2. Contact electrification of moving sand

Knowledge on the phenomenon of sand electrification also stems from a few experimental measurements. For example, friction was performed between the glass rod and the filter paper, whose main components were similar to the sand particles, and then the charge on the glass rod was measured by an electroscope and a Faraday cup [28], or blasting sand were measured [29, 30]. These experiments showed that the larger particles tend to be charged positively, but the smaller particles are charged negatively [31]. In addition, they also find that the atmospheric pressure [32], the ambient humidity [33, 34], and the components [35, 36] all have some significant impact on the particle's charged process [36].

With the development of experimental devices, some scholars found that the polarity of the charge on a particle is related to its grain size. Greeley and Leach [37] analyzed the wind tunnel experimental results, and he finds that the critical particle size is 60 μm. But Zheng et al. found that the negative charge is gained when the diameter is smaller than 250 μm and positive charge is gained if the diameter is larger than 500 μm [38, 39], which have been proven by Forward et al. [40]. Of course, the critical particle size for the charged polarity of sand maybe varies with the incoming wind velocity, the height from the sand surface, and the grain size, as well as its size distribution [25].

It should be specially pointed out that the above researches only obtained the average charge on particles. Due to the limitations of experimental techniques, the experimental devices, and other objective factors, we cannot precisely obtain the quantitative relationship between the charge on single particle and the particle size, the incoming wind speed, the temperature, the humidity, and so on. However, these results have played a positive role in promoting the understanding of the electrification phenomenon of wind-blown sand and enlighten scholars on its physical mechanism.

On the mechanism of contact electrification of sand, the highly accredited conjecture is the contact electrification and the polarization-inducing process [25, 41]. For the contact electrification mechanism, which contains the static contact and the friction, an asymmetric transfer of tiny charged ion or substance is the primary source of it. In addition, it just concerns what these metastatic substances are and why and how many are transferred. But the polarization-inducing process is more intuitive. This mechanism suggests that the particle is polarized by the environmental electric field and the excess charges are repelled to the two sides of the particle. When the moving particle contact with each other, charges with opposite polarity cancel out and then will charge itself after separation. This theory firstly explained the reason of the thunderstorm. Considering that the natural sand is wrapped by a water film [42, 43], some researchers also believed that it also worked in the electrification of wind-blown sand [41]. However, there is still a lack of physical model which is formed by the fusion of those two physical processes. In here, I want to introduce a simple coupling model for it.

#### 2.1. Contact electrification from ion transfer

accompanied by the degradation of vegetation [5] and accelerated by the climate anomalies and drought. Some researchers studied the reason of vegetation degradation and its restoration techniques under the various environmental stresses, for example, the drought [6], the high temperature [7, 8], the wind blowing [9], the sand burial [10, 11], the sand flowing

In addition, some scholars also discussed the influence of various electric fields on the biological system [15]. Murr firstly discussed the physiological influence on plant growth of the electric field environment, and the author found that sufficiently high electric fields have a definite effect on plant growth and the growth response. Andersen and Vad [16] investigated the growth of Serratia marcescens and Escherichia coli at various filed strengths. Some researchers also considered the effect of environmental electric field on the seed germination,

On the other hand, the soil grain and the sand particles incompactly distribute on the surface of desertification land, which can be driven by the strong wind and eventually formed the windblown sand flowing. Some particles will deposition on the earth, but others can enter into the air with the turbulent process and even develop to the dusty weather [23, 24]. A lot of experiments show that the moving sand is charged, which induced a strong electric field in the air [25–27]. As mentioned above, some experimental results have shown that with the increasing of the applied electric field, the electrostatic field has some negative or positive influence on the plant physiological processes. The wind-blown sand electric field must also work on the similar process.

