Migration Processes

Why does dispersion occur?

The causes of dispersion lie in the microscopic heterogeneity of the soil medium:

1. Velocity differences within a single pore. In any capillary, the flow velocity is maximal at the centre and drops to zero near the walls (parabolic velocity profile). Dissolved molecules moving in the centre of the pore are transported faster than those near the walls (Huang et al., 2012).

2. Velocity differences in pores of different diameters. According to Poiseuille’s law, the flow velocity is proportional to the square of the pore radius. Therefore, water and dissolved substances move much faster through large macropores (root channels, cracks, wormholes) than through fine capillaries. This causes the solution front to “stretch” over time: the first portions of the substance reach depth considerably earlier than the bulk mass (Eash et al., 2016; Weil & Brady, 2017).

3. Differences in path lengths and pore tortuosity. Owing to tortuosity and branching of the pore space, molecules in different pores travel paths of different lengths, even if the average flow velocity is the same.

Thus, dispersion is mechanical mixing caused by variations in local flow velocities at the scale of individual pores and their assemblies (Foth, 1990; Marshall et al., 1996).

Quantitative description and relation to diffusion

At the macroscopic level, dispersive spreading is often formally described by analogy with diffusion – through the coefficient of hydrodynamic dispersion, which is added to the molecular diffusion coefficient. Their sum is called the coefficient of hydrodynamic dispersion (or effective dispersion coefficient) D:

where D_diff is the molecular diffusion coefficient (depends on temperature and substance properties, but not on flow velocity), and D_disp is the mechanical dispersion coefficient, which is directly proportional to the flow velocity (Shukla, 2023; White, 2006). The faster the water moves, the more pronounced the dispersion. At low flow velocities (in dense or dry soils), molecular diffusion dominates; at high velocities (in macropores, during irrigation), dispersion plays the main role.

In practice, dispersion is conveniently characterised by dispersivity λ – a parameter having the dimension of length, which relates the dispersion coefficient to the flow velocity: D_disp = λv. Dispersivity reflects the average scale of pore‑space heterogeneity. For laboratory columns (repacked soil), λ values are typically 0.5‑2 cm, whereas for field conditions (undisturbed soil, presence of macropores) dispersivity can reach tens of centimetres or more (Huang et al., 2012; Shukla, 2023).

Dispersion and macropores: preferential flow

Dispersion plays a particularly important role in structured, aggregated soils rich in macropores. Here, the movement of water and dissolved substances becomes extremely uneven. A significant part of the solution may quickly infiltrate through large pores, with virtually no interaction with the soil matrix – the so‑called preferential flow or macropore flow. This process causes some molecules of a substance to reach great depths much earlier than predicted by models based on average velocities (Weil & Brady, 2017). Thus, dispersion together with macroporosity explains the paradoxically rapid detection of certain pesticides or nitrates in groundwater.

Dispersion and diffusion: combined action

It is important to understand that in real soil dispersion and diffusion act inseparably and simultaneously. Their combined effect is the hydrodynamic dispersive smearing of the concentration front. If, for example, we apply a fertiliser solution to the topsoil, then:

• Convection will move the solution downward with the water flow.
• Dispersion will stretch the solution front due to different velocities in different pores.
• Diffusion will additionally smooth out concentration gradients, moving the substance from areas of higher concentration to areas of lower concentration.

As a result, at the outlet of the soil layer (or at some depth) we obtain not a sharp concentration jump but a smooth breakthrough curve, which is flatter the larger the dispersion (Shukla, 2023). It is from the shape of these curves that one can infer the proportion of macropores, the intensity of mixing, and the degree of substance sorption by the soil.

Thus, dispersion is an integral part of any convective transport in soil, making the actual spread of substances much more complex and spatially uneven than would be expected from ideal piston displacement. Now that we have examined the three basic transport mechanisms – diffusion, convection, and dispersion – we can move on to the quantitative law that unites them in a single description of water movement, namely – Darcy’s law.

What is hydraulic potential and its gradient?

To understand Darcy’s law, it is necessary to have a clear idea of hydraulic potential (total head) of soil water. It is the sum of several components, but for practical purposes in unsaturated soils (which is the main state of the root zone), the two most important are:

1. Gravitational potential – determined by the height of a point above some reference level. Water always tends to flow downward under the action of gravity.

2. Matric potential (or moisture potential, capillary potential) – due to attractive forces between water and the solid surface of soil particles (adhesion) and capillary forces. The drier the soil, the more negative the matric potential, i.e., the stronger the soil “pulls” water toward itself.

