# Gas-Dynamic Kinetics of Vapour Sampling in the Detection of Explosives

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{0}of molecules that entered the channel. It was shown that a high rate of explosive vapour accumulation is achieved at a high breakthrough of up to 80%.

^{−14}g/cm

^{3}to the concentrator within 1 min. Hereafter, TNT vapour concentrations are given at room temperature +25 °C. If it is necessary to take into account the temperature dependence of the concentration of TNT vapours, one can use the results from [6].

## 2. Results

#### 2.1. Theoretical Section

_{0}of molecules of the substance enters the channel’s inlet, some of the molecules are adsorbed, and N molecules exit the channel. We determine the value of the breakthrough β equal to:

_{0}

^{−2}·s

^{−1}, of the collisions between the molecules and the surface of the channel:

_{0}= Nt + N. If N

_{0}= const, we obtain: dNt = −dN. Thus, we can write that:

^{2}= 2n

_{d}D${\mathit{\tau}}_{d}$):

_{d}is the number of degrees of freedom, Δ is the root mean square displacement of the diffusion front. For Δ = r and n

_{d}= 3, the function β that determines the breakthrough takes the form

_{d}/q)

_{d}= 6πDls. The physical sense of q

_{d}is the diffusion flow of the substance being concentrated to the surface of the channel.

_{d}/Q)

_{d}= 6πDnls is the diffusion flow of the substance being concentrated to the surface of all n channels.

#### 2.2. Experimental Section

#### 2.2.1. Concentrators

_{p}= 0.05 mm was made of stainless steel. The mesh consists of n square cells (channels). The side of the square cell b was 0.08 mm. The scheme of the concentrator and the square cells’ dimensions are shown in Figure 2. The mesh diameter was 7.5 mm and the number n of square channels was about 2600.

_{c}. The equivalent length l

_{c}of the channel in the mesh was determined from the condition that the calculated and experimental values of the gas-dynamic resistance R of the concentrator are equal. The value of R was calculated from the Poiseuille equation: R = 8ηl

_{c}/(πnr

^{4}); experimentally, it was determined by the equation R

_{0}= P/Q, where η is the dynamic viscosity of the air, and P and Q are the experimental values of the pressure difference and airflow in the air pumping line in the presence of a concentrator, respectively, as shown in Figure 3. For the mesh that we used, the condition of R = R

_{0}with an error not more than 10%, as described in [3], was fulfilled at l

_{c}= 2πd

_{p}. This value of length l

_{c}was used in the value calculations of the breakthrough of molecules through a concentrator made of a mesh.

#### 2.2.2. Experimental Determination of the Breakthrough

## 3. Discussion

#### 3.1. Breakthrough Definition

_{d}—130 cm

^{3}/s (graph 1) and 140 cm

^{3}/s (graph 2), and the results of the breakthrough measurement using the EKHO-M device [3] under normal climatic conditions. The concentrator contained two meshes. In the calculations D = 0.2 cm

^{2}/s, n = 2600, l = 0.028 cm. For these data, at s = 0.5, the diffusion flow Q

_{d}= 140 cm

^{3}/s, and Q

_{d}= 130 cm

^{3}/s corresponds to s = 0.46.

#### 3.2. Express Accumulation of the Substance on the Mesh Concentrator

_{n}Q(1 − β)

_{n}is the accumulation time, Q is the flow through the concentrator. Noting Equation (8) for β, we obtain

_{n}Q[1 − exp(−Q

_{d}/Q)]

_{d}= (Q/Q

_{d})[1 − exp(−Q

_{d}/Q)]

_{d}= CQ

_{d}t

_{n}—is the maximum amount of substance captured by the concentrator with the given Q

_{d}, t

_{n}.

_{d}on the Q/Q

_{d}ratio. The graph illustrates an almost linear increase in mass with increasing flow Q to about Q

_{d}. It can be seen here that too small and too large Q/Q

_{d}values are disadvantageous, because at Q/Q

_{d}< 1, the amount of captured substance sharply decreases, and at Q/Q

_{d}˃ 4, an increase in flow rate does not give a noticeable increase in the captured mass. The increase becomes less than 2% of its maximum value at Q → 0.

