colour camera under intense plasma illumination. A simple powder injector was made by tightly inserting a plastic pipette into a T-type connector. The pipette was filled with alumina powder particles, and then the injector was connected to the tube of coolant gas. The pipette nozzle faced up during plasma ignition, so only pure argon flow was introduced as the coolant gas. After successful ignition, the pipette nozzle was forced to face down, as illustrated in Fig. 1. The alumina powder particles falling down due to gravity were carried away by the coolant gas.

To observe the torch, plasma and tail flame simultaneously by the camera, the frame rate and frame size were set at 50 000 fps and 1280 × 224 pixels, respectively. The pixel resolution was calibrated to be 136 μm per pixel using the physical inner diameter of the outermost tube (18 mm). In Fig. 3a, a steady and several unsteady trajectories of alumina powder particles were observed inside the torch, indicating a rotational flow of the coolant gas. Meanwhile, the powder particles and ion clouds were observed at the outer edge of the plasma and downstream of the NAZ, respectively. The experimental video can be found in ESI 1.† Due to a lack of powder concentration control and insufficient pixel resolution, the identification of individual alumina particles was difficult in this experiment.

Fig. 3 Photograph of ICP when injecting alumina powder particles into the coolant gas. (a) 50 000 fps, 1280 × 224 pixels and (b) 16 000 fps, 1280 × 800 pixels. Flow from right to left. The two experimental videos can be found in ESI 1 and 2.†

To allow identification of individual alumina particles, the pixel resolution was improved by narrowing the field of view, as shown in Fig. 3b. The camera's frame rate and size were set at 16 000 fps and 1280 × 800 pixels, respectively. The pixel resolution under the setting was calibrated to be 33.9 μm per pixel, sufficient to identify individual alumina powder particles, as marked by the green circle in Fig. 3b. The experimental video can be found in ESI 2.† The axial and radial positions of individual powder particles in each frame were retrieved using ImageJ^® software. Finally, the axial and radial velocities of the particle were calculated using the TOF method.

2.3.2 Tracking erbium ion clouds originating from nebulised erbia suspension particles. Erbia suspension was nebulised at an uptake rate of around 50 μl min⁻¹. The suspension was diluted until a discrete ion cloud could be clearly distinguished, as illustrated in Fig. 4a–d. The camera's frame rate and frame size were set at 25 000 fps and 1280 × 496 pixels, respectively. The pixel resolution under the setting was calibrated to be 91.4 μm per pixel. A comparison study was conducted by nebulising an erbium nitrate standard solution (1000 μg ml⁻¹, NCS Testing Technology Co., Ltd), as shown in Fig. 4e. The purple light surrounding the central channel originates from the Er II emission spectrum.⁴⁷ The cyan and green lights in the tail flame both originate from the emission spectra of Er₂O₃, but are generated by different conversion mechanisms at different temperatures.^48–50

Fig. 4 Photographs of ICP when nebulising erbia suspension (a–d) and erbium nitrate standard solution (e). (a) Frame no. 3455, appearance of a blue Er⁺ cloud, (b) frame no. 3475, co-existence of a green Er₂O₃ cloud and blue Er⁺ cloud, (c) frame no. 3495, existence of only a green Er₂O₃ cloud, (d) frame no. 3515, dissipation of the green Er₂O₃ cloud, and (e) a typical frame. The experimental video corresponding to (a)–(d) can be found in ESI 3.†

Fig. 4a–d clearly show the evolution of erbium originating from an individual erbia suspension particle. The expanding, irregular shape of the cloud plume indicates a complex interaction of the cloud with the surrounding flow, especially the turbulent flow in the tail flow.^51–54 The centre points of the circular area (see Fig. 4a), elliptic area (Fig. 4b) and brightest area (Fig. 4c and d) were identified, and their corresponding positions were retrieved. The ion cloud velocity, representing the flow velocity, was determined using the TOF method and then compared with the simulated value from a numerical model developed previously.⁹

2.3.3 Plasma pulsation frequency characterisation method within the NAZ. The above method is not applicable in the NAZ because the erbium ion clouds were not distinguishable from the bright emission background. We have proposed and experimentally verified an expression to describe the relationship between the pulsation frequency and the velocity profile at the torch outlet⁹where V_max is the maximum value of flow velocity in the main flow direction, and λ_g is the characteristic dimension. The radial profile of the axial flow velocity was predicted using the previously developed numerical model, and then the V_max value and the λ_g value corresponding to V_max/2 were retrieved. The pulsation frequency was predicted using eqn (1) and compared with the experimental value determined in this work.

