Surface Coating with Foliar Fertilizers

Abstract

Foliar fertilization, an effective agricultural practice, involves the application of nutrients directly through droplets on plant leaves. The mechanisms of mass transport and deposition that arise from the drying of a drop determine the distribution of mass on a surface. Understanding these processes is crucial for optimizing foliar fertilization, ensuring even nutrient distribution, and improving crop yields and quality. This study experimentally investigates deposit formation from the evaporation of fertilizer droplets in various configurations: sessile, vertical, and pendant. We explored the effects of initial droplet volume, vapor pressure, and sorbitol presence on the final deposit morphology. The results reveal distinctive morphological patterns. Sessile drops exhibit two types of deposits—central crystal accumulation with fibrous structures or entirely fibrous structures. In contrast, vertical drops display two zones—fibrous structures at the bottom and small aggregates at the top. On the other hand, pendant drops predominantly feature intertwined crystals with peripheral fibrous structures. We found that high vapor pressures (RH = 60%) inhibit deposit formation within 72 h. Furthermore, the study measures relative evaporation time, showing that sessile droplets exhibit the longest evaporation times, followed by vertical and pendant droplets. Texture analysis, based on GLCM entropy, reveals that deposits generated under low vapor pressure (RH = 20%) show no significant differences in their entropy values, regardless of the droplet configuration and its initial volume. However, at intermediate vapor pressure (RH = 40%), entropy values vary significantly with droplet volume and configuration, being higher in sessile drops and lower in vertical ones. Additionally, we investigated the impact of sorbitol on the coating of sessile fertilizer droplets. We find that configurational entropy decreases exponentially with sorbitol concentration, inducing a morphological transition from fibrous structures to dispersed small aggregates. These findings highlight the complexity of pattern formation in fertilizer deposits and their potential implications for optimizing surface coating processes.

1. Introduction

Coating surfaces with foliar fertilizers signifies a noteworthy advancement in contemporary agriculture due to its crucial role in augmenting agricultural yields. The direct application of these fertilizers onto plant leaves facilitates the rapid and efficient absorption of vital nutrients, including nitrogen, phosphorus, and potassium, indispensable for crop growth and maturation. This method enables precise and uniform nutrient distribution, thereby resulting in a notable upsurge in agricultural productivity.

The effectiveness of foliar fertilization can be hindered by various biological barriers. The primary obstacle is the leaf cuticle, a hydrophobic waxy layer whose composition and thickness vary, influencing nutrient absorption [1]. Stomata, the pores on the leaf surface responsible for gas exchange, can facilitate the entry of fine aerosols. However, their effectiveness is dependent upon their quantity, distribution, size, and response to environmental conditions. Furthermore, the epidermis, situated below the cuticle, presents a barrier due to its compact structure. Environmental factors such as relative humidity, temperature, and solar radiation play a significant role in absorption by affecting stomatal opening and transpiration rates [2]. Moreover, the characteristics of the foliar fertilizer itself, including concentration, particle size, and the presence of surfactants, are critical determinants of absorption efficiency. Smaller particles, surfactants that lower surface tension, and optimal pH and concentration levels enhance nutrient penetration and absorption, thereby improving the overall efficacy of foliar fertilization [3].

Additionally, incorporating additives like sorbitol can further enhance nutrient transport and absorption, resulting in improved growth and yield. Studies have demonstrated that sorbitol facilitates nutrient movement through the phloem and boosts photosynthesis, leading to superior growth parameters and higher yields [4,5]. This targeted nutrient application also offers practical and economic benefits, making it a valuable addition to foliar fertilization strategies.

Droplet drying has been studied under various configurations, as illustrated in Figure 1: (a) sessile, (b) vertical, and (c) pendant. The process of evaporation of sessile droplets results in a unique deposit characterized by distinctive morphological attributes [6]. This phenomenon is a consequence of the intricate interplay between capillary and Marangoni flows [7]. Capillary flows originate from the droplet’s core, propagating radially towards its periphery [8,9]. Within the droplet, non-volatile particles experience outward displacement due to the influence of capillary flows, resulting in the well-recognized “coffee ring effect” [10]. Conversely, Marangoni flows, which are generated by surface tension gradients resulting from temperature or concentration variations, create intricate recirculatory patterns within the droplet. These flows can either promote uniform deposition or produce diverse deposition patterns, depending on the fluid’s characteristics and surrounding conditions [11]. For example, in pure organic droplets, Marangoni flows centralize deposits due to evaporation, while in saline droplets, they enhance ring-shaped stains by moving particles to the contact line [12,13].

