Primary Study on Influence of Conventional Hydrochemical Components on Suspension of Endogenous Fine Loess Particles in Groundwater over Loess Regions

Abstract

To ascertain the effects of conventional hydrochemical components on the presence of endogenous fine loess particles (EFLPs) in groundwater over loess regions, Na⁺, NO₃⁻ and Cu²⁺, as conventional hydrochemical components, were employed in batch tests with EFLPs from a typical loess as aquifer media in Guanzhong Plain, China. The results showed that EFLPs had high zeta potential (ζ) and remained suspended over 40 h, indicating their good dispersity and potential to be suspended in groundwater. ζ was employed to replace electrostatic repulsion in the DLVO equation to determine the critical coagulation concentrations for Cu(NO₃)₂ and NaF as 0.1 mmol/L and 50 mmol/L for 1.1 µm D₅₀ EFLPs, which were almost consistent with the batch test results and greater than those in the groundwater, respectively, further implying that EFLPs are likely to be suspended in groundwater. The multi-factor tests showed that the key factors including particle size, hydro-chemical component and concentration interacted with each other and their relative magnitudes varied in the test processes, where the effects of concentration strengthened while those of the component weakened. So, hydrogeochemical conditions were beneficial to the suspension of EFLPs and the benefit got strong along the groundwater flow path, which is conducive to the cotransport of EFLPs with pollutants in groundwater over loess regions.

1. Introduction

Fine soil particles, which are defined as soil particles with a diameter of less than 2 μm in soil [1,2], possess a large surface area as well as high contents of clay minerals and play a key role in pollutant adsorption on soils [3,4] and facilitating the transport of adsorbed pollutants into groundwater [5,6,7]. Extensive studies conducted on the transport of clay colloids and engineered nanoparticles along with the infiltration water flow in porous media showed that these particles can be retained and can also be transported in the porous media and groundwater under suitable water environment conditions, which is ascribed to the physical or (and) chemical disturbances of the infiltration water [5,8,9,10,11,12]. Obviously, in this research, most of the studied particles were added to their studied systems and can thus be considered exogenous fine particles; few studies focused on endogenous fine particles (EFPs) [2,13,14,15]. Even though EFPs are one of the most active components in soil and also have the potential to adsorb pollutants [16,17,18], little is known about their characteristics and potential to facilitate the transport of pollutants in groundwater. To achieve this function, one essential issue is to keep EFPs dispersed in groundwater. Thus, the present study will explore EFPs’ existence and influent factors regarding groundwater and then determine their nature and potential for transport in groundwater. The influent factors are mainly the physical and chemical properties of EFPs and their aquatic environment. In special groundwater, the properties of EFPs change relatively little and remain relatively stable on both time and space scales [1,2,9], meaning that the properties of the aquatic environment are essential factors controlling the suspension and existence of EFPs.

The present study, with the groundwater system over Guanzhong Plain as a case study area, aimed to determine the effects of EFLP diameter size and hydro-chemical conditions, including conventional hydro-chemical components and concentrations as representative factors of EFLP suspension, the effects of which vary along groundwater flow paths. We employed the Derjaguin–Landau–Verwey–Overbeek (DLVO) theoretical calculation to verify the batch test study results, provide insights into EFLPs and their potential influent factors, and deepen the understanding of the cotransport of EFLPs carrying pollutants and the related risk of groundwater pollution in soil–groundwater systems.

2. Materials and Methods

2.1. Hydrogeological Background of the Case Study Area

Information is reported in several references [19,20,21,22]. The key point for the present study is that loess is generally considered a water-sensitive geologic material [22,23,24] whose bulk loess matrix has the potential to release fine loess particles when it is exposed to and in contact with water [16,25]. Therefore, loess is used as an ideal medium for the present study.

Loess is widely distributed in Guanzhong Plain, with sediments 1~70 m thick [26,27], and groundwater is widely distributed there. Its shallow groundwater level depth has swiftly declined over the last few decades [28,29], and this decline is more conducive to the infiltration of surface water and agricultural irrigation water, which might increase the risk of degrading the groundwater quality [28]. Chromium, arsenic, ammonium, nitrate and even micro-pollutants including organochlorine pesticides and aniline are present in the groundwater [30,31]. These pollutants can be adsorbed on fine loess particles, implying that their transport in the groundwater system is likely to be realized in the form of particle adsorption [16,17]. Loess has the potential to release endogenous fine loess particles (EFLPs) as responses to hydraulic and hydrochemical disturbances of the groundwater, adsorbing pollutants and then co-transporting them in groundwater systems. However, these releases occur at the beginning of these disturbances and continue [16,17]. Therefore, it is essential that these particles be dispersed and kept in dispersion along the groundwater flow. Many studies have explored their transport characteristics and influencing factors [16,17], most of which focused on deposition and transport in porous media for engineered nanoparticles [19,32]; a few studies have been conducted on EFLPs, of which there are few on EFLPs in groundwater systems [33]. Thus, the knowledge of the generation, aggregation and sedimentation (AS) behaviors and suspension of EFLPs and their responses to hydrochemical conditions in groundwater systems is limited.