3 Results and discussion

3.1 The pulsation frequency of the plasma and its tail flame

3.1.1 Pulsation of the plasma area. In pure argon ICP, a triangular and bright zone exists and extends downstream for about 20 mm from the torch outlet (see Fig. 5), comparable with the inner diameter of the outermost tube (18 mm). When nebulising Ag, Au, Cd, Cs, Cu, Pb, and Sb single-element solutions into ICP, a similar phenomenon was observed, but the pulsation frequency of the plasma total area (f_plasma,total, blue dashed line) varies slightly with the element. The pulsation frequency of the plasma area slice (f_plasma,slice, green hollow circle) at different axial positions is nearly identical for a single element. The difference between f_plasma,total and f_plasma,slice is less than ±0.2 Hz (±0.7 Hz for Au), demonstrating that the bright zone (0 ≤ z ≤ 20 mm) pulsates synchronously as a whole. Schlieren visualisation shows that the plasma becomes unstable beyond a distance of more than one diameter downstream of the torch outlet.²⁰

Fig. 5 The plasma image and pulsation frequency distribution of pure argon ICP and ICP when nebulizing Ag, Au, Cd, Cs, Cu, Pb and Sb single-element solutions separately. The blue dashed line and the green hollow circle indicate the pulsation frequency of the plasma total area and area slice, respectively.

When nebulizing Al, Be, Fe, and Mg single-element standard solutions into ICP, a faint, distinguishable emission zone appears downstream of the triangular, bright zone, as shown in Fig. 6. In the bright zone (0 ≤ z ≤ 20 mm), the f_plasma,slice value is very stable and close to the f_plasma,total value. In the downstream emission zone, the f_plasma,slice value fluctuates and deviates from the f_plasma,total value, reflecting plasma disturbance due to air entrainment into plasma.

Fig. 6 The plasma image and pulsation frequency distribution of ICP when nebulizing Al, Be, Fe and Mg single-element solutions separately.

When nebulizing Ca, Ce, Er, Eu, Li, Na, Nd, Sr, Ti, Y, and W single-element standard solutions, a bright zone and a remarkable emission zone were observed, as shown in Fig. 7. In the bright zone (0 ≤ z ≤ 20 mm), the f_plasma,slice value is also very close to the f_plasma,total value. However, the f_plasma,slice in the emission zone varies depending on the introducing element. For Ca, Li, Nd, Sr and Y introduction, the f_plasma,slice is very close to the f_plasma,total value and seems independent of the axial position until z = 60 mm. For Ce, Er, Eu, Ti and W introduction, the f_plasma,slice fluctuates obviously in the z = 30 mm to 40 mm range, indicating the plasma disturbance due to air entrainment.

Fig. 7 The plasma image and pulsation frequency distribution of ICP when nebulizing Ca, Ce, Er, Eu, Li, Na, Nd, Sr, Ti, W, and Y single-element solutions separately.

From the above discussion, the pulsation of the bright zone (0 ≤ z ≤ 20 mm) is very stable and synchronous. The pulsation of the emission zone at 20 mm < z < 30 mm is also stable. The pulsation of the downstream zone at z > 35 mm fluctuates obviously. Thus, we speculate that the surrounding air is entrained into plasma at z > 20 mm.

3.1.2 Pulsation of the emission line intensity. In pure argon ICP, the pulsation frequencies of the Ar I 811.53 nm and Ar I 810.37 nm emission line intensities agree within the experimental uncertainty. Only the result of the Ar I 811.53 nm line is presented for simplicity. Two discrete peaks at around 100 Hz and 250 Hz are observed in the power spectrum. The 100 Hz peak should be attributed to the main power supply (50 Hz). When nebulizing an Fe solution, the pulsation frequencies of the Ar I 811.53 nm and Fe I 373.49 nm lines at around 250 Hz match well, suggesting that the excitation and emission of the two elements pulse synchronously. Thus, only the Fe I 373.49 nm line data are presented for simplicity. When nebulizing an Al solution, only the emission intensity of the Al I 396.15 nm line was monitored and processed. Compared to pure Ar ICP, no peak is observed at around 100 Hz in the power spectrum of the Al I 396.15 nm line in Al ICP or the Fe I 373.49 nm line in Fe ICP. The results suggest that the fluctuation of the main power supply transfers to the plasma through the r.f. power generator, and the solution introduction suppresses the pulsation at this frequency.