_{d}lies in the range from two to four. Within this interval, there is a high accumulation efficiency in the range of 80–90% and a high (up to 80%) breakthrough β = 0.6÷0.8. The correspondence of the rational area of the Q/Q

_{d}ratio to the area of effective accumulation of the substance is shown in grey in Figure 6.

^{2}/s, flow Q = 280 cm

^{3}/s, calculation according to Equation (11) shows that, for the initial vapour concentration of 10

^{−14}g/cm

^{3}, a sufficient for detection amount of a substance is accumulated in 10 seconds (about 11 pg). This occurs at the ratio Q/Q

_{d}= 2 and the breakthrough of about 0.6.

#### 3.3. Complete Vapour Capture Mode at the Concentrator

_{d}/4; i.e., Q < Q

_{d}/4

^{−14}g/cm

^{3}and sampling to a concentrator of up to 20 pg of TNT, i.e., when passing of up to 250 mL of air sample through a mesh concentrator.

#### 3.4. Vapours Transportation Through the Channels with Small Losses

^{−5}, from which, in particular, it follows that for a TNT molecule diffusion coefficient D = 0.2 cm

^{2}/s, it is necessary to choose a q flow of about 10 L/s. The use of a flow of 6 L/s in [5] showed satisfactory results for the transportation of vapours through a duct system. From Equation (14), the condition on the channel length is also determined under other specified conditions:

## 4. Conclusions

_{d}of the substance being concentrated to the surface of the concentrator to the flow Q of air with the vapour of the substance through the concentrator. The essence of this phenomenological approach to calculating the breakthrough is that the adsorption rate of molecules per unit area of the concentrator is determined as proportional to the specific frequency of collisions of the molecules with the surface. The proportionality coefficient or the coefficient of “adhesion” of molecules to the surface is also introduced. As a result, the breakthrough is defined as a function of the ratio of the diffusion flow of the substance to the channel’s surface to the airflow through the concentrator.

- express accumulation of a substance at the concentrator (breakthrough is up to 80%);
- complete vapour capture at the concentrator (breakthrough is close to zero);
- small vapour losses (breakthrough is close to 1) during the vapour sampling through the extended channels.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Scheme of a metal mesh concentrator, where d—concentrator mesh diameter, b—side of a square cell (channel) of the mesh.

**Figure 3.**Scheme for determination of the gas-dynamic resistance of a concentrator, where 1 is a line for pumping air through a concentrator, 2—a concentrator.

**Figure 5.**Dependence of the breakthrough of TNT molecules through the concentrator on airflow. Designations: calculation 1 for Q

_{d}= 130 cm

^{3}/s, 2 for Q

_{d}= 140 cm

^{3}/s, O, measurements.

Mode Type | Breakthrough | D/Q Ratio, cm^{−1} |
---|---|---|

Vapour transportation | 0.9 | 2 × 10^{−5} |

Rapid substance accumulation | 0.6 | 7 × 10^{−4} |

Full capture | 0.02 | 6 × 10^{−3} |

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**MDPI and ACS Style**

Gruznov, V.M.; Vorozhtsov, A.B.
Gas-Dynamic Kinetics of Vapour Sampling in the Detection of Explosives. *Molecules* **2019**, *24*, 4409.
https://doi.org/10.3390/molecules24234409

**AMA Style**

Gruznov VM, Vorozhtsov AB.
Gas-Dynamic Kinetics of Vapour Sampling in the Detection of Explosives. *Molecules*. 2019; 24(23):4409.
https://doi.org/10.3390/molecules24234409

**Chicago/Turabian Style**

Gruznov, Vladimir M., and Alexander B. Vorozhtsov.
2019. "Gas-Dynamic Kinetics of Vapour Sampling in the Detection of Explosives" *Molecules* 24, no. 23: 4409.
https://doi.org/10.3390/molecules24234409