**1. Introduction**

The intensification of agricultural land use is of great concern mainly due to its environmental impacts in terms of chemical, physical, and biological degradation (e.g., soil loss, faster mineralization of organic matter, biological disturbance, and chemical pollution) [1]. When agrochemicals, such as fertilizers, insecticides, herbicides, and other pesticides, are applied in a cropping to improve plant growth, their organic and inorganic molecules can become readily available in the soil solution through rainwater or irrigation. In other words, since the transport of solutes of the solution in soil is the primary vehicle for groundwater contamination [2], the main driver of water pollution is the migration of contaminated solution from topsoil to groundwater.

Transport processes depend on inherent soil properties and are influenced by crop management practices, including crop rotation and tillage [3]. The adoption of agricultural practices such as crop rotations can improve soil quality, and the choice of cover crops plays an important role in soil properties. Thus, the adoption of different

crop rotations will have different effects on soil aggregation [4]. On the other hand, the formation of soil aggregates is responsible for determining the soil structure and consequently the pore network [5]. Therefore, changes are also observed in the water and solutes movement in the soil. The roots effect on the soil structure varies among plants [6], and apparently the main factor that reflects in the movement of water and consequently dissolved solutes in the soil is the root exudation of organic substances, mainly mucilage [7–9], a polymeric gel released by most plant roots [10]. In addition, the formation of galleries or channels in the soil due to root decomposition also plays an important role in this process. These channels can modify soil porosity and soil permeability, further affecting the dynamics of water flow and nutrient transport within the soil.

Soil structure defines the pore geometry that controls soil water dynamics. Water movement and solute transport in soils are also influenced by soil aggregation, pore volume, pore size distribution, and pore connectivity [11]. Typically, field soils have different soil properties that vary spatially as a consequence of pedogenic processes [12].

The movement and retention of water in soil is very important in agriculture, and the physical attributes that reflect their intensities are the hydraulic conductivity and the water retention curve, respectively [13]. The degree of soil compaction typically decreases the saturated hydraulic conductivity as a result of the reduction in macropores [14, 15]. Soil hydraulic properties such as available water content and hydraulic conductivity can be used to assess the long-term effects of soil land use and management [16]. Bagnall et al. [17] highlighted field capacity as an interesting soil health indicator to evaluate the impact of soil management practices on hydraulic properties, mainly measured in undisturbed soil samples. In addition, soil bulk density, soil organic carbon, and aggregate stability can be important indicators that reflect the response of management practices.

### **2. Water flow in saturated and unsaturated soils**

In 1855, Henry Darcy carried out an experiment on water movement in columns of sand under saturation and steady-state conditions and concluded that under these conditions, flow rate is (i) directly proportional to the difference between piezometric heads acting on the ends of the sand columns, (ii) directly proportional to the cross-sectional area of the sand columns, and (iii) inversely proportional to the length of the columns. The application of *Darcy's Law* is very common nowadays in all fields of science that involve studies about flow in saturated porous media [18].

In **Figure 1**, we can see a saturated uniform soil column scheme with a constant water head (*h*1) at the top (*z = L*) and a constant water head (*h*2) at the bottom (*z = 0*). *H*1 is the piezometric head at the top and *H*2 is the piezometric head at the bottom of the soil column, and water is flowing under steady-state conditions.

The Darcy equation obtained from the conclusions of his experiment is Eq. (1):

$$Q = K\_{\text{sat}} A \frac{H\_{1\text{-}} H\_2}{L} \tag{1}$$

where *Q = Vw/t* is the water flow (*m*<sup>3</sup>  *s*−1), *Vw* is the volume of water (m3 ) measured in the time *t* (*s*), *Ksat* is the saturated soil hydraulic conductivity (*ms−1*), *A* is the *Movement of Water and Solutes in Agricultural Soils DOI: http://dx.doi.org/10.5772/intechopen.114086*

#### **Figure 1.** *A simplified diagram of Darcy's experiment.*

soil cross sectional area (*m2* ), *H1-H2* is the difference in piezometric head (*m*), and *L* is the length of the column (*m*).