In the case of a vertical droplet, the nonvolatile constituents tend to accumulate predominantly at the lower contact line, primarily influenced by the gravitational force [14,15,16]. Gravitational sedimentation of particles, which results in their aggregation in this specific region, becomes evident when the droplet’s lifespan exceeds that of colloidal particle sedimentation. Additionally, an alternative transport mechanism comes into play, triggered by subtle variations in the spherical cap’s shape on the droplet’s surface. This leads to particle adsorption at the interface and subsequent migration toward regions of higher curvature along the interface [17]. Consequently, the effective transport of colloidal particles hinges upon the intricate interplay between sedimentation, interfacial migration driven by the curvature of the droplet, and capillary flow [17,18,19]. Although elegant models have been developed to elucidate the dynamics of volume, shape, contact angle, and drying processes in inclined droplets [20,21,22,23], there remains an absence of a comprehensive theory capable of predicting the intricate processes governing the ultimate morphology of these patterns. Nevertheless, it is commonly observed that the gravitational force acting on a vertical droplet directly correlates with the deposit’s thickness at the lower contact line, dependent on initial droplet volume and particle mass [14,17,24,25].

When drops are placed on inclined substrates, they disrupt the typical azimuthal symmetry observed in particle arrangements within dried sessile drops [25,26]. In these cases, a pendant drop gives rise to a more intricate deposit configuration, characterized by a fine coffee ring enveloping a protrusion formed by a concentrated cluster of colloids [15]. These distinctive patterns, commonly referred to as “coffee eyes”, originate from the adsorption of colloidal particles at the drop’s edge, followed by deposition at regions with elevated curvature at the droplet’s base [17]. Importantly, this mechanism dispenses with the necessity for radial colloidal particle flow along the contact line and instead relies on the variable curvature of the droplet to accumulate the particles [27].

It is noteworthy that there exists no overarching rule capable of predicting the distinct stages of pattern formation in drops containing various solutes. For example, pendant drops containing polystyrene (PS) colloidal particles produce, in the initial stage, mass transport, which is marked by competition between sedimentation and the entrapment of particles from the descending interface. Subsequently, during the second stage, capillary flow assumes dominance and conveys particles from the drop’s interior towards the contact line [28]. Conversely, when drops contain concentrated globular proteins, the dynamic evolution of mass loss and the transformation of the drop’s internal and external shapes give rise to three distinct stages [29].

The use of the Gray Level Co-occurrence Matrix (GLCM) has shown great effectiveness in analyzing patterns within dried droplets, demonstrating its versatility in various scientific contexts, including drug quality control [30], protein folding detection [31], and biofluid characterization [32], while highlighting the complexity of pattern formation in droplets containing different solutions. GLCM serves as a vital tool for evaluating the texture of objects, closely linked to the spatial distribution of pixel intensities within a region of interest. What distinguishes GLCM parameters is their role as indicators of the frequency of gray level combinations present in an image [33].

Although significant contributions have been made to the study of soil–fertilizer pattern formation [34], it is unknown how surface inclination affects nutrient distribution. The identification and texture characterization of new patterns in the deposits could lead to improvements in strategies for coating surfaces and improve nutrient uptake by plants. In this paper, we present experimental analysis exploring the formation of deposits during the evaporation of foliar fertilizer droplets in different configurations, including sessile, vertical, and pendant orientations. The results revealed distinctive morphological patterns that varied depending on the droplet configuration. The sessile droplets showed two types of notable deposits: one characterized by an accumulation of crystals in the center and a fibrous structure at the edges, and another with a fibrous structure that covered the entire surface. In the case of vertical drops, two clearly defined zones were identified: a lower part with fibrous structures and an upper part with amorphous aggregates. On the other hand, the pendant droplets mainly exhibited intertwined crystals in the core, surrounded by fibrous structures at the periphery. Additionally, vapor pressure was observed to have a significant effect on deposit morphology, with high vapor pressures resulting in no deposits over a 72 h period. Finally, sorbitol triggered a morphological transition towards the formation of small aggregates dispersed in the sessile deposits, while the configurational entropy decreased exponentially with the concentration of this surfactant. These results provide a deeper understanding of deposit formation processes in agriculture and surface chemistry.

