Introduction

Ion mobility spectrometry (IMS) is a trace chemical analysis and detection technique that works at atmospheric pressure. Due to several advantages, such as its high detection sensitivity, low equipment cost and easy operation, IMS is widely used for the detection of explosives, drugs, chemical warfare agents, biological and medical samples [1,2,3]. In the drift tube of an IMS instrument, ions move under the force resulting from an electric field and the opposing drift gas. Various ions have different mobilities in the given drift gas condition, allowing the separation of ion mixtures and obtaining structural information [4]. Thus, a homogeneous flow of drift gas is of extreme significance for improving the sensitivity and resolution of the IMS.

Fig. 1 shows the structure of a standalone IMS instrument in which the region inside the red dotted line is the region of our concern. As is shown, the inlet of the drift gas is located at the bottom of the drift tube [5, 6] through which the drift gas flows in. The ion detector is a converter. The collision and annihilation of ions on it will cause a current flow. The most commonly used ion detector is a circular metal plate that serves as the Faraday plate. The ion detector is fixed in the inner part of the tube as a barrier in the gas path. Upon flowing in, the drift gas will be blocked by the detector. Thus, an area of low pressure appears behind the detector and gives rise to the turbulence of the drift gas.

Fig. 1
figure 1

Structure of a standalone IMS instrument

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A similar phenomenon has been commonly found by researchers. Vautz [7] and coworkers showed that severe turbulence can be observed close to the detector plate and that it can influence the sensitivity and resolution of the IMS. Li et al. [8, 9] noted that turbulence appears when the gas flow rate surpasses 600 mL/min and that the turbulence becomes more evident with the increase of the flow rate. In addition, using simulations, Yang [10] also found the existence of turbulence. The presence of turbulence decreases the IMS performance. Nevertheless, currently there are no effective countermeasures for this problem.

To address this phenomenon, we built a simulation platform in COMSOL Multiphysics 5.2a (trial version) to obtain the velocity distribution of the drift gas in the tube. After evaluating the influence of the traditional ion detector on the velocity distribution, we propose a double-layer structure ion detector equipped with a high amount of dense and staggered holes. The simulation results showed that the novel ions detector can still maintain a homogeneous gas flow at a high gas flow rate.

Design and simulation

Novel ion detector

The traditional ion detector is a circular metal plate that gives rise to the turbulence in its vicinity. To ensure the homogeneity of the drift gas, a novel ion detector was proposed as shown in Fig. 2.

Fig. 2
figure 2

Structure of novel ion detector

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The novel ion detector can be described by three features: (1) It consists of a first and second metal plates. The distance between the plates is denoted as L. The first and second metal plates are connected by a conductive ring. Thus, the two plates and the ring are equipotential. The ions can be detected by each plate; (2) The diameter of the detector is equal to that of the drift tube, ensuring that the detector is connected to the tube with no gap. Each plate has many small holes with diameter Φ through which the gas can pass through the detector; (3) The holes in each plate are staggered, which means that there is not a hole in both plates at the same position. This guarantees that the ions will be detected even if they pass through the first plate. The holes are arranged in rows in one plate, and the distance between the rows is denoted as D.

Numerical model

The finite element method software package COMSOL Multiphysics was used for the simulation. In the Cartesian coordinate system, standard RNG (re-normalization group) k − ε [11] is used to calculate the turbulent flow under different inlet gas flow rates. The governing equations for fluid dynamic for viscous flow are called the Navier-Stokes equations which can be given by:

$$ \begin{array}{c}\hfill \mathrm{Continuity}\ \mathrm{equation}:\frac{\partial \rho}{\partial t}+\nabla \cdot \left(\rho \overrightarrow{\mathbf{V}}\right)=0,\hfill \\ {}\hfill \mathrm{Momentum}\ \mathrm{equation}\mathrm{s}:\frac{\partial \left(\rho \overrightarrow{\mathbf{V}}\right)}{\partial t}+\nabla \cdot \left(\rho \overrightarrow{\mathbf{V}}\overrightarrow{\mathbf{V}}\right)=-\nabla p+\rho \overrightarrow{\mathbf{F}}+\nabla \cdot \overset{\Rightarrow }{\sigma},\hfill \end{array} $$