The groundwater over Guanzhong Plain is mainly recharged by rainfall, river leakage and irrigation infiltration [7]. Generally, its hydraulic gradient is drawn from about 12 ‰ in the western plain to 0.9 ‰ in the eastern plain [34]. This means that the groundwater velocity is low and water flows slowly and can thus be considered as one-dimensional. It would have been difficult and time-consuming to change the fine loess particles along the groundwater flow path if a horizontal simulation had been employed in this study. So, one-dimensional vertical column tests were used in the present study.

For the studied groundwater, numerous studies have shown that although the groundwater hydro-chemical characteristics are complex, fluoride, chloride and sulfate are the main anions, that originate from hydrogeological processes; nitrate is also a conventional anion, which has been reported as a pollutant and is considered a result of human activities, including agricultural activity [28,35]. The Na⁺ ion is a major cation and its concentration is high enough to be listed among the types of groundwater hydrogeochemicals [18]. Given these, NaF, NaNO₃ and Cu(NO₃)₂ were employed as typical representatives of conventional hydrochemical components; their concentrations and particle diameter sizes were selected as key parameters affecting the AS and suspension of EFLPs in groundwater in the present study.

2.2. Preparation and Characterization of the Endogenous Fine Loess Particles from Loess Sample

The process for Loess sampling and the preparation and characterization of endogenous fine loess particles were reported by Zhou et al. (2020) [17]. The important step is the high-speed centrifugation method combined with sonication [36,37].

2.3. Designed Tests

A glass graduated volumetric cylinder 50 cm in height and 10 cm in internal diameter was employed as a reaction vessel in the batch test study. In the present study, the batch tests were designed in two groups. The first one was a single-factor test, where the influencing factors included particle diameter size, hydrochemical component and concentration. The second one was a multi-factor test, which was designed through Design-Expert version 10.0.6 [38].

In the single-factor tests, NaF, NaNO₃ and Cu(NO₃)₂ as conventional hydrochemical components were set at 0.1 mol/L to study their effects on the AS and suspension of fine loess particles. During the test processes, the samples were collected at a 20 cm depth at 0, 0.5, 1.0, 3.0, 5.0, 8.0, 12.0, 24.0, 36.0 and 42.0 h and analyzed for the turbidity, diameter size and Zeta potential (ζ) of the fine loess particles. Cu(NO₃)₂ was employed as a conventional hydro-chemical component and its concentration was set at 0.1 mmol/L, 1 mmol/L, 5 mmol/L and 10 mmol/L to explore its effects on the AS and suspension of particles. The AS rate (ƞ) was determined via Equation (1):

$$\mathrm{ƞ}={\displaystyle \frac{{\mathrm{C}}_0-{\mathrm{C}}_{\mathrm{t}}}{{\mathrm{C}}_0}}⤬100\%$$

(1)

where C₀ and C_t stand for the particle concentrations at the beginning and at t hours of the reaction, respectively.

The processes for the multi-factor tests are mainly described by Sleiman et al. (2007) [39]; the key operational parameters including particle size (A), hydrochemical component (B) and its concentration (C) as independent parameters were selected and investigated at three different levels (−1, 0, +1) (

Table 1. Levels of the parameters tested in the Box–Behnken design.

		−1	0	1
Factor Levels
particle size (A, µm)		1.1	1.9	3.4
hydrochemical component (B)		NaF	NaNO3	Cu(NO3)2
component concentration (C, mmol/L)		1	5	10

). ƞ was utilized as the primary response index to evaluate their performance on the AS and suspension of particles. During the test processes, the samples were collected at a 20 cm depth at 0 h, 3 h, 36 h and 42 h and analyzed for turbidity, particle diameter size and ζ value.