When no sample is introduced, the pulsation frequency of the Ar I 811.53 nm line at the torch outlet (z = 0 mm) is determined to be f_Ar = (255.8 ± 1.4) Hz. The f_Ar value increases slightly with increasing z in the range of 0 < z < 17 mm, but still varies within the experimental uncertainty, as shown in Fig. 8. When nebulizing the Al solution, the pulsation frequency of the Al I 396.15 nm line at z = 0 mm was determined to be f_Al = (250.2 ± 2.9) Hz, slightly lower than the f_Ar value at z = 0 mm. The f_Al value decreases slowly with increasing z at z > 15 mm, as shown in Fig. 8, consistent with the trend of Al ICP presented in Fig. 6. When nebulizing the Fe solution, the pulsation frequency of the Fe I 373.49 nm line at z = 0 mm was determined to be f_Fe = (252.1 ± 0.4) Hz, also lower than the f_Ar value at z = 0 mm. In the range of 5 mm < z < 30 mm, the f_Fe value first decreases and then increases with increasing z, consistent with the trend of Fe ICP presented in Fig. 6. As the temperature drops too low to excite Fe, no data were obtained further away.

Fig. 8 The pulsation frequency of the emission line intensity at varying axial positions.

3.1.3 Comparison and preliminary investigation. Comparing Fig. 6 and 8, the f_Ar, f_Al and f_Fe values measured by the emission spectroscopy method are all greater than those obtained using the plasma area method. One reason is that the results are not obtained in a single measurement, and the experiment conditions (torch cleaning and installation and operating conditions) differ. Due to space constraints, deploying and operating high-speed cameras and high-speed fibre-optic spectrometers simultaneously in a single experiment is challenging. Interestingly, both methods indicate f_Ar > f_Fe > f_Al. Fig. 7 also shows that the pulsation frequency varies with the sample introduction conditions, consistent with the previous observation.⁹ The qualitative explanation for this phenomenon is as follows. When large droplets or particles are introduced into the plasma, part of the plasma energy is consumed for evaporation, excitation and ionization of substances, causing the plasma temperature to drop.⁵⁵ According to the ideal gas state equation, the gas flow rate at the torch outlet decreases. Near the inner wall of the outermost tube, the radial gradient of the gas flow rate is large.⁹ It means that the variation of the radial position corresponding to a large velocity variation is relatively small. So, the radial position corresponding to V_max/2 could be considered approximately constant. According to eqn (1), the pulsation frequency f_plasma at the torch outlet (z = 0 mm) increases with increasing T_plasma.

As a preliminary investigation, the plasma excitation temperature was diagnosed using the Boltzmann plot method⁵⁶ under three sample introduction conditions (pure argon ICP, Fe ICP and Ti ICP). The Ar, Fe and Ti emission spectra were recorded using a fibre-optic spectrometer (AVS-DESKTOP-USB2, Avantes), respectively. T_exc,Fe = 4915 K, T_exc,Ti = 5246 K, and T_exc,Ar = 7609 K were obtained at the torch outlet. From Fig. 6 and 7, f_Fe = 227.0 Hz, f_Ti = 227.3 Hz, and f_Ar = 230.6 Hz were obtained using the plasma area method.⁵⁷ The relationship of T_exc,Fe < T_exc,Ti < T_exc,Ar and f_Fe < f_Ti < f_Ar supports the above explanation.

3.2 The flow velocity in the coolant gas

In every 10 frames, the axial (z) and radial (r) positions of eight alumina powder particles were retrieved to calculate the axial velocity (V_z,p) and radial velocity (V_r,p) of the particle. Fig. 9 shows that the particles accelerate in the axial direction and decelerate in the radial direction. Due to large inertia (3.99 g cm⁻³ and 40 μm), the velocity of alumina particles is lower than the flow velocity. So, corrections were made to the particle velocity through force analysis to obtain the flow velocity.