The equipment most commonly used in soil physics laboratories to determine *Ksat* has been the constant water head permeameter in which Darcy's experiment (diagram in **Figure 1**) is developed, but using smaller soil columns with undisturbed (or disturbed) structure. Normally in the permeameter, we set *h1 = h* slightly greater than zero, *h2 = 0*, and also *H*2 *= 0* (reference level coincident with column bottom soil surface) so that *H1 = h + L*. With these fixed values for h1, *h2*, *H1*, and *H2* in Eq. (1) and explaining *Ksat*, we get Eq. (2):

$$\mathbf{K}\_{\rm sat} = \frac{V\_{\rm w} \mathbf{L}}{A t \left(\mathbf{h} + \mathbf{L}\right)} \tag{2}$$

Giving (Eq. (1)) a mathematical treatment and including the concept of water potentials to the Darcy equation (see item 3), it can be written as:

$$q = -K\_{\rm sat} \frac{d\psi\_t}{dz} \tag{3}$$

where now *q = Q/A* is the water flow density (*m/s*); *ψt* is the total potential (*m*), being equal to the sum of the gravitational potential *ψg* (*m*) and the pressure potential *ψp* (*m*); *z* is the vertical position coordinate (*m*); and *dψ/dz* is the total potential gradient; the negative sign has been included to indicate that when *q > 0*, the flow is in the positive direction of *z* (upwards), and when *q < 0*, the flow is in the negative direction of *z* (downwards).

Under unsaturated soil conditions, the development of the equation for water flow under steady-state conditions involved the work of Buckingham [19] and Richards [20] and is currently known as the Darcy–Buckingham equation (Eq. (4)):

$$q = -K(\theta) \frac{d\nu\_t}{dz} \tag{4}$$

In this equation, *K* is a function of the water content *θ* and *ψt = ψ g + ψm*, where *ψ<sup>m</sup>* is the matric potential, which is also a function of *θ*.

Note that the Darcy–Buckingham equation is also valid for the saturation condition since, under this condition, just replace *K(θs*) by *Ksat* and *ψm* by *ψ <sup>p</sup>*; *θs* is the water content in saturated soil.

The equation for water flow in soil under nonsteady-state or transient conditions (flow characteristics vary with time and position) is the Richards differential equation, which is the combination of the Darcy–Buckingham equation with the continuity equation. The continuity equation for the flow density of water in the soil in the vertical direction is Eq. (5) below:

$$\frac{d\theta}{dt} = -\frac{dq}{dz} \tag{5}$$

which combined with the Darcy–Buckingham equation also in the vertical direction results in the Richards equation (Eq. (6)):

$$\frac{d\theta}{dt} = \frac{d}{dz}\left[K(\theta)\frac{d\mu\_t}{dz}\right] \tag{6}$$

The soil hydraulic conductivity that appears in equations of Darcy–Buckingham and Richards has been defined as the soil ability to transmit water [21].

Besides the constant water head method that is the own Darcy experiment to determine *Ksat* (see Eq. (3)), Deb and Shukla [22], in a complete bibliographic review, address about laboratory, field, correlation, and estimation methods for the determination of saturated and unsaturated soil hydraulic conductivity (**Figure 2**).

We believe it is worth noting that since it is difficult to measure the *K(θ)* function under field conditions is difficult, it can be calculated theoretically from data related to water retention in the soil, which is easier to measure [23–29]. In the Mualem-van Genuchten model [24, 25] from SWRC data, a relative soil hydraulic conductivity *Kr* as a function of soil water content *θ*, the *Kr(θ)* function, is calculated by the equation developed by van Genuchten [25] for this function, based on the work of Mualem [24], which has been called the Mualem-van Genuchten equation. To calculate *Kr(θ)* with this equation, there is only one parameter that needs to be known, which comes from the SWRC fitting equation used by van Genuchten [25]. *K(θ)* is then calculated by *K(θ) = Ksat x Kr (θ)*, where *Ksat* can be determined, for example, by the constant water head permeameter.

Now, let's briefly discuss the importance of soil hydraulic conductivity.