2.4. Characterization and Data Analysis

Characterization and data analysis for the basic physicochemical properties and constituents of the fine loess particles are reported by Zhou et al. (2020) [37]. It is worth emphasizing that soil organic matter content was determined via the potassium dichromate oxidation method [40,41]. The data were analyzed by the statistics software SPSS 11.5 for Windows (SPSS Inc., Chicago, IL, USA) [42,43].

3. Results and Discussion

3.1. Characterization of the Endogenous Fine Loess Particles

For the three studied fine loess particle dispersion systems, their diameter size distributions were normal, their relative median particle sizes (D₅₀) were determined as 1.1 µm, 1.9 µm and 3.4 µm, and their particle concentrations were about 3.5 g/L.

These particles had relatively small differences in essential metallic oxides (Table S1). However, among these oxides, SiO₂ was more than 50% in mass percentage, further implying that the clay minerals were rich in these particles. Compared with the bulk loess matrix, these particles had no difference in metallic oxide composition but the contents, which is consistent with results reported by Tang et al. (2009) [37] and Tripathi et al. (2009) [38], proving that the particles inherit the mineral composition of their bulk matrix, which are called EFLPs in the present study. Although the EFLPs had a higher content of CaO and smaller contents of other metallic oxides, Na₂O in particular showed the greatest decreasing percentage regarding its content. This may indicate that the minerals containing Na₂O are likely to have relatively high water solubility, which might be a source for Na⁺ and result in a high concentration of Na⁺ in the groundwater over the studied plain [28,31].

The EFLPs at 3.4 µm, 1.9 µm and 1.1 µm D₅₀ had ζ values of −3.19 ± 0.16 mV, −13.9 ± 0.23 mV and −14.6 ± 0.25 mV, respectively, showing that these EFLPs had negative charges, and the larger the particle size, the smaller the absolute ζ value and the more they deposited in sediment, which is consistent with the results obtained by other researchers [44]. The absolute values were greater than 10, showing that the EFLPs had relatively good dispersity and great potential to exist and transport in groundwater.

3.2. Effect of a Single Factor on the AS and Suspension of EFLPs

3.2.1. EFLP Diameter Size

The data from the tests on the effects of diameter size on the AS and suspension of EFLPs (Figure 1) showed that regardless of their particle diameter size, their ƞ values clearly varied in the initial stage (about 6 h) of the test process and then gently reached a stable balance over 36 h in all the studied systems. This meant that although a large portion of the EFLPs had already precipitated, there was still a portion being dispersed and suspended and then becoming stable in the solutions. So, these EFLPs had the potential to be suspended and transported in the groundwater along with the groundwater flow, which is consistent with the results obtained above by analyzing the ζ values.

The ƞ values were also different for the three size particles and increased rapidly with increasing sizes, with their maximum values at 25, 34 and 39 h for EFLPs with 3.4, 1.9 and 1.1 µm D₅₀ (Figure 1), respectively. Thus, the smaller the particle size, the more difficult the AS of the particle and the stronger its dispersion and suspension in the groundwater. In any case, regardless of the particle size, the ƞ value reached a stable balance over 36 h. This was consistent with the results from the column tests [16], implying that diameter size is an important factor in the stability of EFLPs dispersed and suspended, and then a certain amount of these EFLPs could be kept suspended in the studied systems. Considering the low velocity of groundwater flow, these EFLPs could achieve suspension stability within a short transport distance in porous media, benefiting their suspension and transport along the groundwater flow.

3.2.2. Hydrochemical Component Concentration

The critical coagulation concentration (CCC), defined as the minimum concentration of counterions required to induce coagulation, is one of the most important basic properties of a colloidal dispersion and is often applied to assess its status. Once its concentration reaches or exceeds this threshold, the particles will be aggregated and deposited and then the stability of the colloidal system will be destroyed [45].

In this study, the influence of copper (Cu²⁺) ions was obvious and increased with increasing concentration (Figure 2I). The increase was great when the ion concentration was low (less than 0.1 mmol/L) and small when the ion concentration was high, hardly changing until its concentration was more than 0.1 mmol/L, indicating that the CCC value for Cu²⁺ was approximately 0.1 mmol/L in the studied systems. The same characteristic was found for the influence of sodium (Na⁺) ions, and their CCC value was about 50 mmol/L (Figure 2II). Obviously, the CCC value for Cu²⁺ was smaller than that for Na⁺, which was mainly because Cu²⁺ could provide two countercharges, while sodium ions provided only one counter charge at the same concentration [46,47]. Regarding EFLP dispersion, the CCC values for Cu²⁺ and Na⁺ were greater than their respective concentrations in the groundwater over Guanzhong Plain [29,34], implying that the EFLPs released from the loess are likely to be suspended in groundwater, further proving that EFLPs can migrate in the groundwater.