2. Experimental Details

2.1. Sample Preparation and Storage

We used commercial foliar fertilizer (Bayfolan^® Forte, BAYER, Leverkusen, Germany) to carry out our experiments.

Table 1. Percentage composition of Bayfolan^® Forte as described in the product specification.

Active ingredient:
N, P, K + Microelements
Percentage composition:
Total Nitrogen (N)	11.470%
Potassium (K2O)	6.000%
Boron (B)	0.036%
Copper (Cu)	0.040%
Iron (Fe)	0.050%
Molybdenum (Mo)	0.005%
Zinc (Zn)	0.080%
Thiamine hydrochloride	0.004%
Phosphorus (P2O5)	8.000%
Sulfur (S)	0.230%
Calcium (CaO)	0.025%
Cobalt (Co)	0.002%
Manganese (Mn)	0.036%
Magnesium (MgO)	0.025%
Indole-3-acetic acid	0.003%

presents the general data of the inorganic foliar fertilizer/liquid, as described in the product specification.

Table 2. Critical relative humidity (%) of pure salts and mixtures at 30 °C, according to [35].

	Calcium Nitrate	Ammonium Nitrate	Sodium Nitrate	Urea	Ammonium Chloride	Ammonium Sulphate	Diammonium Phosphate	Potassium Chloride	Potassium Nitrate	Monoammonium Phosphate	Monocalcium Phosphate	Potassium Sulphate
Calcium Nitrate	46.7	-	-	-	-	-	-	-	-	-	-	-
Ammonium Nitrate	23.5	59.4	-	-	-	-	-	-	-	-	-	-
Sodium Nitrate	37.7	46.3	72.4	-	-	-	-	-	-	-	-	-
Urea	-	18.1	45.6	72.5	-	-	-	-	-	-	-	-
Ammonium Chloride	-	51.4	51.9	57.9	77.2	-	-	-	-	-	-	-
Ammonium Sulphate	-	62.3	-	56.4	71.3	79.2	-	-	-	-	-	-
Diammonium Phosphate	-	59	-	62	-	72	82.5	-	-	-	-	-
Potassium Chloride	<22.0	67.9	66.9	60.3	73.5	71.3	70	84.0	-	-	-	-
Potassium Nitrate	31.4	59.9	64.5	65.2	67.9	69.2	-	78.6	90.5	-	-	-
Monoammonium Phosphate	52.8	58.0	63.8	65.2	-	75.8	78	72.8	59.8	91.6	-	-
Monocalcium Phosphate	46.2	52.8	68.1	65.1	73.9	87.7	78	-	87.8	88.8	93.6	-
Potassium Sulphate	76.1	69.2	73.3	71.5	71.3	81.4	77	81	87.8	79.0	-	96.3

summarizes the critical relative humidity (CRH) values of key pure fertilizer components and their respective blends [35]. The foliar fertilizer was diluted using tap water to form the standard sample used for agriculture purposes (90% tap water in the sample). Thereafter, sorbitol was added to generate concentrations ${\varphi }_s=$ 0.1, 0.2, 0.3, 0.4, and 0.5 g/mL in the samples. These solutions were used at an interval of fewer than 8 h.

2.2. Drop Evaporation

Twelve drops of different volumes, ranging from 3 to 15 μL, were placed on a pristine substrate of poly(methyl methacrylate) (PMMA) and Coffea arabica leaves. The droplets were dried within a sealed, temperature-controlled chamber maintained between 23 and 25 °C, while concurrently controlling relative humidity (RH) at set levels of $20\%$, $40\%$, and $60\%$. Temperature and RH were measured using a CMIIT ID: 2019DP8115 sensor. RH was controlled using silica gel, an amorphous and porous form of silicon dioxide, which absorbs water molecules from the environment to reduce moisture content and water activity ($a_w$). Water activity, ranging from 0 (no available water) to 1 (pure water), represents the ratio of vapor pressure in a substance to that of pure water at the same temperature. Relative humidity, expressed as a percentage, indicates the air’s moisture content relative to its maximum capacity at a given temperature.