Saturated hydraulic conductivity (K*sat*), for instance, is very important for soil management in terms of soil erosion. Since soil structure and texture determine the geometry of the soil pores, they are essential factors influencing soil hydraulic conductivity [13]. Tillage and intensive use without conservation practices cause soil compaction and indirectly change soil hydraulic properties [30]. A decrease in soil

#### **Figure 2.**

*Soil hydraulic conductivity determination methods. Source: Adapted from: Deb and Shukla [22].*

porosity and an increase in soil bulk density are the main consequences of soil compaction: conducting pores (e.g., macropores and mesopores) are the most affected. A decrease in conducting pores and an increase in micropores (retention pores), in turn, decrease *Ksat* and change *K(θ*) function. Soil hydraulic conductivity is higher when the soil pore space is higher, when the soil is fractured (*Ksat* in this case), when the soil is well aggregated with better pore connectivity than when it is tightly compacted, and it also depends on the geometry of the pore space. Other aspects, such as changes in the composition of the exchange complex (e.g., the concentration of solutes) and the dispersion of clay particles clogging the pores, can reduce the conductivity [31]. Anyway, soil hydraulic conductivity under saturated and unsaturated conditions plays a fundamental role in estimating water and solutes movement and in studying soil-plant-water interactions [22].

Unsaturated *K* can be determined (i) in the laboratory using steady-flow methods that induce evaporation or infiltration (e.g., soil column under constant flow) or by transient methods (e.g., pressure plate method, by instantaneous profile method, and others); (ii) under field conditions, the instantaneous profile method and flux control methods; and (iii) finally by estimation methods using empirical equations or statistical models.

### **3. Water potentials and available water content in soil**

Understanding the potential energy concepts of water in soil is crucial as they aid in predicting the potential movement of water in soil. The universal tendency of a body in nature is to move in response to its total potential energy (summation of the several potential energy components resulting from the several existing force fields acting in the body); i.e. the body moves from a position where its total potential energy is higher to a position where it is lower [32–34].

For convenience, in the case of water movement in the soil, it was defined the *total water potential in the soil* (ψ *<sup>t</sup>* ) as the difference between the total potential energy in the units of mass, volume, or weight of water inside the soil (ε) and the total potential energy in the units of mass, volume, or weight of the same water in the soil, but out of the soil (ε*0*), that is, free from the influence of the matrix or free water also called *standard water.* Thus, the movement of water in the soil always takes place from the position where total water potential is highest to the position where it is lowest.

According to the force fields acting on the water in the soil, it follows that:

$$
\boldsymbol{\nu}\_{\rm t} = \boldsymbol{\nu}\_{\rm g} + \boldsymbol{\nu}\_{\rm p} + \boldsymbol{\nu}\_{\rm n} + \boldsymbol{\nu}\_{\rm m} \tag{7}
$$

where ψ εε = − <sup>0</sup> *g gg* is the gravitational potential, ψ εε = − <sup>0</sup> *pPP* is the pressure potential, ψ εε = − <sup>0</sup> *n nn* is the pneumatic potential, and ψ εε = − <sup>0</sup> *mmm* is the matric potential. ε ε, *g P* , ε ε , and *n m* are gravitational, pressure, pneumatic, and matric potential energies of the unit mass, volume, or weight of the water in the soil, respectively, and εεε ε 000 0 *gPn m* , , , and are gravitational, pressure, pneumatic, and matric potential energies of the unit mass, volume, or weight of the standard water, respectively.

The matric potential has the greatest influence on the total potential under unsaturated soil conditions and it will be more emphasized in this chapter. The retention of water by the soil is controlled by the capillary and adsorption forces (i.e., components of the matric forces) (**Figure 3**).

Soil pore space heterogeneity does not allow to obtain a theoretical equation for the matric potential [29]. Consequently, devices were developed to establish a relation between matric potential and soil water content. The curve resulting from this relation is the soil water retention curve (SWRC) (**Figure4**). **Figure4** shows two examples of SWRC for clayey and sandy soils. SWRC can be used to estimate soil available water content, among other soil science applications. SWRC is affected by soil texture and structure. Soil structure is more important at higher matric potentials, while texture is more important at lower potentials. However, soil structure and texture together determine water retention and conduction throughout the SWRC. Using SWRC, it is possible to study the effects of compaction and management on soil structure (i.e., porosity, volume, distribution, and frequency of pores) and therefore on the soil physical-hydric properties.