The CCC value for Cu²⁺ from Cu(NO₃)₂ was 0.65 mmol/L, as reported by Gao et al. (2011 and 2019) [48,49], which is much higher than the 0.1 mmol/L found in the present study, implying that the effect of the same hydrochemical component varies with different systems. CCC values for Na⁺ have also been reported in other references and are generally unequal and even differ greatly. For example, for Na⁺ from sodium chloride (NaCl), its CCC value was 91.6 mmol/L according to Ding et al. (2017) [50], and 62.47 (soil nanoparticles) and 45.69 mmol/L (colloidal particle) according to Xu et al. (2020) [36], implying that these differences are due to the interaction between Na⁺ and different particles. However, even in the same conditions, the CCC values reported for Na⁺ (from NaCl) and K⁺ (from KCl) were 91.6 mmol/L and 47.8 mmol/L in one report [50], respectively, and 11.38 mmol/L (KCl) and 46.84 mmol/L (KNO₃) in another reports [48,49], respectively. Gao et al. (2011, 2023) [46,47] reported that the CCC values for K₂SO₄, KCl and KH₂PO₄ were 9.915, 11.38 and 180.7 mmol/L, respectively. Katz et al. (2013) reported [51] a CCC value of 3 mmol/L for CaCl₂ and 4 mmol/L for MgCl₂. All these values are different, although they had equivalent countercharges in all studied systems. These differences are ascribed to the effects of anions on particle AS and suspension [46]. Anions and cations coexist and both inevitably have impacts on the fine particles in a solution; in other words, there may be a combined effect between their impacts [48,52,53] that needs to be further proved.

3.2.3. Hydrochemical Component

Figure 3 shows that the effects of the three hydrochemical components (NaF, NaNO₃ and Cu(NO₃)₂) on the AS and suspension of EFLPs at 1.1 µm D₅₀ were different. Among them, Cu(NO₃)₂ had the most obvious influence, mainly because the positive charge of Cu²⁺ was more than that of Na⁺ [46]. Meanwhile, although there was the same concentration (5 mmol/L) of Na⁺ from NaF and NaNO₃, the former was significantly greater than the latter in terms of the effect, which is difficult to explain in terms of the amount of ionic charge and even inconsistent with conventional understanding [54]. A similar phenomenon has been reported in other references. For example, Tian et al. (2020) [55] found that Li⁺, Na⁺, K⁺, Rb⁺ and Cs⁺ exhibit substantially different effects on the colloidal aggregation of inorganic clay minerals; the effect of KCl was bigger than that of NaCl. This proved that anions affect the aggregation, deposition and suspension of particles as cations do [46,49,56]. Therefore, since both anions and cations have an effect on EFLP existence, at the same time, there may also be interactions between their effects. This also indicates that the effects of anions and cations are not simply additive or subtractive, but have complex interaction relationships [46,57,58]. This means that a multi-factor test is better to determine the characteristics of these complex interaction relationships.

3.3. Multiple Factors’ Interaction in EFLP Suspension

The ƞ values varied quickly within the first 3 h and then gently became stable over 36 h (Figure 1, Figure 2 and Figure 3), which could have been due to the complex interaction of the factors studied above. To reveal the complex interaction and their variations, the three parameters were optimized using the software Design Expert version 13 for the AS and suspension of EFLPs at 3-h and 36-h reactions. The ƞ value as the primary response was utilized to evaluate the system performance, and the test data at 3-h and 36-h reactions are listed in

Table 2. Box–Behnken designed tests and test data at 3-h and 36-h reactions.

Run	B	C	A	Ƞ (at 3 h)	Ƞ (at 36 h)
1	NaNO3	10	1.9	54.77	94.34
2	NaNO3	5	3.4	65.71	94.82
3	NaNO3	5	1.1	28.39	84.02
4	NaF	1	3.4	15.27	80.13
5	Cu(NO3)2	10	1.9	94.27	99.18
6	Cu(NO3)2	5	3.4	97.63	99.14
7	NaNO3	1	1.9	16.09	79.15
8	Cu(NO3)2	1	1.9	83.97	98.69
9	NaF	10	3.4	87.65	97.16
10	NaF	10	1.1	12.44	78.98
11	Cu(NO3)2	5	1.1	90.54	99.37
12	NaF	5	1.9	9.04	85.96
13	NaF	5	1.9	9.52	89.03
14	NaNO3	5	1.9	14.25	90.98
15	NaNO3	5	1.9	17.26	89.25
16	NaNO3	5	1.9	17.96	94.02
17	NaF	1	1.1	5.61	78.92

.