However, there is no any related report published on the effect of wind-blown sand electric field on the plant physiological processes. In view of this situation, this chapter firstly introduced the research status of sand electrification phenomenon and then proposed some physical models to analyze the effect of environmental electric field on the physiological processes of plants, for example, the root-water absorption process, the water transport processes in the stem, the permeability of cell membranes, etc. Through these discussions, we want to furtherly

Knowledge on the phenomenon of sand electrification also stems from a few experimental measurements. For example, friction was performed between the glass rod and the filter paper, whose main components were similar to the sand particles, and then the charge on the glass rod was measured by an electroscope and a Faraday cup [28], or blasting sand were measured [29, 30]. These experiments showed that the larger particles tend to be charged positively, but the smaller particles are charged negatively [31]. In addition, they also find that the atmospheric pressure [32], the ambient humidity [33, 34], and the components [35, 36] all have some

With the development of experimental devices, some scholars found that the polarity of the charge on a particle is related to its grain size. Greeley and Leach [37] analyzed the wind tunnel experimental results, and he finds that the critical particle size is 60 μm. But Zheng et al. found

[12, 13], the dust deposition on plant leaf [14], and so on.

84 Community and Global Ecology of Deserts

plant growth, respiration, and tolerance [17–22].

demonstrate the influence of sand flow on plant growth.

2. Contact electrification of moving sand

significant impact on the particle's charged process [36].

Xie et al. [44] proposed a contact electrification model of glass sphere, which can precisely predict the effect of particle size and the impact velocity on the electric quantity. So here, we directly used it to express the contribution of ion transfer to the contact electrification process. Of course, you can replace it with other suitable models, which have more precision. The model can be expressed as follows:

$$Q\_1 = \rho P\_D (1 - P\_D) (\mathbf{A}\_2 - \mathbf{A}\_1) \tag{1}$$

where r is the charge density and PD is the probability of any position on the particle surface as a donor; the reference suggests that it is 0.5. Aið Þ i ¼ 1; 2 is the contact area in the collision process, which can be expressed as follows:

$$A\_1 = 2\pi R\_1^2 \left(1 - \sqrt{R\_1^2 - 2R\delta\_{\text{max}}^1} / R\_1\right) \\ A\_2 = 2\pi r\_1^2 \left(1 - \sqrt{r\_1^2 - 2R\delta\_{\text{max}}^2} / r\_1\right)$$

$$\delta\_{\text{max}}^1 = \frac{R\_1}{R\_1 + r\_1} \left(\frac{5}{4} \frac{M}{K} v\_r^2\right)^{0.4} \\ \delta\_{\text{max}}^2 = \frac{r\_1}{R\_1 + r\_1} \left(\frac{5}{4} \frac{M}{K} v\_r^2\right)^{0.4}$$

$$R = \frac{r\_1 R\_1}{r\_1 + R\_1} M = \frac{m\_1 m\_2}{m\_1 + m\_2} E = \left(\frac{1 - \nu\_1^2}{E\_1} + \frac{1 - \nu\_2^2}{E\_2}\right)^{-1} K = {}^{4ER^{0.5}}\Big/\_{33}$$

In here m1, m<sup>2</sup> is the mass of two particles with radius R1, r1, Ei, ν<sup>i</sup> is its elastic modulus and Poisson's ratio, and vr is the collide velocity.

#### 2.2. Polarization-inducing process

The atmospheric electric field is 100–200 v/m, but it may be up to hundreds of kilovolts per meter in the thunderstorm or dust storm [45]. Under the polarization of the electric field, the conductor particles also can be charged after being separated from contact. Latham and Mason [46] deduced the contact electrification of two conductive spheres under the electrostatic field:

$$
\Delta q\_0 = \gamma\_1 E r^2 \cos \theta + \gamma\_2 q\_1 R\_1^2 / r\_1^2 \tag{2}
$$

So, the charge on the smaller particles after it contacts another sand in a strong electric field can

Considering that the sand is not an imperfect conductor, and the contact time is finite, so we have to add the impact of relaxation time [48]. Then, Eq. (6) is replaced by the following

<sup>Q</sup><sup>2</sup> <sup>¼</sup> <sup>1</sup> � expð Þ �tc=<sup>τ</sup> � � <sup>Δ</sup>q<sup>1</sup> <sup>þ</sup> <sup>Δ</sup>q<sup>2</sup>

β ¼ 1 � expð Þ �tc=τ , tc is the contact time, while particles collide each other. τ is the surface conductivity of sand, which is connected with the thickness of water film, denoted as n, on the

<sup>6</sup>:<sup>5</sup> � <sup>10</sup>�<sup>18</sup> <sup>n</sup> <sup>¼</sup> <sup>0</sup>