2.3. Image Acquisition

To examine the formations resulting from evaporation in ambient conditions, we employed a Velab microscope (model VE-M4) equipped with 4× and 10× magnifications, complemented by a Nikon camera (D3200). The images were captured at a high-resolution setting of 300 pixels per inch (PPI), yielding approximately 4000 pixels along the longest side. For a comprehensive analysis of the droplets’ drying process, we conducted measurements of the contact angle, drop height, and radius using the ImageJ (version 1.52a) software.

Gray Level Co-Occurrence Matrix (GLCM)

We use Entropy based on gray level co-occurrence matrix (GLCM) to measure the texture of patterns in dried droplets. Higher (lower) entropy values indicate large (small) heterogeneous regions in an image. Texture analysis based on GLCM has been used successfully in characterizing protein films containing complex crack patterns [36] and salt crystals [32].

A gray level co-occurrence matrix (GLCM) is a matrix with dimensions equal to the number of gray levels, denoted as $N_g$, within an image. It is employed for pixel correlation analysis in images. Mathematically, the matrix element $p(i,j)$ represents the probability of transitioning from gray level i to gray level j at a specific displacement distance (d) and angle ($\varphi$) within an image, and it can be expressed as:

$$p(i,j)={\displaystyle \frac{C(i,j)}{{\sum }_{i=0}^{N_g-1}{\sum }_{j=0}^{N_g-1}C(i,j)}},$$

(1)

Here, $C(i,j)$ is the count of occurrences of gray levels i and j within the specified window at the ($d,\varphi$) pair. The denominator represents the total count of gray level pairs $(i,j)$ within the window, bounded by an upper limit of $N_g\times N_g$.

The mean ($u_x$ and $u_y$) and standard deviation (${\sigma }_x$ and ${\sigma }_y$) for both rows and columns of the matrix are defined as:

$$u_x=\sum _{i=0}^{N_g-1}\sum _{j=0}^{N_g-1}i·p(i,j),u_y=\sum _{i=0}^{N_g-1}\sum _{j=0}^{N_g-1}j·p(i,j),$$

(2)

$${\sigma }_x=\sum _{i=0}^{N_g-1}\sum _{j=0}^{N_g-1}{(i-u_x)}^2·p(i,j),{\sigma }_y=\sum _{i=0}^{N_g-1}\sum _{j=0}^{N_g-1}{(j-u_y)}^2·p(i,j),$$

(3)

Subsequently, the entropy (H) can be defined using the following equation:

$$H=-\sum _{i=0}^{N_g-1}\sum _{j=0}^{N_g-1}p(i,j)log\left(p(i,j)\right).$$

(4)

3. Results

Pattern in Dried Droplets of Fertilizer

Figure 2 shows the morphological patterns of dried fertilizer droplets under three different configurations: sessile, vertical, and pendant. Each configuration was observed at two relative humidities: 20% and 40%. At 20% relative humidity, the sessile configuration exhibited two distinct types of patterns, depicted separately on the left and right sides of the corresponding image. The left pattern showed well-defined elongated crystalline structures, indicating strong directional growth typical of low-humidity conditions where evaporation rates are higher and crystallization occurs rapidly. The right pattern displayed a more fibrous structure, suggesting a heterogeneous nucleation process possibly influenced by local variations in concentration and evaporation dynamics. At 40% relative humidity, the sessile droplets developed intricate and varied crystalline structures. The increase in relative humidity reduced the evaporation rate, leading to a slower crystallization process. The pattern shows a mixture of fibrous and elongated crystalline structures with regions of amorphous deposits, indicating a more complex and less homogeneous crystallization process compared to the lower-humidity condition.

In the vertical configuration at 20% relative humidity, the morphology of dried droplets is characterized by an aggregation of small crystal clusters in the upper region and denser fibrous patterns in the lower region. This configuration promotes a directional movement of solute towards the lower part of the droplet due to gravity, enhancing the formation of interconnected crystalline structures. At 40% relative humidity, the vertical configuration resulted in a more dispersed cluster pattern in the upper region with a denser crystalline region in the lower region. At this relative humidity, it is observed that liquid is retained in the denser fibrous regions. The slower evaporation rate at higher humidity levels allowed the migration of solutes to the lower region before crystallization, leading to a concentrated aggregation region pattern. The crystalline structures in the upper region appear more isolated and smaller compared to those formed at 20% HR.

