**3. Current status of particle thermophoretic deposition**

At present, there are three main ways to study the thermophoretic effect: theoretical research, numerical simulation, and experimental research. Researchers deduce new empirical expressions based on existing theories through numerical simulations or experiments under selected specific experimental conditions. The force characteristics and motion trajectory of the particles are analyzed, and the particle motion model of the thermophoresis effect under different conditions is established. The main work is divided into three categories. One is the influence of particle shape on thermophoretic effect, the other is the study of thermophoretic deposition effect of particles in pipes or small spaces, and the changes in particle concentration distribution or deposition law caused by thermophoretic effect in indoor and outdoor temperature fields. The following is an overview of the results of the main research groups currently working on both types of work.

#### **3.1 Research on thermophoretic deposition in pipes and tiny spaces**

Thermophoretic effects in pipes or tiny spaces are a hot topic in current thermophoretic research. The researchers selected specific flow field conditions and pipeline structures and established corresponding particle motion models based on existing theories through experiments and numerical simulations. The research team of Lin and Tsai of National Chiao Tung University used the critical trajectory method to study the effect of developing flow in a circular tube on the deposition efficiency of thermophoretic particles [26]. Through theoretical and numerical analysis, a dimensionless equation for calculating thermophoretic deposition efficiency under laminar flow conditions is established. The research results show that the inlet section where the velocity and temperature are both developing is more conducive to the formation of thermophoretic sedimentation of particles due to the existence of a relatively large temperature gradient, resulting in higher thermophoretic deposition efficiency. They determined the effect of particle diffusion and particle electrostatic charge induced deposition on thermophoretic deposition efficiency in laminar and turbulent tubes [27] (**Figure 5**). It is found that the deposition efficiency caused by the electrostatic charge of particles is comparable to the thermophoretic deposition efficiency when the thermophoretic efficiency is usually lower than 10% in their experiments (**Figure 6**), so this effect should be excluded when calculating the thermophoretic deposition efficiency to obtain accurate experimental data. Even for particles in Boltzmann charge balance, the deposition efficiency of the particle electrostatic charge has a considerable effect compared to the thermophoretic deposition efficiency. In addition, Tsai et al. also studied the inhibition process of particle thermophoretic deposition through the tube wall when the tube wall temperature exceeds the gas temperature in a circular tube [28]. The particle transport equations of convection, diffusion, and thermophoresis were numerically solved, and the particle concentration distribution and deposition laws were obtained. The results show that for all particle sizes, the particle deposition rate decreases with increasing tube wall temperature and gas flow rate. When the tube wall is heated to a certain temperature

slightly above the gas temperature, particle deposition is completely suppressed. And given dimensionless deposition parameters, an empirical expression is established to predict the dimensionless temperature difference required for zero deposition in laminar flow tubes (**Figures 5** and **6**).

The Lee's team studied the effect of thermophoresis on the deposition rate of particles above the wafer in a clean room environment [29, 30]. Using the statistical

#### **Figure 5.**

*Schematic diagram of the experimental apparatus by Lin and Tsai [27].*

#### **Figure 6.**

*Comparison of experimental deposition efficiencies (nonthermophoretic) and theoretical predictions of diffusional and electrostatic deposition under laminar flow conditions (Re = 1340).*

Lagrangian particle tracking (SLPT) model, under the condition of parallel airflow, particle deposition rates above individual wafers were measured. The law of particle deposition velocity as a function of temperature difference (temperature difference between plane and ambient air), particle density, and parallel airflow velocity is summarized. With and without thermophoresis, some numerical simulation results are as follows.The results show that with the increase of particle density, the particle deposition velocity decreases sharply with the increase of particle size, and the increase of airflow velocity also leads to the increase of particle deposition velocity (**Figures 7** and **8**).