3.3.1. Multiple Factors’ Interaction in EFLP Suspension at 3-h Reaction

The test data (Table 2) were analyzed by standard analysis of variance (ANOVA) (

Table 3. Summary of statistics of the quadratic model fitted to the test data using RSM analysis at 3-h reaction.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F-Value	p-Value	Significant/Non-Significant
Model	20,397.73	9	2266.41	70.37	<0.0001	significant
A	4240.13	1	4240.13	131.65	<0.0001	significant
B	2662.29	1	2662.29	82.66	<0.0001	significant
C	2329.83	1	2329.83	72.34	<0.0001	significant
AB	196.98	1	196.98	6.12	0.0426	significant
AC	255.84	1	255.84	7.94	0.0258	significant
BC	1245.07	1	1245.07	38.66	0.0004	significant
A2	8444.89	1	8444.89	262.21	<0.0001	significant
B2	23.98	1	24.04	0.75	0.4167	non-significant
C2	228.67	1	228.67	7.13	0.0323	significant
Residual	225.46	7	32.21
Lack of Fit	154.31	3	51.44	2.89	0.1657	non-significant
Pure Error	71.15	4	17.79
Cor Total	20,623.18	16

) and the Box–Behnken design was fitted with the second-order polynomial equation (Equation (2)).

ƞ = 19.50 + 23.60A + 18.64B + 17.12C − 7.00AB − 7.82AC + 17.20BC + 44.79A² + 2.42B² + 8.32C²

(2)

The statistical significance of Equation (2) was evaluated by the F-test for ANOVA (Table 3). There was only a 0.01% chance that the model’s F-value could occur due to noise. The model’s F-value of 70.37 and p-value (<0.0001) indicated that the model was significant. Hence, Equation (2) could be used in the present study. The p-values for the three factors were all less than 0.0001, indicating that their influences were significant. The p-values for AB, AC and BC were 0.0426, 0.0258 and 0.0004, all less than 0.05, showing that their interaction was significant in the order of BC > AC > AB [59].

Furthermore, the adjusted R² value was approximately 0.975, whereas the predicted R² value was higher at around 0.989, which was very close to the experimental level, confirming a satisfactory adjustment of Equation (2) to the test data.

The term “Lack of Fit (LOF)” refers to the contrast between estimated and obtained values and the repetition of actual value errors [60]. The LOF of Equation (2) stayed at 0.19, which revealed that Equation (2) was well fitted to the experimental findings. Also, variation in the data was measured by the coefficient of variation (CV), which was 13.39%. “Adequate Precision” measures the signal-to-noise ratio. A ratio greater than 4 is desirable [39]. In the present study, a ratio of 20.863 was obtained for the 3-h reaction, indicating an adequate signal. All this indicated that Equation (2) had high reproducibility.

An assessment of Equation (2)’s desirability was performed through an investigation of residuals. The normal distribution plots revealed whether the residual values were close to a straight line. Figure 4 represents a random scatter plot of the actual and predicted n values, and the actual and predicted points are almost equal. Thus, Equation (2) could be effectively used in the present study.

It is worth noting that the negative or positive sign of each term showed antagonistic or synergistic effects of the term on the ƞ value [46]. The signs of all the parameters in Equation (2) were positive, showing that they all contributed to ƞ; in particular, their related values were 23.60, 18.64 and 17.12, indicating that particle size was the most important, followed by hydrochemical component and its concentration, which agreed with the results obtained by the single-factor test described above (Figure 2 and Figure 3).

The ƞ values were different for different hydrochemicals (Figure 5I-a,I-A). In one condition, the ƞ value was the greatest for Cu(NO₃)₂, followed by NaNO₃, and the smallest for NaF, which supports the results from Figure 3 above. No matter the hydrochemical component, the ƞ value increased with increasing concentration. These results agreed with those obtained in the single-factor tests described above (Figure 2 and Figure 3) and reported by Huang and Yang (2020) [50] and Gao et al. (2023) [46]. The contour line for the interaction of BC (Figure 5I-b,I-B) was elliptical, indicating that the interaction was significant [39]. The straight lines of the hydrochemical components and concentrations were approximately parallel to the short and long axes of the ellipse, showing that the effects of hydrochemical composition were more significant than those of hydrochemical concentration on particles AS and existence in the studied systems with a 3-h reaction.