The pendant configuration at 20% relative humidity produced a fibrous pattern, similar to the sessile configuration but with a combination of large crystals and amorphous structures. The influence of gravity in this inverted position caused a more pronounced separation of solute and solvent, leading to distinct radial crystallization patterns. The overall morphology suggests a strong directional influence of the droplet’s orientation on the crystallization process. At 40% relative humidity, the pendant droplets displayed more elongated crystal patterns and coarse amorphous crystalline structures. The increased humidity reduced the evaporation rate, allowing for a more complex distribution of solutes across the droplet surface before crystallization. The resulting pattern is a combination of small, evenly distributed crystalline domains with amorphous aggregates in the interior of the deposit.

An intriguing inquiry pertains to the influence of vapor pressure on the formation of patterns within fertilizer deposits. Our observations revealed that under high-vapor-pressure conditions (RH = 60%), fertilizer droplets fail to produce deposits even after a prolonged period of 72 h. This phenomenon is primarily due to the markedly reduced evaporation rate at elevated humidity levels, which impedes the crystallization and aggregation processes essential for pattern development. The persistent liquid state under these conditions prevents the solutes from reaching the critical concentration needed for nucleation and solid structure formation.

Figure 3 displays magnified views of different regions of the dried droplet patterns shown in Figure 2, highlighting the variations in morphology based on drying configurations and humidity levels. In the peripheral regions (Figure 3a), sessile droplets dried at 20% relative humidity (HR) exhibited two distinct morphologies: elongated crystalline structures and fibrous patterns. At 40% HR, these droplets developed intricate crystalline structures with regions of amorphous deposits, suggesting a complex and varied crystallization process. Vertical configuration droplets at 20% HR displayed clustered patterns in the upper region and dense fibrous morphologies in the lower region. Under 40% HR, the peripheral regions showed fewer clusters in the upper zone and larger hydrated aggregates in the lower zone. Pendant configuration droplets at 20% HR produced a dark, fibrous appearance with a combination of large crystals and amorphous structures, while at 40% HR, they revealed a mix of fine and coarse features, including partially hydrated regions and elongated crystal patterns.

In the central regions (Figure 3b), sessile droplets at 20% HR exhibited detailed crystalline patterns and fibrous structures, whereas at 40% HR, they featured a mix of intricate crystalline and amorphous structures, indicating a varied crystallization process. The vertical configuration at 20% HR showed clustered patterns in the upper central part with some fibrous regions and denser fibrous patterns in the lower part of the central region. At 40% HR, the central regions of vertical droplets displayed smaller, isolated clusters in the upper part and amorphous hydrated aggregates in the central lower part. Pendant droplets in the central region showed dense, mottled patterns at 20% HR, while at 40% HR, they exhibited a combination of fine and coarse structures, reflecting a complex distribution of solutes before crystallization.

Figure 4a panel I shows the pattern formation process due to drying of a sessile droplet at 20% relative humidity. In the first stage, t = 1260–1980 s, the drop has a smooth and uniform appearance, with few irregularities, which suggests a homogeneous distribution of the solute in the liquid. Between 2040 s and 2100 s, local supersaturation leads to the spontaneous formation of solid crystals, marking the onset of crystallization. Crystals emerge as microscopic entities and can gradually expand into elongated structures. Between 3420 s and 5700 s, a transition is observed towards the formation of more complex and intertwined structures. Finally, at t = 11,657 s, the droplet reaches an advanced state of drying, characterized by dense and fibrous structured crystals, which marks the culmination of the evaporation process. The deposit shows a completely dehydrated state, forming an interconnected network of fibrous characteristics. The formation of patterns by the drying of a sessile drop at 40% relative humidity is very similar with a clear distinction. We observe regions with liquid retention; see Figure 4b panel I. In these regions, the fibrous structure traps liquid between its interstices, which induces the presence of partially hydrated structures, favored by vapor pressure. This can occur because some components of the fertilizer are close to its critical relative humidity at room temperature, allowing it to easily absorb moisture from the air; see Table 1.