Research on the deposition effect of particles in pipes or tiny spaces is a very popular direction in thermophoretic research both at home and abroad. Many scholars choose different parameters or channel and space conditions to establish corresponding particle motion models under thermophoretic effects. Yu et al. [31] carried out numerical simulation and analysis on the influence of thermophoretic force in MOCVD horizontal reactor on the concentration distribution of reaction precursors during deposition. For the TMGa molecules in the MOCVD reactor, the calculation formulas of the thermophoretic force, thermophoretic velocity, and diffusion velocity were deduced; Ho et al. [32] studied the effect of thermophoresis on particle deposition rate in mixed convection on vertically corrugated plates, using a cubic spline method, combining dimensionless variables, Prandtl transforms, and parabolic transform to obtain the final result.The results show that the smaller the particle size, the greater the influence of electrophoresis and thermal swimming, the greater the influence of temperature gradient and electric field on the deposition rate of particles.

**Figure 7.** *Effect of particle density.*

*A Review of Particle Removal Due to Thermophoretic Deposition DOI: http://dx.doi.org/10.5772/intechopen.109628*

**Figure 8.** *Effect of airflow velocity.*

### **3.2 Research on thermophoretic deposition under indoor and outdoor temperature fields**

Compared with the first type of work, there are few international studies on particle thermophoretic deposition in indoor temperature fields, and the experimental conditions chosen by various scholars are quite different.

The team of Xu and Chen [33, 34] proposed a zero-equation model to simulate the three-dimensional distribution of indoor air velocity, temperature, and pollutant concentration. This method assumes that turbulent viscosity is a function of length scale and local average velocity. This new computational model is much faster than the standard model. A two-layer model was then used to predict the flow. The model adopts the single equation model for the near-wall region and the standard model for the outer wall region, which improves the calculation efficiency again. Some scholars have also applied it to the utilization of water resources.

Lai [35] used two chambers to simulate indoor and outdoor conditions and the crack module to simulate wall cracks to study the effect of thermophoresis on particle penetration cracks. By simulating summer and winter conditions in temperate climate regions, it is found that the penetration ratio of particles from indoor to outdoor in winter conditions is significantly higher than that in summer and isothermal conditions when the particle size is less than 100 *μm*. And the effect of temperature on the particle penetration ratio decreases with the increase of particle size.

### **3.3 Study on the influence of thermophoresis effect on particle deposition between rotating disks**

Due to the geometry of the disk, the fluid flow under the action of the rotating disk is widely used in many engineering fields. In the past decade, with the development of mechanical technology, the effect of thermophoretic deposition on the fluid flow on the rotating disk has gradually become a hot topic.

Khan and Mahmood [36] investigated the effect of thermophoretic deposition on MHD flow of Oldroyd-B nanofluids between radiatively stretched disks. They used the homotopy analysis method to solve the transformed ordinary differential equations, and analyzed the convergence of the obtained series solutions. Through the analysis of the obtained results, it was found that the fluid temperature and the nanoparticle concentration decreased with the increase of the thermophoretic velocity parameter value. But it will increase with the increase of thermophoretic diffusion parameters. Hafeez et al. [37] also studied the thermophoretic deposition of particles in Oldroyd-B fluid between rotating disks, using von Karman similarity variables to convert partial differential equations into dimensionless ordinary differential equations, and with the help of Maple Numerical format (BVP-Midrich technique) to obtain numerical solutions. The results show that the axial thermophoretic velocity of the particles between the discs increases with the increase of the relative thermophoretic coefficient; the slope of the particle concentration growth curve decreases with the increase of the thermophoretic coefficient; the inward axial thermophoretic deposition velocity (Local Stanton number) increases with the increase of the thermophoresis coefficient (**Figure 9**).