There is a relationship between soil water content and water availability to plants. When the soil is saturated, water drains easily and is available to plants for a short period of time. As soil water content decreases and fast-draining macropores empty, the water-holding force of soil rises, decreasing considerably its downward movement. The soil reaches its field capacity (FC) at this stage, with water held only in micropores. The FC is typically referred to the "upper limit of soil water availability". The use of water by plants leads water to be also removed from the larger micropores, remaining in the smaller micropores and around the solid particles. When water is strongly retained by the soil matrix and the water uptake becomes very slow due to the high suction force demanded by the plants, the permanent wilting point (PWP) occurs. The PWP is also defined as the "lower limit of soil water availability" because the absorbed water content is no longer sufficient to maintain plant turgidity. The available water content is related to soil structure and texture. Clayey soils have a

*Movement of Water and Solutes in Agricultural Soils DOI: http://dx.doi.org/10.5772/intechopen.114086*

#### **Figure 4.**

*Typical soil water retention curves (SWRCs) of clayey and sandy soils.*

higher available water content than sandy soils because their greater specific surface area allows for greater water retention. Usually, clayey soils have a pore network with smaller pores (micropores) that are electronically charged and have a greater ability to hold water than sandy soils.

Soil organic matter (SOM) can also affect water availability due to its high water holding capacity. Consequently, an increase in SOM will result in an increase in the available water content. Costa et al. [35] observed higher FC and PWP in the soil surface layer due the higher SOM content in this layer. The effects of SOM on water availability are dependent on several factors. Lal [36] highlighted factors influencing this phenomenon, such as inherent soil properties, crop management, land use, and others (**Figure 5**).

Isolate measurements of soil physical properties should not always reflect the soil condition for plant growth and development [37]. Crop production can be limited by water and soil physical parameters [38]. Only when these limitations are removed can the difference between FC and PMP, i.e., the water available to plants, reflect the effect of soil structure on plant growth and development and crop production. However, this range of water content can be integrated into an indicator that overcomes the limitation of isolated measurements: the least limiting water range (LLWR) [39].

Initially, Letey [40] conceptualized and defined a range of non-limiting water contents for plant growth, called the non-limiting water range (NLWR). This parameter can be affected by mechanical resistance and/or aeration, especially in poorly structured soils with high bulk density, and is considered a way to relate soil physical properties to plant growth. It is based on the fact that mechanical resistance inhibits root growth, while roots require accessible water reservoirs and oxygen [38]. The NLWR was improved by Silva et al. [41] to quantify physical and structural soil quality. These authors used the term least limiting water range (LLWR) to describe this concept, which is an improvement over the NLWR. It consists of the range of soil water content in which limitations to plant growth are minimal and was considered an indicator of soil function for biomass production [42]. The LLWR can identify physical conditions that influence the functionality of physical, chemical, and biological processes [43].

The LLWR is a range of soil water contents that delimits critical soil physical limits for root growth (**Figure 6**) [38]. Basically, it is defined by an upper limit (wetter)

#### **Figure 5.**

*Factors that influence soil water retention and available water content. Source: Lal [34].*

*Movement of Water and Solutes in Agricultural Soils DOI: http://dx.doi.org/10.5772/intechopen.114086*

#### **Figure 6.**

*The concept of least limiting water range (LLWR): (a) Soil water content as a function of soil bulk density based on changes in FC, PWP, and of soil water contents corresponding to air-filled porosity (AFP) and soil penetration resistance (SR); (b) LLWR as a function of soil bulk density. Source: Keller et al. [38].*

and a lower limit (drier), where plant growth is not restricted [41]. The upper limit is considered to be the FC or the water content corresponding to 10–15% of soil aeration, while the lower limit is the PWP or the water content corresponding to a soil resistance (SR) value that limits root growth (varying between 2 and 4 MPa). However, other authors have made adjustments to the LLWR by replacing the PWP of the LLWR with the critical water content resulted in good results for both a perennial crop and crop rotations in Brazil [44, 45]. Recently, Silva et al. [46] added the critical soil water content for the crop at each phenological stage as the lowest limit of LLWR.