Fig. 9 The measured axial (a) and radial (b) velocity of eight alumina particles in the coolant gas. The symbol size indicates the velocity magnitude. Flow from right to left.

Data points close to the torch axis were chosen, as circled by a dashed rectangle in Fig. 9b. Hence, the force analysis is simple. A particle in the horizontal symmetry planes undergoes a drag force, a gravity force, a friction force, and a supporting force. Assuming the particle is in a state of force equilibrium, the force components are as follows:

The supporting force:

The friction force:

f = μF_sup

In the axial direction:

3πηd_p(V_z,f − V_z,p) = f sin θ

In the radial direction:

3πηd_p(V_r,f − V_r,p) = m_pg + f cos θ

Particle mass:

The angle of particle velocity relative to the vertical direction:

So the corrections can be estimated using

where V_z,f and V_r,f are the axial and radial components of flow velocity, V_z,p and V_r,p are the axial and radial components of particle velocity, ρ_p is the particle density (3.99 g cm⁻³ for alumina), d_p is the particle spherical diameter (40 μm for the alumina powder particle used in this work), η is the gas viscosity (2.2 × 10⁻⁵ Pa s for argon at 293.15 K and 101.3 kPa), R is the curvature radius of spiral motion (9 mm, equal to the inner radius of the outermost tube), g is the acceleration of gravity (9.8 m s⁻²), and μ is the translational friction coefficient.

In this study, it is not easy to know the accurate value of μ between the sliding alumina particles and the inner wall of the outermost tube. The literature values of μ for the Al₂O₃–SiO₂ (0.4 (ref. 57)) and Al₂O₃–Al₂O₃ (0.3 to 0.6 (ref. 58)) pairs were scarce. Assuming μ = 0, 0.3, 0.6 and 1, the flow velocity was obtained using eqn (2) and (3). Fig. 10 shows that the effect of the μ value on the correction is significant. Due to long injection and high mass load, alumina particle deposition was observed on the inner wall of the outermost tube. The μ between the alumina powder particles and the inner wall where the alumina particles are deposited can be approximated using the values of the Al₂O₃–Al₂O₃ pair. So, using the μ value in the 0.3 to 0.6 range is reasonable.⁵⁸ When μ = 0.6 is used, the average value of axial and radial velocities at the outer edge of the coolant gas are determined to be V_z,f = (2.5 ± 0.4) m s⁻¹ and V_r,f = (4.1 ± 1.0) m s⁻¹. When μ = 0.3 is used, V_z,f = (1.7 ± 0.3) m s⁻¹ and V_r,f = (2.9 ± 0.6) m s⁻¹ are obtained.

Fig. 10 The flow velocity obtained by correcting the particle velocity using different μ values. (a) Axial velocity and (b) radial velocity.

In the annular gap between the outermost and intermediate tubes, the average value of axial flow velocity is estimated using , where Q_cool is the coolant gas flow rate and D₂ and D₁ are the outer and inner diameters of the annular gap, respectively. By substituting Q_cool = 13 L min⁻¹, D₂ = 18 mm, and D₁ = 16 mm into the above equation, V_z,th is estimated to be 4.1 m s⁻¹. At the inlet of the tangentially introduced coolant gas, the average value of radial flow velocity is calculated using , where D₃ is the inner diameter of the coolant gas inlet. By substituting Q_cool = 13 L min⁻¹ and D₃ = 5 mm into the above equation, V_r,th is calculated to be 11.0 m s⁻¹. Mostaghimi and co-workers¹⁹ presented the experimental and simulated values of the axial velocity on the axis, but did not report the flow velocity in the coolant gas. In the 2D numerical model used in this work, the coolant gas is introduced axially into the torch, which is different from the real design. Thus, a 3D numerical model is essential for describing the complex flow pattern inside the torch.

3.3 The flow velocity on the plasma axis

3.3.1 Downstream of the bright NAZ. Under r.f. power settings of 900 W, 1000 W, 1100 W, 1200 W and 1300 W, the axial (V_z) and radial (V_r) velocities of 60 ion clouds were obtained downstream of the bright NAZ. For example, Fig. 11 shows the contour of V_z and V_r for plasma operating at an r.f. power of 1200 W. The profiles of V_z and V_r on the plasma axis were obtained by interpolating data points within the region of −0.5 mm ≤ r ≤ +0.5 mm. Then, the profiles of experimental V_z and V_r on the plasma axis under varying r.f. power settings are plotted and linearly fitted in Fig. 12. The simulated curves under the given r.f. powers were predicted using a previously developed 2D numerical model⁹ and presented for comparison.