Energy equation:

$$ \frac{\partial }{\partial t}\left[\rho \left( e+\frac{V^2}{2}\right)\right]+\nabla \cdot \left[\left( e+\frac{V^2}{2}\right)\rho \overrightarrow{V}\right]=-\varDelta p+\rho \overrightarrow{\mathbf{F}}\cdot \overrightarrow{V}+\nabla \cdot \left(\overrightarrow{V}\cdot \overset{\Rightarrow }{\sigma}\right)+\rho \dot{q}+\nabla \cdot \left(\lambda \nabla T\right), $$

where ρ is the density, \( \overrightarrow{\mathbf{V}} \) is the velocity vector, p is the static pressure, \( \overset{\Rightarrow }{\sigma} \) is the stress tensor, e is the internal energy, \( \overrightarrow{\mathbf{F}} \) is the external body force and λ is the second viscosity coefficient. Stokes hypothesized that λ =  − 2/3μ, where μ is the molecular viscosity coefficient.

The turbulence kinetic energy k and its rate of dissipation ε are obtained from the following transport equations [12]: k-equations: 

$$ \kern4em \rho \frac{\partial k}{\partial t}+\rho \mathbf{u}\cdot \nabla k=\nabla \cdot \left(\left(\mu +\frac{\mu_{\mathrm{T}}}{\sigma_{\varepsilon}}\right)\nabla k\right)+{P}_k- p\varepsilon $$

where the production term is

$$ \begin{array}{c}\hfill {P}_k={\mu}_{\mathrm{T}}\left(\nabla \mathbf{u}:\left(\nabla \mathbf{u}+{\left(\nabla \mathbf{u}\right)}^{\mathrm{T}}\right)-\frac{2}{3}{\left(\nabla \cdot \mathbf{u}\right)}^2\right)-\frac{2}{3}\rho k\nabla \cdot \mathbf{u}\hfill \\ {}\hfill \varepsilon -\mathrm{equations}:\rho \frac{\partial \varepsilon}{\partial t}+\rho \mathbf{u}\cdot \nabla \varepsilon =\nabla \cdot \left[\left(\mu +\frac{\mu_{\mathrm{T}}}{\sigma_{\varepsilon}}\right)\nabla \varepsilon \right]+{C}_{\varepsilon 1}\frac{\varepsilon}{k}{P}_k-{C}_{\varepsilon 2}\rho \frac{\varepsilon^2}{k},\hfill \end{array} $$

where u is the velocity vector of the fluid, t is the time, C μ , C ε1, C ε2,are constants and σ k , σ ε are the turbulent Prandtl numbers for k and ε.

Simulation platform

To evaluate the effect of the ion detector on the drift gas, a simulation platform was built. The parameters for simulations of the traditional ion detector consisting of a single plate are shown in Table 1.

Table 1 Simulation parameters of drift tube and ion detector
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The boundary condition of the inlet was “Flow rate”, and the values of 200 mL/min, 500 mL/min, 800 mL/min and 1000 mL/min were set successively. Additionally, the boundary condition of the outlet was “Pressure”, with the value of 1 atm. The result obtained after meshing is shown in Fig. 3a.

Fig. 3
figure 3

Ion detector and drift tube after meshing. (a) using the traditional ion detector and (b) using the novel detector

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The novel ion detector has the structure of a double-layer plate with dense and interlaced holes. We set the distance between the two plate L as 1 mm, the thickness of each plate as 1 mm, the diameter of the hole Φ as 0.5 mm and the distance between the holes D as 2 mm. The result after meshing is shown in Fig. 3b.

Results and discussion

Velocity distribution by using traditional ion detector

Since the inlet drift gas rates were 200 mL/min, 500 mL/min, 800 mL/min and 1000 mL/min, the velocity field distributions in the cross-section of the tube for the traditional ion detector are shown in Fig. 4. The color characterizes the velocity of the gas. When the drift gas flows in, it hits the detector, and the drift gas fights its way around the detector. It can be seen from Fig. 4a that the gas flow is almost homogeneous when the flow rate of the gas is 200 mL/min. As the rate increased, some turbulence can be observed in the vicinity of the detector plate. The turbulence becomes more evident as the gas flow rate increases, which decreases the performance of the IMS. The results are consistent with those obtained in previous work.

Fig. 4
figure 4

Distribution of velocity field for different inlet gas rates for traditional ion detector

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The axis of the drift tube and the velocity field distribution on it under the different inlet flow rates are shown in Fig. 5. When the flow rate is 200 mL/min, the gas velocity on the right side of the detector gradually increases from 0 cm/s and finally stabilizes at 0.5 cm/s. It can be considered that no turbulence exists under this flow rate. When the inlet gas flow rate increases, turbulence, i.e., the unstable region, begins to appear. The velocity of the gas flow increases from zero to the maximum value and then decreases to zero, making a peak, and then gradually increases to a stable value. The region of fluctuation from zero to zero signifies the unstable region. When the inlet gas flow rate is 500 mL/min and 800 mL/min, the unstable region starts at 10 mm and 15 mm, respectively. In addition, when the inlet gas flow is 1000 mL/min, the unstable region is located at 20 mm.