If the air humidity is H, the thickness of water film can be calculated by the following

Based on the above equations, the electrification of sand contact in a strong electrostatic field

Under the real conditions, both of the above two processes occurred when the particles contact

We supposed the particles are colliding along its center line; the radius of larger sand is 6 mm, the radius ratio is 0.5, the humidity of sand is 0.1, the collision velocity is 0.5 m/s, and Ei, ν<sup>i</sup> are all 15 GPa and 0.4. Taking into account these parameters, we discussed the effect of environmental electric field on the contact electrification of sand. The simulation results are shown in Figure 1. From it, we can see that while the environmental electric field is up to 100 kv/m, the charge increased by 10%. Considering that the wind-blown sand electric field may be up to 200 kV/m, we believe that the polarization-induced electrification mechanism plays a very important role in the phenomena of wind-blown

<sup>3</sup>:<sup>0</sup> � <sup>10</sup>�<sup>18</sup> � <sup>10</sup><sup>0</sup>:44<sup>n</sup> <sup>n</sup> <sup>&</sup>gt; <sup>0</sup>

τð Þ¼ n

<sup>n</sup> ¼ �1:<sup>588</sup> � <sup>10</sup>�<sup>6</sup>

2.3. Electrification of sand in sand flowing

8 < :

<sup>x</sup><sup>4</sup> <sup>þ</sup> <sup>2</sup>:<sup>567</sup> � <sup>10</sup>�<sup>4</sup>

each other. So, the total charge on sand can be calculated through Eq. (7):

ΔQ<sup>1</sup> ¼ Δq<sup>1</sup> þ Δq<sup>2</sup> (5)

Sand Electrification Possibly Affects the Plant Physiology in Desertification Land

<sup>x</sup><sup>3</sup> � <sup>0</sup>:01193x<sup>2</sup> <sup>þ</sup> <sup>0</sup>:2999<sup>x</sup> <sup>þ</sup> <sup>0</sup>:<sup>02099</sup>

Q ¼ Q<sup>1</sup> þ Q<sup>2</sup> (7)

� � (6)

http://dx.doi.org/10.5772/intechopen.74976

87

be obtained:

equation:

sand:

equation:

can be forecasted.

2.4. Discussions

sand electrification.

Here, E is the environmental electric field. r is the particle radius and θ is the angle between the two particles' centers and the electric field line. qi ð Þ i ¼ 1; 2 is the initial net charge on the particle before they collide. The first term in Eq. (2) represents the contribution from the polarization, and the last one is the charge redistribution on the charged sphere. Here, we just keep the first term. Those meanings of the charge after two spheres collide in the electric field can be calculated through the last equation:

$$
\Delta q\_1 = \gamma\_1 E r^2 \cos \theta \tag{3}
$$

If two particles all are charged before they contact, the charge may redistribute on each surface. Davis [47] and Ziv and Levin [48] proposed a simple relation:

$$
\Delta \mathfrak{q}\_2 = (\omega - 1)\mathfrak{q}\_1 + \omega \mathfrak{q}\_2 \tag{4}
$$

here, ω is the transfer fraction, which means how many charges on the smaller particle transfer to the relative larger particle. γ<sup>1</sup> is a parameter related to the radius ratio of two particles. And, we set α ¼ r=R, and then the values of γ<sup>1</sup> and ω have been shown in Table 1.

To simply, we obtain a fitting relationship used the MATLAB software, and it is shown as follows:

<sup>γ</sup><sup>1</sup> <sup>¼</sup> <sup>1</sup>:915α<sup>2</sup> � <sup>6</sup>:132<sup>α</sup> <sup>þ</sup> <sup>4</sup>:<sup>894</sup> <sup>ω</sup> <sup>¼</sup> <sup>0</sup>:5152α<sup>3</sup> � <sup>0</sup>:8769α<sup>2</sup> � <sup>0</sup>:1397<sup>α</sup> <sup>þ</sup> <sup>1</sup>:<sup>003</sup>


Table 1. Values for the parameters γ<sup>1</sup> and ω.