Fig. 11 Contours of axial velocity (a) and radial velocity (b) determined at an r.f. power of 1200 W and the interpolated profile on the plasma axis.

Fig. 12 The experimental profiles of axial flow velocity on the axis of plasma operating at r.f. powers of (a) 900 W, (b) 1000 W, (c) 1100 W, (d) 1200 W, and (e) 1300 W. The simulated profiles and the linear fitting of experimental data are presented for comparison.

Fig. 12 shows that the experimental value of V_z is significantly lower than the simulated value at the same nominal r.f. power. The reason is that the power coupling efficiency from the r.f. power generator to ICP plasma is lower than unity.¹ In Fig. 12a, the simulated curve of V_z at a given power of 700 W matches the experimental curve at an r.f. power setting of 900 W in the range of 10 mm < z < 30 mm. Hence, the power coupling efficiency is estimated to be 78% (=700 W/900 W). The same phenomenon is observed in Fig. 12b–e, and the power coupling efficiency is estimated to be 80%, 82%, 83%, and 81%, respectively. We conclude that the power coupling efficiency of the ICP facility used is around 80%. In Fig. 12d, the linear fitting of the experimental data obtained at an r.f. power of 1200 W can be expressed as

V_z = 23.8 − 0.114 × z (4)

where z is in units of mm. It is observed that the fitted value of V_z using eqn (4) in the range of 0 ≤ z ≤ 50 mm is in good agreement with the simulated value.

In the range of 30 mm < z < 70 mm, the experimental curve of V_z is lower than the simulated one, considering a power coupling efficiency of 80%, and the deviation increases with increasing z. The reason is explained below. The experimental video (see ESI 1†) clearly shows that the alumina powder particles injected from the annular channel between the outermost and intermediate tubes maintain their movement direction for around 20 mm, comparable with the inner diameter of the outermost tube. In the range of z > 30 mm, the interaction of plasma with the surrounding air becomes remarkable. Ambient air was entrained into hot plasma, resulting in rapid cooling and plasma disturbance, as indicated by the spatially resolved pulsation frequency presented in this work. However, the 2D numerical model used in this work cannot describe the air entrainment process and the resulting cooling effect. Flow velocity decreases with decreasing flow temperature, so the simulated flow velocity value is overestimated.

Fig. 13a shows that the experimental value of V_r on the plasma axis is close to zero in the range of 10 mm < z < 30 mm, indicating that the ion cloud mainly moves along the axial direction. Further, in the range of z > 30 mm, the ion cloud obtains a non-zero radial velocity. As the r.f. power increases, the position at which the ion cloud begins to fly radially moves upstream, and the magnitude of the radial velocity also increases, as shown in Fig. 13b to 11e. At an r.f. power of 1200 W, if a pulsation frequency (f_plasma) of 230 Hz (see Fig. 5) and an axial velocity of 20 m s⁻¹ (see Fig. 12d) were used, the distance that an ion cloud flies over in one cycle is around 87 mm. In the region of interest from z = 13 mm to 70 mm, no more than one rotation cycle of the ion cloud could be observed in the field of view.

Fig. 13 The experimental profiles of radial velocity on the axis of plasma operating at r.f. powers of (a) 900 W, (b) 1000 W, (c) 1100 W, (d) 1200 W, and (e) 1300 W.

3.3.2 Within the bright NAZ. Comparing Fig. 4 and 5, the plasma morphology did not change before and after injecting individual erbia suspension particles. At given r.f. powers of 600 W, 700 W, 800 W, 900 W, 1000 W, 1100 W and 1200 W, the profiles of axial velocity (V_z) at the torch outlet were simulated using the previously developed numerical model. The maximum value (V_max) and the characteristic dimension (λ_g) were retrieved, as shown in Fig. 14a. Then, the pulsation frequency at the given r.f. power was predicted using eqn (1). Fig. 14b shows that the predicted value of pulsation frequency (f_predict) increases linearly with the given r.f. power. The f_predict value at a given r.f. power of 1000 W agrees well with the experimental value (f_exp = 230 Hz) of pure Ar ICP operating at an r.f. power of 1200 W. So, the power coupling efficiency is determined to be 80%, consistent with the result obtained in the previous section. From the simulated profile of V_z at a given r.f. power of 1000 W (see Fig. 14a), the axial velocity at the axis of the torch outlet (r = 0 and z = 0) is retrieved to be V_z = 23.4 m s⁻¹, and the corresponding characteristic dimension is retrieved to be λ_g = 7.3 mm. The V_z value determined by this method agrees with the fitted value obtained from eqn (4).