In a simple way, the LLWR allows the identification of physical properties that act as a limiting factor with increasing soil compaction as a function of bulk density (**Figure 6**). The LLWR can be used to evaluate the physical and structural quality of soils for crops grown in different soils and management systems and also in relation to processes related to nitrogen dynamics and soil carbon [39]. It is considered an effective index for influencing grain yield and for detecting the effects of tillage and cover crops [47, 48].

### **4. Movement of solutes in soils**

Water and solute movement occur simultaneously in the soil. Understanding the processes of solute transfer in this environment, as well as the ionic interactions between the liquid and solid phases, is important for establishing management practices in the soil–plant–atmosphere system. Contaminants (e.g., heavy metals, salts, and organic molecules) and fertilizers can be rapidly transported by water flow into streams or soil layers where water is stored [49]. These substances are the main sources of groundwater and surface water contamination [50, 51]. To assess and reduce risks to human health, it is necessary to predict and know the mechanisms that influence the movement and fate of contaminants in runoff water [52]. Water flow and mass transfer in soils are very complex at the field scale due to the process of variation of fluid properties in the soil [53].

Solute movement through a porous medium is the process of displacement of ions in solution under unsaturated or saturated conditions of that medium [49]. In a porous medium, the mixture of two miscible fluids can be analyzed by different mathematical models [54]. Two processes dominate the flow of ions in soils: mass transfer and

diffusion. Mass transfer refers to the movement of ions by the water flow, whereas diffusion process is the movement of ions due to gradient of activity of the ions [55].

**Figure 7** shows a diagram of an experimental setup of a miscible displacement experiment. In this scheme, with the water already flowing in the column, when the solution of a solute of interest of concentration *C0* is placed in the column, it displaces the water; that is, in this case, the solute solution is the displacing fluid and the water is the displaced fluid. The study of solute movement is carried out using *Breakthrough Curves* (BTCs). BTCs are defined as the graph of *C/C0* (solute relative concentration) as a function of pore volume (*Qt/V0*), where *C* is the concentration found in the effluent, *C*0 is the initial concentration of the solute in the displacing fluid, *Q* is the volume of effluent collected per unit time, *t* is the time elapsed since the displacing liquid was added, and V0 is the volume of the soil column occupied by the fluid [54–56].

Miscible displacement is the process that occurs when one liquid mixes with and displaces another liquid. The mixture occurs in the interface of the two fluids by diffusion and mass flow and depends on the fluid properties, such as viscosity and ionic concentration, and the material in which the fluids are contained. In the case of solute movement in soil, the properties are inherent to the soil. The solute transport process varies with the surface of the medium (adsorption and desorption processes, among others) and depends on the degree of saturation of the medium and the structure of the medium (e.g., pore size distribution, pore connectivity, and type of soil aggregates). Solute movement is the result of complex phenomena, and the interactions of this process can be analyzed by comparing measured data with simplified models [54].

**Figure 7.** *Schematic representation of the miscible displacement experiment.*

*Movement of Water and Solutes in Agricultural Soils DOI: http://dx.doi.org/10.5772/intechopen.114086*

Physical-mathematical models are developed to describe solute transport in soil. They are valuable tools in the study of this process, and their success depends on the degree of reliability of the involved variables. The porous matrix controls solute transport through different flow velocities and through different water viscosities in pores of different sizes. The greater the transport distance, the greater the spatial distance of molecules or colloids transported in coarse and fine pores, respectively [57]. The principal equation describing solute transport in soils is the convection-dispersion equation (CDE), in which solute movement is a result of several processes, including diffusion and microscale variations in water flow velocity [58]. Transport models of a chemical species in the soil–air–water system are considered using the CDE [59].

