Particle triboelectric charging, being ubiquitous in nature and
industry, potentially plays a key role in dust events, including the lifting and transport of sand and dust particles. However, the properties of the electric field (

Contact or triboelectric charging is ubiquitous in dust events (Schmidt et
al., 1998; Zheng et al., 2003; Kok and Renno, 2008; Lacks and Sankaran,
2011; Harrison et al., 2016). The pioneering electric field (

The significant influences of the

Most field observations, such as Schmidt et al. (1998) and Bo et al. (2014),
have studied the electrical properties of sand particles in dust events.
However, many environmental (lurking) factors, such as relative humidity,
soil moisture, surface crust, etc., cannot be fully controllable (recorded)
in these field observations. The uncertainties in the field observations
provide the motivation for numerical studies of the particle triboelectric
charging in saltation. In addition, unlike pure saltation, the dust storm is
a very complex dusty phenomenon that is made up of numerous polydisperse
particles embedded in a high Reynolds number turbulent flow. Such a high
complexity of dust storms challenges the accurate simulation of the 3D

In this study, we evaluate the effects of the 3D

Map of the Qingtu Lake Observation Array (QLOA) site and the layout of all instruments.

We performed 3D

A detailed description of VREFM can be found in the Supplement of Zhang et
al. (2017), but we briefly describe it here. The working principle of VREFM
is based on the dynamic capacity technique, as illustrated in the inset of
Fig. 1b. Unlike a traditional atmospheric electric field mill, VREFM is
composed of only one vibrating electrode. As the electrode oscillates, it
charges and discharges periodically. The magnitude of the induced electric
current

The measurement uncertainties in our field campaign are threefold, namely wind velocity (CSAT3B), particle mass flux (SPC-91), and

In general, the actual wind direction exits at a specific angle to the
prevailing wind direction. A projection step is therefore needed to obtain
the streamwise

After completing the projection step, we then perform the following steps
sequentially to reveal the pattern of 3D

The DWT uses a set of mutually orthogonal wavelet basis functions, which are
dilated, translated, and scaled versions of a mother wavelet, to decompose
an

On the other hand, according to the empirical mode decomposition (EMD)
method, the time series

The resulting DWT and EEMD components from a measured vertical

The mean frequencies of DWT and EEMD components of

In this study, the time-varying mean values

Since the 3D

Finally, the dimensionless vertical profiles of the 3D

For modelling steady state saltation, there are four primary processes including (1) particle saltating motion, (2) particle–particle midair collisions, (3) particle–bed collisions, and (4) particle–wind momentum coupling (Dupont et al., 2013; Kok and Renno, 2009). Also, the changes in both the momentum and electrical charge of each particle are taken into account in the particle–particle midair and particle–bed collisions. To avoid overestimating midair collisions in the 2D simulation (Carneiro et al., 2013), we simulate saltation trajectories in a real 3D domain. We use the discrete element method (DEM), which explicitly simulates each particle motion and describes the collisional forces between colliding particles encompassing normal and tangential components, to advance the evaluation of the effects of particle midair collisions. In a steady state saltation, the mean streamwise wind speed is statistically stationary and statistically 1D so that the mean wind flow can be modelled as a 1D field. In other words, in this study the numerical simulation is a 3D DEM model for particle motion but a 1D model for wind field. In the following subsections, we will describe each process in detail.