Fig. 14 The simulated profiles of axial velocity at the torch outlet at given r.f. powers (a) and the predicted frequency of plasma pulsation (b).

At a given r.f. power of 1000 W, the simulated profiles of V_z at axial positions of z = 0, 5 mm, 10 mm, 15 mm, 20 mm, 25 mm and 30 mm are plotted in Fig. 15. After retrieving the V_max and λ_g values, the pulsation frequency (f_predict) was predicted using eqn (1) and compared with the experimental value (f_exp). Table 2 illustrates that the relative deviation between f_predict and f_exp is less than 8% in the range of 0 ≤ z ≤ 20 mm. This good agreement demonstrates the accuracy of the simulated profile of V_z.

Fig. 15 The simulated profiles of axial velocity at varying axial positions at a given r.f. power of 1000 W.

Table 2 Comparison of the predicted value of pulsation frequency with the experimental value for pure Ar ICP

z/mm	V max/m s^−1	λ g/mm	f predict/Hz	R.D.^a
a Relative to the experimental value fexp = 230.5 Hz, as shown in Fig. 5. b f exp at z > 20 mm not available, as shown in Fig. 5.
0	23.7	7.3	232.6	0.9%
5	23.5	7.2	233.8	1.4%
10	23.2	7.2	230.9	0.2%
15	22.5	7.2	223.9	−2.9%
20	21.8	7.3	213.6	−7.3%
25	21.1	7.4	204.2	—^b
30	20.5	7.5	195.6	—^b

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Unlike Mostaghimi's finding,¹⁹ no plateau is observed in the experimental or simulated profile of V_z on the plasma axis in the NAZ. On the plasma axis, by comparing the simulated value of V_z with the experimental value determined using two independent methods, the numerical model used in this work is verified. We conclude that the numerical model used can accurately predict flow velocity in the range of 0 ≤ z ≤ 50 mm, taking into account the power coupling efficiency of 80%.

4 Conclusion

This paper presents a comprehensive experimental study on the dynamic characteristics of an analytical ICP and its tail flame. The spatially resolved pulsation frequency and flow velocity were determined using independent techniques. Compared with previous studies,^9,43,59–61 the pulsation frequency of ICP was spatially resolved using two independent methods (high-speed camera and high-speed fibre-optic spectrometer). It is beneficial to characterize the plasma turbulence and air entrainment process. Compared with Mostaghimi's work,¹⁹ the experimental data gap on flow velocity downstream of the NAZ is filled, and no plateau is observed in the experimental or simulated profile of V_z along the plasma axis in the NAZ. Flow velocities downstream of the NAZ and within the NAZ were experimentally determined using the ion cloud TOF method and pulsation frequency characterization method, respectively.

The above results provide detailed information on the dynamic properties of the analytical ICP, which is beneficial for developing and verifying numerical models of ICP. The variation of the pulsation frequency with the sampling element and axial position will be further investigated. A 3D numerical simulation model for analytical ICP is now under development.

Data availability

The data that support the findings of this study are available on request from the corresponding author.

Author contributions

Xin Han (methodology, data acquisition and preliminary analysis), Yongyang Su (conceptualization, data analysis and writing), Zhiming Li (discussion and project administration), Yuxuan Wang (experiment and discussion), Wei Wang (material and discussion), Ruiyang Xi (experiment), Shiyou Zhou (instrument upgrade), Guanyi Wei (particle analysis), Sui Fang (experiment), Yalong Wang (instrument), Jiang Xu (experiment), and Xiaofei Lan (discussion and reviewing).

Note added after first publication

This article replaces the version published on 24th June 2025, which contained errors in Fig. 2, 3, and 4.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work is financially supported by the National Natural Science Foundation of China under contract no. 11975185.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ja00072f

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