Since the transformed ordinary differential equations are coupled and nonlinear, it is difficult to obtain closed-form solutions. Therefore, in recent years, many scholars have adopted the shooting technique and used the Runge-Kutta integral scheme to solve the ordinary differential equations obtained after similarity transformation. M.S. Alam et al. [38] used this method to study the deposition mechanism of micron-sized particles caused by thermophoresis during transient forced convection heat and mass transfer on an impermeable rotating disk with a surface temperature lower than that of the surrounding fluid. Doh and Muthtamilselvan [39] studied the effect of a rotating disk in a uniform electromagnetic field on the deposition of thermophoretic particles during unsteady heat and mass transfer in forced convection in a micropolar fluid. Gowda et al. [40] investigated the deposition of thermophoretic particles in a mixed nanofluidic flow suspended by ferrite nanoparticles. For different fluid or particle objects, most scholars have obtained relatively consistent results on the changing trends of related thermophoretic parameters in the thermophoretic deposition between rotating discs.

**Figure 9.** *A physical sketch of the problem by Khan and Mahmood [36].*

**Figure 10.**

*SEM microphotographs of* Staphylococcus aureus *biofilm on uncoated aluminum substrates and TiO2 coated aluminum substrates for the three different flame conditions.*

#### **3.4 Research on thermophoretic deposition technology in other works**

In addition to the above main types of work, thermophoretic deposition technology is also widely used in other aspects. Shi and Zhao [41] considered the deposition velocity of particles on the human body surface under Brownian and turbulent diffusion, gravitational settling and thermophoresis. The results show that for particles below 1 μm, thermophoresis is the main deposition mechanism. Brugière and Gensdarmes et al. [42] designed a radial flow thermophoretic velocity analyzer device. By developing the transfer function of the device they designed, the instrument can directly measure the particle velocity in the temperature field with high resolution. Effective thermophoretic velocity, eliminating the need to build a model to calculate the thermophoretic behavior of particles. De Falco et al. [43] achieved a highly controllable and tunable technique for the production of nanostructured TiO₂ coating films on aluminum substrates by combining aerosol flame synthesis and direct thermophoretic deposition. Self-cleaning and self-disinfecting coating materials with near superhydrophilicity and high antibacterial activity can be prepared. As shown, the number of *Staphylococcus aureus* was significantly reduced on the substrate with the titanium dioxide layer (**Figure 10**).

### **4. Conclusion and outlook**

Nowadays, the international research on the thermophoretic deposition effect has been very extensive, and a lot of achievements have been achieved. However, there are still many deficiencies and limitations in both the theoretical understanding of the thermophoretic mechanism and the application of the thermophoretic deposition effect in practical work.

Regarding the understanding of the thermophoretic mechanism, there have been relatively mature research results in the thermophoretic particle motion model in the continuum region and free molecular region, but some scholars have extended their theory to the transition region but found that the results are not ideal; Most of the studies are carried out under the condition that the thermal conductivity of particles is similar to the thermal conductivity of gas. When the thermal conductivity of particles is higher, the experimental results have a large deviation from the theoretical calculation values; In terms of particle shape, there are many studies on spherical particles, and the theoretical and experimental data are in good agreement. However, there are few studies on non-spherical particles, and most of the particles are non-spherical in reality. Errors introduced by thermophoretic force measurements on non-spherical particles may affect the data accuracy of the entire experiment.

In terms of experiments, the experimental conditions selected by various scholars are quite different, and it is difficult to make horizontal comparisons; Thermophoretic force is a short-range force. To obtain higher particle deposition efficiency in practical engineering applications, it is necessary to design an effective removal device structure; In the process of particle deposition, there is often the problem of particle resuspension, so the subsequent treatment of the deposited particles is also very important. At present, many studies have not considered the effects of particle agglomeration and fragmentation. In practical engineering applications, the characteristics of the flow field where the particles are located are usually much more complicated than the conditions selected in the experiment, so there are still many problems to be explored to widely apply thermophoresis technology to practical work.

### **Acknowledgements**

The authors thank the Key R & D plan of Zhejiang Province (2019C03097), National Natural Science Foundation of China (11872353) and Natural Science Foundation of China of Zhejiang Province (LZ22A020004) for their support.

### **Nomenclature**