The total hydraulic potential is the algebraic sum of these components. Water always moves from a region of higher (less negative) hydraulic potential to a region of lower (more negative) potential (Weil & Brady, 2017).

Hydraulic potential gradient is the change in potential per unit distance. This gradient is the driving force for water. The steeper this gradient (for example, a sharp difference in moisture between wet and dry zones of the soil), the more intense the water movement. Darcy’s law states: the water flow is directly proportional to this gradient.

Coefficient of hydraulic conductivity

The second key parameter in Darcy’s law is hydraulic conductivity K. It characterises the ability of the soil to transmit water. Hydraulic conductivity is not a constant but a function strongly dependent on:

• Pore size and shape. According to Poiseuille’s law, the flow rate through a capillary is proportional to the fourth power of its radius. This means that even a small number of large macropores (cracks, root channels, wormholes) can account for a huge proportion of the total flow, despite their small volume (Scheffer et al., 2018; Foth, 1990).
• Soil moisture. Hydraulic conductivity drops sharply (by several orders of magnitude) with decreasing moisture. In saturated soil, all pores participate in transport, and conductivity is maximal (this value is called the saturated hydraulic conductivity K_sat). Upon drying, large pores become air‑filled, and water must move through fine capillaries and films, where resistance is considerably higher (Huang et al., 2012; Radcliffe & Simunek, 2012).
• Structure and texture. Sandy soils with large, well‑connected pores have high conductivity, whereas clay soils, even though they have high porosity, have low conductivity because of fine pores and high tortuosity of pathways (Eash et al., 2016).

Darcy’s law under saturated and unsaturated conditions

It is important to understand that Darcy’s law is applicable to both soil states, but the interpretation of parameters differs.

Under saturated conditions (all pores filled with water), hydraulic conductivity is constant (K = K_sat), and the driving force is mainly the gravitational gradient (if there is no additional head). This case is typical of the groundwater zone, as well as short periods after heavy rainfall or irrigation. Water movement here is percolation, which effectively leaches soluble substances (nitrates, chlorides) downward through the profile (White, 2006).

Under unsaturated conditions (the main state of soils during the growing season), the picture is fundamentally different. Here, hydraulic conductivity K becomes a function of moisture content (or matric potential). Water moves through fine capillaries and water films, and the driving force is the matric potential gradient, which often outweighs the gravitational component. This is why water can rise from groundwater to the surface (capillary rise) or move horizontally from wet to dry zones (Marshall et al., 1996; Scheffer et al., 2018).

Darcy flow and transport of dissolved substances

Darcy’s law describes the movement of water, but for dissolved substances it forms the basis of convective transport, which we discussed earlier. The velocity of water calculated from Darcy’s law (v = K · grad Φ) is called the filtration velocity (or Darcy velocity). However, the actual velocity of dissolved molecules moving in the pores (true velocity) is higher, because water moves only through the pore space, not through the entire cross‑section of the soil (Shukla, 2023). This relationship is expressed by a simple ratio:

where θ is the volumetric soil moisture. The drier the soil, the smaller the effective cross‑section for flow and the higher the true water velocity for the same potential gradient. This seemingly paradoxical phenomenon is important when assessing the rate of salt or contaminant leaching under variable moisture conditions.

Qualitative meaning of Darcy’s law

Thus, qualitatively Darcy’s law can be formulated as follows:

Water moves through soil the faster, the greater the hydraulic potential drop per unit distance and the more easily the soil transmits water (i.e., the higher its hydraulic conductivity).

This simple principle is the cornerstone of all soil water physics. It allows us to understand:

• why water quickly drains from sandy soils (high K_sat);
• why clay soils remain wet for a long time (low K under unsaturated conditions);
• why after irrigation water first infiltrates quickly and then slows down (decrease in gradient and conductivity);
• why, as the soil dries, plants find it increasingly difficult to extract water (sharp drop in K, despite increasing gradient).

In the next section, we will consider how the architecture of the pore space – its inherent heterogeneity and hierarchical organisation – determines not only hydraulic conductivity but also the nature of all three processes discussed: diffusion, convection, and dispersion.