So, the charge on the smaller particles after it contacts another sand in a strong electric field can be obtained:

$$
\Delta Q\_1 = \Delta q\_1 + \Delta q\_2 \tag{5}
$$

Considering that the sand is not an imperfect conductor, and the contact time is finite, so we have to add the impact of relaxation time [48]. Then, Eq. (6) is replaced by the following equation:

$$Q\_2 = \left[1 - \exp(-\mathbf{t}\_\varepsilon/\tau)\right] \left(\Delta q\_1 + \Delta q\_2\right) \tag{6}$$

β ¼ 1 � expð Þ �tc=τ , tc is the contact time, while particles collide each other. τ is the surface conductivity of sand, which is connected with the thickness of water film, denoted as n, on the sand:

$$\pi(\mathbf{n}) = \begin{cases} 3.0 \times 10^{-18} \times 10^{0.44n} & n > 0 \\\\ 6.5 \times 10^{-18} & n = 0 \end{cases}$$

If the air humidity is H, the thickness of water film can be calculated by the following equation:

$$m = -1.588 \times 10^{-6} \text{x}^4 + 2.567 \times 10^{-4} \text{x}^3 - 0.01193 \text{x}^2 + 0.2999 \text{x} + 0.02099$$

Based on the above equations, the electrification of sand contact in a strong electrostatic field can be forecasted.

#### 2.3. Electrification of sand in sand flowing

Under the real conditions, both of the above two processes occurred when the particles contact each other. So, the total charge on sand can be calculated through Eq. (7):

$$Q = Q\_1 + Q\_2 \tag{7}$$

#### 2.4. Discussions

<sup>R</sup> <sup>¼</sup> <sup>r</sup>1R<sup>1</sup> r<sup>1</sup> þ R<sup>1</sup>

86 Community and Global Ecology of Deserts

Poisson's ratio, and vr is the collide velocity.

two particles' centers and the electric field line. qi

Davis [47] and Ziv and Levin [48] proposed a simple relation:

can be calculated through the last equation:

Table 1. Values for the parameters γ<sup>1</sup> and ω.

follows:

2.2. Polarization-inducing process

<sup>M</sup> <sup>¼</sup> <sup>m</sup>1m<sup>2</sup> m<sup>1</sup> þ m<sup>2</sup> <sup>E</sup> <sup>¼</sup> <sup>1</sup> � <sup>ν</sup><sup>2</sup>

In here m1, m<sup>2</sup> is the mass of two particles with radius R1, r1, Ei, ν<sup>i</sup> is its elastic modulus and

The atmospheric electric field is 100–200 v/m, but it may be up to hundreds of kilovolts per meter in the thunderstorm or dust storm [45]. Under the polarization of the electric field, the conductor particles also can be charged after being separated from contact. Latham and Mason [46] deduced the contact electrification of two conductive spheres under the electrostatic field:

Here, E is the environmental electric field. r is the particle radius and θ is the angle between the

particle before they collide. The first term in Eq. (2) represents the contribution from the polarization, and the last one is the charge redistribution on the charged sphere. Here, we just keep the first term. Those meanings of the charge after two spheres collide in the electric field

<sup>Δ</sup>q<sup>1</sup> <sup>¼</sup> <sup>γ</sup>1Er<sup>2</sup>

If two particles all are charged before they contact, the charge may redistribute on each surface.

here, ω is the transfer fraction, which means how many charges on the smaller particle transfer to the relative larger particle. γ<sup>1</sup> is a parameter related to the radius ratio of two particles. And,

To simply, we obtain a fitting relationship used the MATLAB software, and it is shown as

<sup>γ</sup><sup>1</sup> <sup>¼</sup> <sup>1</sup>:915α<sup>2</sup> � <sup>6</sup>:132<sup>α</sup> <sup>þ</sup> <sup>4</sup>:<sup>894</sup>

<sup>ω</sup> <sup>¼</sup> <sup>0</sup>:5152α<sup>3</sup> � <sup>0</sup>:8769α<sup>2</sup> � <sup>0</sup>:1397<sup>α</sup> <sup>þ</sup> <sup>1</sup>:<sup>003</sup>

α 0 0.2 0.4 0.6 0.8 1 γ<sup>1</sup> 4.93 3.9 3.1 2.55 2.06 1.64 ω 1 0.948 0.838 0.714 0.6 0.5

we set α ¼ r=R, and then the values of γ<sup>1</sup> and ω have been shown in Table 1.