Granular materials in natural phenomena, such as sand, aerosols, pulverized
material, seeds of crops, etc., are made up of discrete particles with a
wide range of sizes ranging from a few micrometres to millimetres. The
log-normal distribution is generally used to approximate the size
distribution of the sand sample (Marticorena and Bergametti, 1995; Dupont et
al., 2013). Thus, the mass distribution function of a sand sample with two
parameters, average diameter

The total force acting on a saltating particle consists of three distinct
interactions (Minier, 2016). The first one refers to the wind–particle
interaction, which is dominated by the drag force with lifting forces, such
as the Saffman force and Magnus force, being of secondary importance (Kok and
Renno, 2009; Dupont et al., 2013). The second interaction refers to the
particle–particle collisional forces or cohesion caused by physical contact
between particles. Such interparticle collisional forces can be described as
a function of the overlaps between the colliding particles. The third
interaction refers to the forces due to external fields such as gravity and the

In the absence of saltating particles, the mean wind profile over a flat and
homogeneous surface is well approximated by the log law (Anderson and Haff,
1988) as follows:

Since sand particles are much heavier than the air and are far smaller than
the Kolmogorov scales, the drag force is the dominant force affecting the
particle motion, which is expressed by (Anderson and Haff, 1991) the following:

Additionally, we also account for the effects of particle rotation on
particle motion using the Magnus force expressed as follows (White and Schulz, 1977; Anderson and Hallet, 1986; Loth, 2008):

Under moderate conditions, saltation is a dilute flow in which the particle–particle collisions are negligible. However, as wind velocity increases, midair collisions become increasingly pronounced, especially in the near-surface region (Sørensen and McEwan, 1996). Previous studies found that the probability of midair collisions of saltating particles almost increased linearly with wind speed (Huang et al., 2007), and such collisions indeed enhanced the total mass flux substantially (Carneiro et al., 2013). For spherical particles, one of the most commonly used collisional force models is the non-linear viscoelastic model, consisting of two components, i.e. elastic and viscous forces (Haff and Anderson, 1993; Brilliantov et al., 1996; Silbert et al., 2001; Tuley et al., 2010).

Considering that two spherical particles

As a saltating particle collides with the sand bed, it not only has a chance
to rebound but may also eject several particles from the sand bed. For
simplicity, we use a probabilistic representation, termed as the “splash
function”, to describe the particle–bed interactions quantitatively (Shao,
2008; Kok et al., 2012). Currently, the splash function is primarily
characterized by wind-tunnel and numerical simulations (e.g. Anderson and
Haff, 1991; Haff and Anderson, 1993; Rice et al., 1996; Huang et al., 2017).
The rebounding probability of a saltating particle colliding with the sand
bed is approximately (Anderson and Haff, 1991) the following:

It is reasonable to assume that the number of ejected particles depends on
the impact speed and its cross-sectional area. Thus, the number of ejected
particles from the

In this study, the calculation of the charge transfer between sand particle
collisions is based on the asymmetric contact model, assuming that the
electrons trapped in high-energy states on one particle surface can relax on
the other particle surface (Kok and Lacks, 2009; Hu et al., 2012). Thus, the
net increment of the charge of particle

Similar to particle momentum flux (i.e. Eq. 14), the particle horizontal mass flux

A schematic illustration of the DEM simulation of saltation and
the numerical algorithm of the saltation model.

We consider polydisperse soft-spherical sand particles to have a log-normal
mass distribution in a 3D computational domain

As shown in Fig. 4b, the model is initiated by randomly releasing 100
uncharged particles within the region below 0.3 m, and then, these released
particles begin to move under the action of the initial log-law wind flow,
triggering saltation through a series of particle–bed collisions. We use
cell-based collision-searching algorithms, which perform a collision search
for particles located in the target cell and its neighbouring cells, to find
the midair colliding pairs. The random processes, particle–bed collisions
described previously, are simulated using a general method called the
inverse transformation. The particle motion and wind flow equations are
integrated by predictor-corrector method AB3-AM4; that is, the third-order
Adams–Bashforth method is used to perform the prediction and fourth-order Adams–Moulton method is used to perform the correction. One of the main advantages of using such a multi-step integration method is that the accuracy of the results is not sensitive to the detection of exact moments of collision (Tuley et al., 2010). The charge transfer between the colliding pairs is caused by their asymmetric contact and can be determined by Eqs. (25)–(27). When calculating the particle–bed charge transfer, the bed is regarded as an infinite plane. According to the law of charge conservation, the surface charge density of the infinite bed plane and the newly ejected particles,

Description of all variables used in this study.