No matter the hydrochemical component, the ƞ value increased as the particle size increased (Figure 5I-c,I-C). This result agreed with those obtained in the single-factor tests described above (Figure 2). The contour line for the interaction of BA was also elliptical, and the straight lines for hydrochemical component and particle size were almost parallel to the short and long axes of the ellipse, showing that the effect of hydrochemical component was more significant than that of particle size in a 3-h reaction.

The ƞ value increased as either the hydrochemical concentration or particle size increased (Figure 5I-c,I-C), similar to the results described above (Figure 2 and Figure 3). The contour line for their interaction was also elliptical, and the straight lines for particle size and hydrochemical component were approximately parallel to the short and long axes, showing that the effects of particle size were more significant than those of hydrochemical concentration in the studied systems.

In conclusion, there was a clear interaction between the studied factors, and their significance was ranked in the order of hydrochemical component, diameter size and component concentration, showing that these interactions had a certain dependence on the hydrochemical components in a 3-h reaction.

3.3.2. Multiple Factors’ Interaction on EFLP Suspension at 36-h Reaction

As for the test data for the 3-h reaction (Supplementary Material), the second-order polynomial Equation (3) was obtained for the test data for the 36-h reaction, and Equation (3) could be effectively used in the present study.

ƞ = 91.85 + 4.87A + 4.74B + 3.97C − 3.64AB − 2.87AC + 4.21BC + 6.84A² − 4.29B² − 3.77C²

(3)

The ƞ value was different for different hydro-chemical components: the ƞ value was the greatest for Cu(NO₃)₂, followed by NaF, and the smallest for NaNO₃ (Figure 6II-a,II-A). This order was different from that obtained for the 3-h reaction (Figure 5). The contour line for the interaction of hydro-chemical component and concentration in the 36-h reaction was saddle instead of elliptical in nature, showing that the interaction between the corresponding variables was significant and their effects were almost equal in magnitude [61]. These differences showed that the roles of the two factors changed in their interaction processes and indicated that the influence of the hydrochemical components varied along the groundwater flow.

The interaction between hydrochemical component and particle size (Figure 6II-b,II-B) was roughly the same as that between hydrochemical component and concentration in the 36-h reaction (Figure 6II-a,II-A) discussed above. The contour was saddle instead of elliptical in nature and the relative strength of their influence depended on the components and particle size in the 36-h reaction, which was different from the 3-h reaction (Figure 5I-b,I-B). This further proved that the influence of the hydrochemical components varied along the groundwater flow. However, the interaction between component concentration and the particle size in the 36-h reaction (Figure 6II-c,II-C) was almost the same as that in the 3-h reaction (Figure 5 I-c,I-C), showing that the interaction between component concentration and particle size for 1.1 µm particle sediments almost remained stable during the whole experimental process. Thus, all this showed that the role of the hydrochemical component weakened while the role of particle size strengthened along the groundwater flow path. Ultimately, the significance ranked in the order of hydrochemical component, diameter size and hydrochemical concentration.

Comparing Equations (2) and (3) showed that the symbols of each coefficient for the three factors were not changed, indicating that they always had the potential to enhance the particles’ AS and suspension along the groundwater flow path, but their coefficient values in Equation (3) were smaller than those in Equation (2), showing that their potential decreased with increasing reaction time, as discussed above. Further analysis of these values revealed that the values decreased by nearly 75% over the 36-h reaction compared with the 3-h reaction, implying that the main hydrochemical components were more conducive to EFLP AS and suspension along the groundwater flow path, which was also in turn beneficial to the transport in the groundwater system.

Although the studied factors enjoyed a combined effect on particle AS and suspension, their effects weakened throughout the whole reaction process, and the relative contribution of the component decreased while the contributions of the component concentration and particle size both increased, showing that the relative contributions for these studied factors were changed in magnitude and tended to be equal and stable. Therefore, considering the effect characteristics of the studied factors, the CCC value for each solute depended on these studied factors, just like the results obtained above for the single-factor experiment.