Pore sizes: not just “large” and “small”

In soil science, several categories of pores are distinguished by their equivalent diameter (Scheffer et al., 2018; Weil & Brady, 2017). Although the boundaries are arbitrary, the functional significance of these classes is fundamentally different:

Macropores (diameter > 50‑80 µm) – large voids: cracks, earthworm burrows, root channels, inter‑aggregate spaces. They do not retain capillary water against gravity – after rain, they quickly drain. Their main role is to provide rapid convective transport (filtration) and gas exchange with the atmosphere. However, dissolved contaminants can also move rapidly through these pores, bypassing the soil matrix (preferential flow).

Mesopores (diameter from 0.2 to 50‑80 µm) – the main capillary pores, where water is retained against gravity but remains available to plants. This is where the main convective transport of water and dissolved substances takes place in the unsaturated state, as well as effective diffusion of ions to roots. This pore class determines the water‑holding capacity and hydraulic conductivity of the soil in the moisture range from field capacity to the wilting point (Eash et al., 2016).

Micropores (diameter < 0.2 µm) – the finest voids within microaggregates and between clay mineral plates. Water in them is held very tightly (matric potential below –1.5 MPa) and is practically unavailable to plants. Here, diffusion in the bound water film dominates, which is extremely slow. However, it is in micropores that ion sorption occurs, affecting their availability and the rate of the diffusive flux (Marshall et al., 1996).

Tortuosity – the main enemy of rapid transport

Real pores are never straight cylinders. They meander, narrow, widen, and have dead‑end branches. This property is called tortuosity. Tortuosity increases the effective path length that a molecule or particle must travel and sharply slows down both diffusive and convective transport (Huang et al., 2012; White, 2006). Diffusion coefficients of gases and ions in soil are always significantly lower than in free air or water, precisely because of tortuosity. To quantify this effect, the tortuosity factor is used – the ratio of the actual path length to the shortest distance. In aggregated soils with well‑developed microstructure, tortuosity is particularly high, reducing the movement rate of nutrients, but at the same time increasing the contact time of the solution with the solid phase, promoting sorption and buffering.

Dual porosity: aggregates as separate “micro‑worlds”

Many structural soils (especially in humus horizons) are characterised by dual porosity (or bimodal pore space). In such soils, two types of pores can be distinguished:

1. Inter‑aggregate pores – large gaps between peds (aggregates). These serve as the main highways for rapid water and gas filtration.

2. Intra‑aggregate pores – fine pores within the aggregates themselves, where water is held by capillary forces, and exchange with the external solution is slowed.

This division has enormous practical significance. Water and dissolved substances can move rapidly through inter‑aggregate pores (preferential flow), with little interaction with the interior of the aggregates. Inside the aggregates, water and ions move much more slowly, and diffusion dominates (Foth, 1990; Shukla, 2023). This duality explains why some contaminants can reach groundwater very quickly, while most of the soil solution remains within aggregates and undergoes biochemical transformation. This regime is called physical non‑equilibrium – when “fast” and “slow” transport zones coexist in the soil simultaneously (Radcliffe & Simunek, 2012).

Macropores and preferential flow: “bypass” of substances to depth

The presence of macropores, especially those that penetrate the profile continuously (vertical cracks, root channels, wormholes), fundamentally changes the transport picture. Water during heavy rainfall or irrigation rushes along these “express routes,” bypassing the bulk of the soil matrix. As a result, dissolved substances (nitrates, pesticides, pathogens) can be transported to depths of tens of centimetres or metres within hours, which is completely unpredicted by classical convection‑dispersion equations averaged over the entire profile (Weil & Brady, 2017; Eash et al., 2016). This process is called preferential (or bypass) flow. It explains why, under field conditions, contaminants are often detected in groundwater much earlier and at higher concentrations than would follow from laboratory experiments on intact columns without macropores.

Influence of architecture on diffusion, convection, and dispersion

Let us summarise how pore architecture modifies each of the three mechanisms:

• Diffusion: sharply slowed down in micropores and tortuous channels; effective only over very short distances (millimetres). In macropores, gas diffusion is rapid, but ionic diffusion in the liquid phase is practically absent due to short contact time.
• Convection: the velocity and direction of flow are determined by the hydraulic potential gradient, but the true velocity in pores varies greatly: in macropores it is orders of magnitude higher than in mesopores. It is this variation that gives rise to dispersion.
• Dispersion: the magnitude of dispersive spreading is directly proportional to the heterogeneity of pore velocities. The more contrasting the architecture (e.g., alternation of dense aggregates and wide cracks), the stronger the dispersion, and the flatter the breakthrough curve of the dissolved substance (Shukla, 2023).