The CDE is nothing more than the continuity equation in which the solute total flux density in the soil (*J*) is equal to the sum of the solute diffusion flux density (*f*) and the solute convection flux density (mass flux) (*j*). Thus, in the vertical direction:

$$\frac{d\theta \mathbf{C}}{dt} = -\frac{d\mathbf{J}}{dz} \tag{8}$$

Since = + =− + ′ , *dC J f j D qC dz*

then

$$\frac{d\theta \mathcal{C}}{dt} = -\frac{d}{dz}\left[-D'\frac{d\mathcal{C}}{dz} + q\mathcal{C}\right] \tag{9}$$

In this equation:

*θ* = soil water content (*m*<sup>3</sup>  *of solution/m*<sup>3</sup>  *of soil*), *C* = solute concentration (*kg of solute/m*<sup>3</sup>  *of solution*), *D*′ = coefficient of diffusion (dispersion) in soil (*m*<sup>3</sup>  *of solution/m of soil.s*), *q* = flow density of solution (water) in soil (*m*<sup>3</sup>  *of solution/m*<sup>2</sup>  *of soil.s*), *t* = time (*s*), and. *z* = vertical coordinate of position (*m of soil*). Assuming that *θ*, *D*′, and *q* are constant, Eq. (9) becomes:

$$\frac{d\mathbf{C}}{dt} = D \frac{d^2\mathbf{C}}{dz^2} - \overline{\nu} \frac{d\mathbf{C}}{dz} \tag{10}$$

where *D=D*′*/θ* and *v = q/θ* is the mean solution (water) speed in the soil, because the soil pores are not all the same size.

The differential Eq. (10) is for the model of solute miscible displacement in the soil, where there is neither reaction nor adsorption.

Several solutions and models for fitting data from BTCs are presented by van Genuchten et al. [60] in the software STANMOD (STudio of ANalytical MODels). The STANMOD is an interesting tool to assess different analytical solutions based on CDE for solute transport in porous media. The software integrates seven separate codes with a wide range of solute transport applications. For example, models that

assume equilibrium or non-equilibrium transport conditions during steady unidirectional water flow and models that assume non-equilibrium transport.

The greatest interest in solute transport studies in soils has been in the field of agronomy, because the influence of fertilizers, nutrients, and salt concentrations is important for plant growth. However, in recent decades, the interest in solute transport in environment soil science has increased because of the risk of chemical contamination in soil and groundwater caused by agricultural and other chemical substances [59]. Simonin et al. [61] studied the influence of texture and soil organic matter content of six agricultural soils on the transport of two nanoparticles (CuO-NPs and TiO2-NPs). The solute transport experiments were carried out in water-saturated soil columns, and the breakthrough curve data were fitted to the CDE model with the aim of identifying the dominant process of nanoparticle transfer. The main results show differences between the transport of TiO2 and CuO. The mobility of TiO2 was low in all conditions, suggesting a low risk of groundwater contamination. On the other hand, CuO nanoparticles were mobile in all soils. Thus, in the contrasting agricultural soils, the transport of CuO-NPs was mainly controlled by solutes dissolved in the soil solution compared to the solid phase.

Phosphorus (P) and nitrogen (N) are important sources of fertilizers used in agriculture. In some cases, P and N may be associated to risks of potential groundwater contamination, and therefore, indiscriminate use of these sources in agricultural soils should not be recommended. Mahmood-Ul-Hassan [62] assesses the effect of soil structure on the potential for nitrate (NO3 − ) and phosphate (H2PO4 − ) leaching. Laboratory leaching experiments were carried out on undisturbed columns sampled from two types of calcareous soils, Aridisols and Entisols. The leaching curves were fitted with CDE models to determine transport parameters. In general, for Aridisols, the NO3 − and H2PO4 − were found in the effluent immediately after pulse application, whereas for Entisol, NO3 − was found in the effluent delayed. The experiments showed the importance of knowing the variability of soil structure in predicting the fertilizer losses. Kolachi and Jalali [63] evaluated the movement and retention of P in the columns of two calcareous soils. The concentrations of P and other elements such as K+ , Ca2+, and Mg2+ were also determined. P leaching was influenced by supersaturation of P-Ca minerals and undersaturation of Mg-P minerals. BTCs of P and K<sup>+</sup> showed a good fit to equilibrium models using the code CXFIT of STANMOD. The mobility of P in these types of soils may reflect a greater downward movement of water soluble P; that is, these soils require adequate P management to avoid leaching and contamination of groundwater and surface water.