3.4. CCC Value Determined Based on DLVO Theory

According to the results of the SEM analysis above and the EFLPs’ diameter size, the EFLPs could be considered spherical in geometric structure, and their interactions were mainly dominated by face-to-face association. The total interaction energy between two surfaces is usually calculated by the sum of the van der Waals force (V_R) and electrostatic repulsion (V_A) [62]:

$${\mathrm{V}}_{\mathrm{T}}={\mathrm{V}}_{\mathrm{R}}+{\mathrm{V}}_{\mathrm{A}}$$

(4)

V_R and V_A can be determined by Equations (5) and (6), respectively:

$${\mathrm{V}}_{\mathrm{A}}=-{\displaystyle \frac{\mathrm{A}\mathrm{r}}{12}}$$

(5)

$${\mathrm{V}}_{\mathrm{R}}={\displaystyle \frac{64\mathsf{\pi }\mathrm{r}{\mathrm{n}}_0{\mathrm{k}}_{\mathrm{B}}\mathrm{T}}{{\mathsf{\kappa }}^2}}{\mathsf{\gamma }}^2\mathrm{e}\mathrm{x}\mathrm{p}\left(-\mathsf{\kappa }\mathrm{h}\right)$$

(6)

where r is the ionic radius, n₀ is the number of background anions and cations determined from the molar concentration of background electrolyte, k_B is the Boltzmann constant (1.4 × 10⁻²³ J/K), T is the absolute temperature (K), A is the Hamaker constant (2.3 × 10⁻²⁰ J), h denotes the distance between particle surfaces and κ is the reciprocal of the Debye length, which can be calculated by Equation (7):

$$\mathsf{\kappa }={({\displaystyle \frac{1000{\mathrm{e}}^2{\mathrm{N}}_{\mathrm{A}}{\sum }_{\mathrm{i}}^2{\mathrm{C}}_{\mathrm{i}}}{{\mathsf{\epsilon }}_0{\mathsf{\epsilon }}_{\mathrm{r}}{\mathrm{k}}_{\mathrm{B}}\mathrm{T}}})}^{1/2}$$

(7)

where N_A is the Avogadro constant (6.0 × 10²³), C_i is the electrolyte concentration, ε₀ is the vacuum permittivity (8.85 × 10⁻¹² C²/J/m) and ε_r is the dielectric constant of water (78.36 F/m).

γ as a parameter depended on the surface potential (ψ₀) of the particles and could be calculated via Equation (8):

$$\mathsf{\gamma }={\displaystyle \frac{\mathrm{e}\mathrm{x}\mathrm{p}(\frac{\mathrm{z}\mathrm{e}{\mathsf{\psi }}_0}{2{\mathrm{k}}_{\mathrm{B}}\mathrm{T}})-1}{\mathrm{e}\mathrm{x}\mathrm{p}(\frac{\mathrm{z}\mathrm{e}{\mathsf{\psi }}_0}{2{\mathrm{k}}_{\mathrm{B}}\mathrm{T}})+1}}$$

(8)

where z is the charge of background ions and e is the basic electric charge (1.6 × 10⁻¹⁹ C).

The variation of the electrical interaction energy between two spherical particles as a function of fine particle size was reported in [63]; so, in order to facilitate comparison with other research results, 1.1 µm fine loess particles were selected for the present study. As mentioned above, with CCC as a threshold, which was close to the molar concentration of the background electrolyte, C_i = CCC, the following Equations (9) and (10) needed to be satisfied [62]:

$${\mathrm{V}}_{\mathrm{T}}=0$$

(9)

$${\displaystyle \frac{d{V}_T}{dh}}=0$$

(10)

Thus, by substituting Equation (5) into Equation (4), we obtain Equation (11).

$$V_T={\displaystyle \frac{64\pi r{n}_0{k}_{B}T}{{\mathsf{\kappa }}^2}}{\mathsf{\gamma }}^2\exp (-\mathsf{\kappa }\mathrm{h})-{\displaystyle \frac{Ar}{12\mathrm{h}}}$$

(11)

Equation (9) can be expressed as Equation (12).

$${\displaystyle \frac{d{V}_T}{dh}}=-{\displaystyle \frac{64\pi r{n}_0{k}_{B}T}{{\mathsf{\kappa }}^2}}{\mathsf{\gamma }}^2\exp \left(-\mathsf{\kappa }\mathrm{h}\right)+{\displaystyle \frac{Ar}{12h^2}}$$

(12)

Substituting Equation (12) into Equation (11), Equation (13) is obtained:

$${\mathsf{\kappa }}^3={\displaystyle \frac{\mathrm{768,000}\mathsf{\pi }{\mathrm{N}}_{\mathrm{A}}{{\mathrm{C}}_{\mathrm{C}\mathrm{C}\mathrm{C}}\mathrm{k}}_{\mathrm{B}}\mathrm{T}{\mathsf{\gamma }}_0^2}{\mathrm{A}\mathrm{e}}}$$