Thus, pore architecture is not merely a passive characteristic but an active regulator of all migration processes. It determines what proportion of water and dissolved substances moves rapidly and with almost no contact with the matrix, and what proportion moves slowly with intensive exchange and sorption. This is precisely why the physical properties of soil (particle‑size distribution, structural condition, bulk density) are key factors determining plant water supply, nutrient leaching, and the environmental safety of agroecosystems. In the next section, we will consider how all these processes – diffusion, convection, and dispersion – act together to create the real picture of transport in the soil profile.

Unified mechanism: convection‑dispersion‑diffusion

To generalise, the total flux of a dissolved substance in soil consists of two components:

1. Convective component – the substance is transported together with moving water (mass flow). This process dominates during active infiltration, irrigation, and after rainfall.

2. Dispersive‑diffusive component – the substance is additionally spread due to concentration gradients (diffusion) and heterogeneity of pore velocities (dispersion). This component is particularly important when water moves slowly or when convection is weakened (e.g., in dry soil or in dense horizons).

In the end, the resulting flux is larger than just the sum of these two parts, because they act in concert. In soil hydrology, this combined process is described by the convection‑dispersion equation (or advection‑dispersion equation). Without formulas, its essence can be expressed as: the change in concentration of a substance at any point in soil over time is determined by the rate at which the substance is brought in by the water flow and the rate at which it is dispersed (smeared) due to diffusion and dispersion, also taking into account sources and sinks – sorption, degradation, root uptake (Shukla, 2023; Radcliffe & Simunek, 2012). This equation is the foundation of all modern models of transport of salts, nitrates, pesticides, and other pollutants.

Interaction with pore architecture: sorption and physical non‑equilibrium

Pore architecture not only determines flow velocities but also creates conditions for physical non‑equilibrium. Recall that in aggregated soils, water in inter‑aggregate macropores moves rapidly, while inside aggregates it moves slowly or is nearly stagnant. This leads to:

• A dissolved substance that enters the fast flow may be transported to considerable depth, with virtually no interaction with the interior of aggregates – preferential transport.
• Simultaneously, part of the substance may diffuse from macropores into the aggregates, where it is sorbed on the surface of clay particles or organic matter. This process slows down the overall movement of the substance, because the sorbed portion is temporarily removed from the flow (Weil & Brady, 2017; Foth, 1990).

Thus, two zones of transport coexist in the soil – a “fast” one (macropores, cracks) and a “slow” one (intra‑aggregate space). Exchange between them occurs through diffusion at the interface, which can be very slow. This duality explains why the leaching (elution) curves of many substances have a characteristic “long tail” – after the main peak of concentration has passed, concentrations remain elevated for a long time, as the substance slowly releases from the intra‑aggregate zones.

Sorption and chemical interaction: slowing down or speeding up?

Besides physical non‑equilibrium, the combined action of transport mechanisms is significantly affected by chemical interaction between the dissolved substance and the solid phase of the soil. This is especially important for ions (phosphates, ammonium, potassium, micronutrients) and some organic molecules (pesticides).

• Sorption – attraction of ions or molecules to the surface of solid particles – can be reversible (ion exchange) or irreversible (chemisorption). Sorbed matter ceases to move with the water flow, which is equivalent to slowing down convection. To describe this effect in models, the retardation factor is used – it shows how many times the substance velocity is less than the water velocity. For weakly sorbing anions (nitrates, chlorides), this factor is close to 1; for cations (ammonium, potassium) it can reach 10‑100; and for some pesticides it is even higher (Huang et al., 2012; White, 2006).
• Degradation – breakdown of organic molecules by microorganisms or chemical reactions – acts as a sink of the substance. It reduces the total mass moving with the flow and can completely stop penetration into deeper layers if the degradation rate exceeds the convection rate.
• Feedback with moisture: all these processes strongly depend on soil water content. In wet soil, diffusion is faster, convection is more active, and microbial activity is higher – hence degradation accelerates. However, in waterlogged, anaerobic soil, some processes (nitrification) are inhibited, while others (denitrification) are enhanced, changing the entire nitrogen transport balance (Scheffer et al., 2018).