Fig. 5
figure 5

Axis and velocity distribution on the axis when using a traditional ion detector

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The transversal of x = 20 mm located on the right side of the ion detector and the velocity distribution on it are shown in Fig. 6. For the velocity distribution plot, the y-axis represents the velocity, the horizontal axis y = ±15 mm indicates the wall of the tube and y = 0 mm represents the center of the tube. The gas velocity distribution on either side of the axis is symmetrical. At the wall, the gas velocity is 0 cm/s. The velocity begins to increase remarkably from the wall, reaches a certain maximum value, and then decreases to a stable value. The shape of the velocity distribution is that of a pair of humps. When the flow rate is 200 mL/min, the humps are sufficiently small that we can consider the velocity distribution of gas flow to be approximately stable. With the increase of the gas flow rate, the humps become sharp, indicating the occurrence of turbulence. When the flow rate is 1000 mL/min, the height of the hump is 7.5 cm/s, the stable velocity on the axis is 0.8 cm/s, and the stable region spreads from y = −7 mm to 7 mm.

Fig. 6
figure 6

Transversal of x = 20 mm and the velocity distribution on it using a traditional ion detector

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The existence of turbulence will decrease the resolution and sensitivity of IMS instruments. Therefore, designing an optimized ion detector with no effect on the stability of drift gas is a strategy to improve the performance of IMS instruments.

Velocity distribution by using novel ion detector

The velocity distributions obtained upon changing the ion detector to the novel design are shown in Fig. 7. It can be seen that a higher gas flow rate corresponds to the higher drift gas velocity. For a high flow rate, the drift gas is still stable, in stark contrast with the distributions shown in Fig. 4.

Fig. 7
figure 7

Distribution of velocity field with different inlet gas rate for novel ion detector

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Fig. 8a shows the velocity distribution in the axis of the tube. For different flow rates, the gas velocity increase from 0 cm/s and tends to stabilize gradually. In contrast to Fig. 4, there is no unstable region resembling a hill. When the gas flow rate is 1000 cm/s, a small range of unstable gas flow at approximately 6 mm appears. Fig. 8b shows the distribution of velocity in the transversal of x = 20 mm. The velocity increases from 0 and reaches a steady value. No turbulence appears.

Fig. 8
figure 8

For novel ion detector, (a) is the velocity distribution on axis and (b) is velocity distribution on the transversal of x = 20 mm

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Comparison of velocity distributions

Comparison of velocity distributions for the ion detector types for the inlet flow rate of 1000 mL/min are shown in Fig. 9. Table 2 shows the quantization of the unstable range. Fig. 9a indicates the velocity distribution in the axis of the tube, with the solid and the dashed lines representing the traditional and the novel ion detectors, respectively. The novel ion detector significantly reduces the distribution range of the unstable region. Using the novel ion detector, the size of the unstable region in the axis changes from 20 mm to 0.6 mm, decreasing by 97%. The comparison of velocity distribution in the transversal of x = 20 mm is shown in Fig. 9b. The use of a novel ion detector eliminates the existence of the hump-like unstable region near the tube wall.

Fig. 9
figure 9

Comparison of velocity distributions for the inlet gas flow rate of 1000 mL/min. (a) is velocity distribution in the axis of tube and (b) is velocity distribution in the transversal of x = 20 mm

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Table 2 Quantization of unstable range by using two kinds of ion detectors
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Conclusions

To eliminate the turbulence near the ion detector that reduces the sensitivity and resolution of the IMS instrument, a novel ion detector with double-layer plates was proposed. We built a simulation platform for the drift tube based on the finite element method. The simulation results showed that under high inlet flow rates, the distributions of the velocity in the drift tube was still stable when using the novel ion detector. When the inlet flow rate was 1000 mL/min, the use of the novel ion detector reduced the size of the unstable gas region in the axis of the drift tube by 97% relative to the value obtained for the traditional detector. It can be estimated that such gains may lead to the increase of the sensitivity and resolution by 10% for a standalone IMS instrument. In subsequent work, we install the novel ion detector into an actual IMS instrument and evaluate the enhancement of sensitivity and resolution.