(13)

Therefore, the CCC value can be determined by Equation (14).

$$\mathrm{C}\mathrm{C}\mathrm{C}=1.51\times {10}^{80}{\displaystyle \frac{{\left({\mathsf{\epsilon }}_0{\mathsf{\epsilon }}_{\mathrm{r}}\right)}^3{\left({\mathrm{k}}_{\mathrm{B}}\mathrm{T}\right)}^3{\mathsf{\gamma }}_0^4}{{\mathrm{N}}_{\mathrm{A}}{\mathrm{e}}^2{\mathrm{A}}^2}}{\displaystyle \frac{1}{{\mathrm{z}}^6}}$$

(14)

The electric potential energy is dependent upon the amount of charge on the object experiencing the field and its location within the field. The influence of ions on the diffusion layer and their electrical properties of fine particles can be comprehensively manifested as the surface site accumulation on the particles and their effects, namely, the moving sites, which are generally represented as ζ [64]. Thus, in the present study, for EFLPs with 1.1 µm D₅₀, the surface potential could be considered equal to the ζ value and employed in the calculation process. So, γ² and κ were determined as 0.98 and 1 × 10⁸/m, respectively. Then, according to Equation (14), CCC values were obtained for Cu(NO₃)₂ and NaF as 0.12 mmol/L and 54.04 mmol/L, respectively. Comparing their values (0.1 mmol/L and 50 mmol/L) determined by the tests above (Figure 2 and Figure 3) showed that their errors were rather small, and even the results obtained by the two methods were approximately consistent. So, the CCC values that were determined based on the DLVO equation with electrostatic repulsion replaced by the ζ value were acceptable.

Indeed, there was an error between the results of the test and the theoretical methods. This phenomenon was also reported in other studies [60,61,62,63,64,65,66,67]. For example, the CCC value for NaCl was reported by Ding et al. (2017) as 91.6 mmol/L [50], by Xu et al. (2020) as 62.47 mmol/L [36] and by Tomba’cz and Szekeres (2004) as 100 mmol/L [68], respectively, showing that there is error among them. Even in the present study, the errors for Cu(NO₃)₂ and NaF were not the same, and the former was obviously smaller than the latter. All these errors were likely caused by numerous influent factors including flow type, flow strength, anion, cation and ionic valence, and nonaqueous hydrochemical components [46,69], and the CCC value is probably affected by the combined effect of ions, which is consistent with the results obtained from the multi-factor tests above, and also worth further exploration.

The CCC values determined by both the test and DLVO theoretical methods for Cu(NO₃)₂ and NaF were greater than those for the groundwater, indicating that the EFLPs were suspended and present in the groundwater and thus transported and even cotransported with pollutants in the groundwater, which may be one of the main reasons for the occurrence of chromium, arsenic and other pollutants in the groundwater over Guanzhong Plain, China [28,30,31].

4. Conclusions

To the best of our knowledge, this is the first study focused on the suspension of EFLPs in groundwater systems over loess regions. EFLPs with 1.1 µm, 1.9 µm and 3.4 µm D₅₀ had large ζ values and a relatively high potential to be dispersed and exist in the studied groundwater. The conventional hydrochemical components and their concentrations and particle size had significant impacts on the AS and suspension of EFLPs, and their impacts changed along the groundwater flow path. Meanwhile, both anions and cations had impacts and interactions regarding this behavior and exhibited a combined effect, whereby the effect of component concentration strengthened while that of hydrochemical component got weakened along the path. ζ was employed to represent electrostatic repulsion to determine the CCC value for the EFLPs in the studied systems based on the DLVO theory, and the CCC values were determined to be 0.12 mmol/L and 50.04 mmol/L for Cu(NO₃)₂ and NaF, almost consistent with the results of 0.1 mmol/L and 50 mmol/L, respectively. These CCC values were greater than their relative concentrations in the studied groundwater. All these imply that the hydrogeochemical conditions are beneficial to the suspension of EFLPs, with effects being enhanced along the groundwater flow. EFLPs can be present, suspended and then transported and even cotransported with adsorbed pollutants in the groundwater over Guanzhong Plain, China. These results deepen our understanding of the behavior mechanisms of fine soil particles and further help in predicting their environmental behaviors in groundwater systems.