The role of the living root as a “pump” and “barrier”

Plant roots are not passive observers of transport. They actively modify substance flows:

• Uptake of water and ions creates local concentration and potential gradients, enhancing diffusion and convection in the rhizosphere. The plant acts as a powerful “pump,” drawing water and nutrients toward the root surface (Foth, 1990; Eash et al., 2016).
• Exudation of root exudates changes the chemical composition of the solution (pH, organic acids), which may affect sorption and solubility of elements.
• Physical compaction by roots and formation of root channels create additional macroporosity, enhancing preferential flow, but at the same time may improve aeration.
• At the same time, roots can serve as a biological barrier, absorbing a significant portion of mobile nitrates and thereby reducing their leaching beyond the root zone. This is particularly important in agroecosystems, where proper timing and rates of fertiliser application allow minimising nitrogen losses (Weil & Brady, 2017).

Integration: from mechanisms to prediction

Thus, the combined action of transport processes in soil can be visualised as a conveyor on which several mechanisms operate:

1. Convection provides long‑distance transport of the substance with the water flow.

2. Dispersion stretches the concentration front due to velocity heterogeneity in different pores.

3. Diffusion smoothes gradients at the microscale, especially in zones with slow flow.

4. Sorption and chemical reactions (degradation, transformation) partially remove the substance from the flow or change its form, affecting the rate and depth of penetration.

5. Pore architecture sets the spatial scales of all these processes, determining the balance between fast and slow pathways.

6. Biological activity (roots, microorganisms) creates additional sources and sinks, altering local conditions.

It is this integrated understanding of these interrelationships that allows an agronomist, ecologist, or reclamation specialist not merely to state the fact of leaching but to manage the process: choose optimal irrigation timing, adjust fertiliser rates, create buffer zones, use cover crops to bind mobile nitrogen. In the next, concluding section, we will move from general principles to specific, well‑studied examples of the movement of water, oxygen, nitrates, and pesticides – those practical cases that every agronomist encounters in their work.

1. Water: the main “carrier”

Water movement in soil is a classic example of convective transport governed by Darcy’s law. However, the nature of this movement changes dramatically depending on soil moisture and structure.

In saturated soil (after heavy rain, irrigation, or in the groundwater zone), all pores are filled with water. The driving force is mainly the gravitational gradient, and hydraulic conductivity is maximal. Water rapidly percolates downward, carrying all soluble substances with it. This process is called percolation, and it is responsible for the bulk of nitrate, sulphate, and chloride leaching from the root zone (Eash et al., 2016; White, 2006).

In unsaturated soil – the typical state during the inter‑irrigation period – water moves through fine capillaries and films under the action of the matric gradient. Hydraulic conductivity drops sharply with decreasing moisture, so the flow becomes slow. However, it is in this regime that water can move horizontally and even upward – for example, during capillary rise from groundwater (Marshall et al., 1996; Scheffer et al., 2018). This process is critical for supplying water to plants during dry periods.

The influence of macropores fundamentally changes the picture. In structured soils (especially in chernozems, grey forest soils), water can rapidly infiltrate through cracks, root channels, and wormholes, bypassing the bulk of the matrix. This phenomenon – preferential flow – explains why, after heavy rainfall, moisture can reach deep horizons in hours rather than days, as predicted by models based on averaged parameters (Weil & Brady, 2017). For the agronomist, this means that irrigation rates and timing must take into account not only the average water‑holding capacity but also the structural condition of the soil.

2. Oxygen: a diffusive “limit” for roots

Oxygen is one of the few gaseous substances whose movement in soil is determined almost exclusively by diffusion in the gas phase. Convective transport of oxygen (e.g., with air flow) is negligible under normal conditions, except for strong wind at the surface or barometric fluctuations.

Driving force – the gradient of partial pressure (or concentration) of oxygen between the atmosphere (20.9 %) and the soil air, where oxygen is consumed by roots and microorganisms. The more intense the respiration, the higher the gradient and the faster the diffusion (Huang et al., 2012; Foth, 1990).

The main limiting factor is moisture. The diffusion coefficient of oxygen in air is about 10,000 times higher than in water. Therefore, when pores are filled with water (after irrigation, in waterlogged soils), diffusion slows abruptly, and roots may suffer from oxygen deficiency (hypoxia). This is precisely why plants on clayey, poorly drained soils suffer from lack of air, despite abundant moisture (Scheffer et al., 2018).

The role of macropores in aeration cannot be overstated. Root channels and worm burrows provide rapid gas exchange between the atmosphere and deeper horizons, creating “ventilation shafts.” In compacted, structureless soils, this network is disrupted, and the depth of oxygen penetration may be limited to just a few centimetres (Eash et al., 2016). For the agronomist, this means that maintaining good soil structure is not only a guarantee of water permeability but also a necessary condition for root respiration and aerobic microbial activity.