cos<sup>θ</sup> <sup>þ</sup> <sup>γ</sup>2q1R<sup>2</sup>

<sup>1</sup>=r 2

<sup>Δ</sup>q<sup>0</sup> <sup>¼</sup> <sup>γ</sup>1Er<sup>2</sup>

1 E1 þ <sup>1</sup> � <sup>ν</sup><sup>2</sup> 2 E2

�<sup>1</sup>

<sup>K</sup> <sup>¼</sup> <sup>4</sup>ER0:<sup>5</sup>

=3

<sup>1</sup> (2)

ð Þ i ¼ 1; 2 is the initial net charge on the

cosθ (3)

Δq<sup>2</sup> ¼ ð Þ ω � 1 q<sup>1</sup> þ ωq<sup>2</sup> (4)

We supposed the particles are colliding along its center line; the radius of larger sand is 6 mm, the radius ratio is 0.5, the humidity of sand is 0.1, the collision velocity is 0.5 m/s, and Ei, ν<sup>i</sup> are all 15 GPa and 0.4. Taking into account these parameters, we discussed the effect of environmental electric field on the contact electrification of sand. The simulation results are shown in Figure 1. From it, we can see that while the environmental electric field is up to 100 kv/m, the charge increased by 10%. Considering that the wind-blown sand electric field may be up to 200 kV/m, we believe that the polarization-induced electrification mechanism plays a very important role in the phenomena of wind-blown sand electrification.

storm, and they found that the electric field is no-monotonic changed with the increase of height in the process of sandstorm and the direction may reverse [54]. These studies further revealed the complexity of wind-blown sand electric field, but they all reported that the magnitude of electric field is generally tens of kilovolts per meter, and it is even up to more than a hundred kilovolts per meter, which is sufficient to affect the physiological processes of

Sand Electrification Possibly Affects the Plant Physiology in Desertification Land

http://dx.doi.org/10.5772/intechopen.74976

89

Numerous studies have shown that the electric fields, as a physical stimulus, have a wide range of effects on the physiological processes of plant; for example, an appropriate strength of the electric field can affect cell proliferation, enzyme activity, biofilm permeability, and DNA synthesis, which will have an impact on plant growth and even improve the plant tolerance [21]. Some experiment also reported that the high-level electric field accelerated the drying of the hydrous plants [21]. In general, plants used to adapt a couple of abiotic effects like drought, ice, and sandstorm causing spectacular physical damage in plant tissues, especially the psammophyte. However, the psammophyte is the product of evolution, but others are more common, which would not adapt the damage from electric field, for example, the crop on the desertification land. In my knowledge, no any references concerned about the impact of windblown sand electric field on plant's physiological processes. In this chapter I want to discuss the effect of environmental electric field on the plant sap flow, the potential root water, and the

For the part between the crown and the root, which also named as xylem duct system, Parlange et al. proposed a theoretical model to simulate the sap flow of plant, and he suggest that the Poiseuille equation can be used to describe the sap flow in the stalk [55]. The driving force of the sap flow is the water potential differences between the plant root and the soil water. We set it as Δp. The water flux in a duct of the stem can be calculated through the

here, Q is the water flux, r is the duct radius, L is the duct length, Δh is the height difference of the duct, η is the fluid viscosity coefficient, and rgΔh represents the gravity of water in the

It is clear that Eq. (8) does not consider the effect of environmental electric field. The plants in desertification land are located in a strong wind-blown sand electric field. The duct of the stem can be equivalent to tubules, the water in the duct can be simplified to a tiny conductor rod,

<sup>8</sup>η<sup>L</sup> ð Þ <sup>r</sup>gΔ<sup>h</sup> <sup>þ</sup> <sup>Δ</sup><sup>p</sup> (8)

<sup>Q</sup> <sup>¼</sup> <sup>π</sup>r<sup>4</sup>

plant (Figure 2).

cell membrane permeability.

Poiseuille equation:

duct.

4. Effects of sand electrification on plants

4.1. Effect on plant sap flow and root absorption

Figure 1. The effect of environmental electric field on the sand's electrification.