Continued.

Measured data during a dust storm occurring on 6 May 2014 at the
QLOA site. Panels

On 6 May 2014, field measurements began at

Vertical profiles of the normalized 3D

Fitting coefficients of the third-order polynomial curves in Fig. 6.

As shown in Fig. 6a–c, in different periods, each component of the
normalized 3D

Verification of the steady state numerical model in the case of
pure saltation. That is, only the vertical

Before quantifying the effects of the 3D

Effects of midair collisions on the probability density function
(PDF) of the charge-to-mass ratio of saltating particles for various wind
velocities of

In addition to affecting sand transport, midair collisions also affect charge exchanges between saltating particles. When considering midair collisions, the charge-to-mass ratio distribution shifts slightly towards zero as the wind velocity increases, as shown in Fig. 8a–c. As the wind speed increases, the difference in the charge-to-mass ratio distribution between the cases with and without midair collisions is increasingly notable. This is because the probability of midair collisions becomes more significant for larger wind speed (Sørensen and McEwan, 1996; Huang et al., 2007).

Comparison of the simulated mass flux

Vertical profiles of the particle mass concentration

By substituting the formulations of the 3D

Effects of the density of charged species

Additionally, we also explore how the key parameter, the density of charged
species

To determine the effects of particle triboelectric charging on saltation
precisely, 3D

In

Like many previous studies, the

Additionally, one possible explanation for the intense streamwise and
spanwise

Although most physical mechanisms, such as asymmetric contact, polarization
by external

One limitation of our model is that the effects of turbulent fluctuations on particle charging and dynamics are not explicitly accounted for. In actual conditions, saltation is unsteady and inhomogeneous at small scales, and the wind flow is mathematically described by the continuity and Navier–Stokes equations. However, in many cases, wind flow is statistically steady and homogeneous over a typical timescale of 10 min (Durán et al., 2011; Kok et al., 2012). For example, in the relatively stationary period in Fig. 5, all long period-averaged statistics become independent of time. In this case, the governing equations of the wind flow can be reduced to a simple model described by equation Eq. (13). There is no doubt that 3D turbulent fluctuations could affect particle charging and dynamics considerably (e.g. Cimarelli et al., 2014; Dupont et al., 2013). Further work is therefore needed to incorporate turbulence into the numerical model.

It is generally accepted that the

However, a remaining critical challenge is still to simulate particle
triboelectric charging in dust storms precisely. The driving atmospheric
turbulent flows, having a typical Reynolds number of the order of 10

Severe dust storms occurring in arid and semiarid regions threaten human
lives and result in substantial economic damages. An intense

We have also performed discussions about various sensitive parameters such
as the density of charged species, the coefficient of restitution, and the
height-averaged time-varying mean of the 3D

The

The supplement related to this article is available online at:

HZ performed the field observations, numerical simulation, and data analyses and wrote the paper, which was guided and edited by YHZ. Both authors discussed the results and commented on the paper.

The authors declare that they have no conflict of interest.

We thank the editor and anonymous reviewers for their insightful comments that greatly improved the final paper. This work was supported by the National Natural Science Foundation of China (grant no. 11802109), the Young Elite Scientists Sponsorship Program by the China Association for Science and Technology (CAST; grant no. 2017QNRC001), and the Fundamental Research Funds for the Central Universities (grant no. lzujbky-2018-7).

This research has been supported by the National Natural Science Foundation of China (grant no. 11802109), the Young Elite Scientists Sponsorship Program by CAST (grant no. 2017QNRC001), and the Fundamental Research Funds for the Central Universities (grant no. lzujbky-2018-7).

This paper was edited by Ulrich Pöschl and reviewed by four anonymous referees.