3. Nitrates: a mobile “target” for leaching

Nitrate nitrogen (NO₃⁻) is one of the most mobile ions in soil. It is weakly sorbed on negatively charged surfaces of clay particles and organic matter (anion repulsion). Therefore, its behaviour is mainly governed by convection with water and dispersion.

Main transport mechanism – mass flow with water. During irrigation or rainfall, nitrates are easily leached down the profile, especially from the upper, well‑leached horizons. This creates a serious environmental problem: nitrate contamination of groundwater and surface water bodies (Foth, 1990; Weil & Brady, 2017).

Role of diffusion – secondary, but not negligible. In dry soil or in zones with slow flow (inside aggregates), diffusion ensures concentration equalisation and supply of nitrates to roots when convection is weak (Shukla, 2023).

Factors slowing leaching:

• Root uptake – plants can absorb up to 80‑90 % of nitrate nitrogen from the root zone if their root system is well developed and fertiliser application coincides with active growth (Eash et al., 2016).
• Denitrification – under anaerobic conditions (waterlogging), nitrates can be reduced to gaseous nitrogen (N₂) and volatilise, partially reducing the load on groundwater.
• Intra‑aggregate diffusion – in structured soils, part of the nitrates may diffuse into aggregates and be temporarily “held” there, reducing their export with the fast macropore flow (Radcliffe & Simunek, 2012).

For the agronomist, this means that managing the nitrate regime requires a precise balance between application rates, timing, and water regime. Split application of nitrogen fertilisers in small doses during active growth is an effective way to minimise losses.

4. Pesticides: a complex “puzzle” of sorption, degradation, and preferential flow

Pesticides are organic molecules whose behaviour in soil is determined simultaneously by several processes: convection, diffusion, dispersion, but most importantly – sorption and degradation.

Sorption – the key factor determining pesticide mobility. The greater its affinity for soil organic matter (distribution coefficient K_oc), the stronger it is retained on the solid phase and the slower it moves with water. This phenomenon is described by the retardation factor – it indicates how many times the pesticide velocity is less than the water flow velocity. For strongly sorbed compounds (e.g., DDT), retardation can reach hundreds and thousands of times, and they practically do not migrate (Huang et al., 2012; White, 2006).

Degradation – breakdown of the pesticide by microorganisms or chemical reactions – acts as a sink, reducing the total mass available for transport. The degradation rate depends on temperature, moisture, pH, and oxygen availability. In warm, moist, well‑aerated soil, many pesticides degrade within days or weeks, significantly limiting their penetration depth (Weil & Brady, 2017).

The role of macropores – critical. Despite the high sorption capacity of many pesticides, they can be transported to depth precisely through preferential flow along cracks and wormholes. In this case, the dissolved pesticide moving through large pores practically does not contact the organic matter of the matrix, and sorption does not have time to act. This explains the detection of pesticides in groundwater at depths where their presence would seem impossible (Eash et al., 2016; Scheffer et al., 2018).

Diffusion plays a role in redistributing the pesticide from macropores into aggregates, where it may be sorbed or undergo degradation. This process slows leaching, but may also lead to the formation of “stagnant zones” with residue accumulation.

For the agronomist and ecologist, this means that predicting the fate of a pesticide requires consideration not only of its chemical properties but also of the structural state of the soil, water regime characteristics, and biological activity.

Final summary

Mass transfer in soil is not a sum of disparate processes but a single, dynamic system in which convection, diffusion, and dispersion act simultaneously, and their relative contributions are determined by pore architecture, chemical properties of the substance, and biological factors.

• Water moves mainly by convection (Darcy’s law), but its redistribution strongly depends on moisture and structure.
• Oxygen moves almost exclusively by diffusion, which sharply slows down in wet soil.
• Nitrates – mobile anions – are easily leached by convective flow, but may be retained by roots or denitrified.
• Pesticides – the most complex behaviour, where sorption and degradation compete with convection, and preferential flow can lead to unexpectedly deep penetration.

Understanding these regularities is not merely an academic interest. It underpins rational fertility management: calculation of irrigation rates, split fertiliser application, selection of cover crops and tillage systems, and assessment of environmental risks of groundwater contamination. As a classic of soil science wrote, “water is the blood of the soil”; knowing how it moves and what it carries is the key for the skilled agronomist and responsible land user.