Figure 4a panel II presents the lateral drying process of a sessile fertilizer droplet through a series of images. In the first stages, t = 30 s and 570 s, the drop maintains a high and symmetrical profile, characteristic of a strong surface tension that works to maintain the compact and spherical shape of the drop, minimizing the contact surface, and therefore the evaporation rate. Starting at t = 1110 s the drop appears flatter, suggesting that the surface tension is losing its ability to maintain the original shape of the drop in the face of the disruptive forces of gravity and accelerated evaporation. Finally, at t = 2340 s, the drop presents an extremely thin and extended profile, indicative of an advanced drying stage where most of the solvent has evaporated and the solute begins to dominate the physical interactions within the drop. It is worth mentioning that the lateral drying behavior of a sessile drop at 40% relative humidity is very similar to that observed in conditions of 20% relative humidity; see Figure 4b panel II. It is important to mention that the drying process, in the different configurations, is incomplete when the drop profile appears flat, because liquid is still trapped in the cavities of the fibrous structure, potentially altering the final morphology of the droplets.

The height profile provides complete information about the spatial distribution of the drop throughout the entire drying process. Contrary to classical parameters such as contact angle, drop height, and radius, this approach allows detecting and quantifying asymmetries in the liquid distribution that may arise due to inhomogeneities in the substrate surface, variations in the liquid composition, or effects induced by external fields. Figure 4a panel III shows the evolution of the corresponding normalized height profile $h/h_0$ of a sessile fertilizer droplet with the normalized radius ($r/r_0$) throughout several stages of its drying process. Each curve represents a specific temporal state, offering an overview of drying dynamics. Initially, higher and symmetrical dome-like profiles are observed. As time passes, these profiles flatten progressively. In the final stages, the droplet profile becomes flatter and more extensive, indicating significant changes in geometry. The curves illustrate that the droplet remains anchored to the substrate and maintains profile symmetry, reflecting a homogeneous solute distribution. The gradual height change suggests uniform and controlled evaporation. Figure 4b panel III indicates that the height profile behavior at 40% relative humidity mirrors the trends observed at 20% relative humidity, with similar progressive flattening and extension of the droplet profile throughout the drying process.

Figure 5a panel I shows the pattern formation in a vertical droplet at 20% relative humidity. Initially, the drop appears as a uniform layer. During the early stages of drying (1620 s), gravity significantly influences the movement of solutes, drawing them downwards. However, at this stage, there are no visible signs of substantial solute sedimentation or segregation. As evaporation progresses (t = 1980–2040 s), the solute concentration increases, reaching a supersaturation point that promotes nucleation. Nucleation sites, which act as centers where solute particles begin to agglomerate, form small aggregates near the drop contact line. Between t = 2580 s and 4500 s, this aggregation process intensifies, with existing aggregates growing by incorporating more solute from the solution. This growth occurs throughout the deposit, resulting in an extensive network of interlocking aggregates. Towards the end of the process (t = 6180 s to 17,340 s), the droplet has lost much of its initial liquid content, resulting in a predominantly solid structure with fibrous characteristics. At 40% relative humidity (Figure 5b panel I), liquid retention is observed due to the fibrous structure, similar to what occurs in a sessile droplet at this humidity level. This retention leads to regions with partially hydrated structures.

Figure 5a panel II presents a series of images capturing the lateral drying process of a fertilizer drop in a vertical configuration. From the initial stages (t = 210 s to 810 s), the droplet maintains an asymmetric profile, as gravity pulls the liquid downward while surface tension attempts to minimize the surface area. This results in a higher concentration of liquid in the lower part of the droplet. As evaporation continues (t = 1410 s and 1860 s), the droplet profile elongates due to the reduction in volume from continuous evaporation, diminishing surface tension’s ability to sustain the original shape. At t = 2160 s, an abrupt change in droplet dynamics occurs, causing the droplet to move towards the lower end as it reduces in volume. By t = 2520 s, most of the liquid has evaporated, leaving residual water in the fibrous structure’s interstices. The lateral drying process at 40% relative humidity (Figure 5b panel II) shows similar patterns to those observed at 20% relative humidity.

Figure 5a panel III shows the normalized height profiles ($h/h_0)$ of the fertilizer droplet as a function of the normalized radius ($r/r_0$) throughout various drying stages. Initially, the profiles are tall and asymmetrical, corresponding to the early drying stages when the droplet retains most of its volume and evaporation is minimal. As evaporation progresses, the profile flattens and extends, indicating liquid redistribution towards the base of the drop due to gravity. The curves demonstrate a notable decrease in height in the central and upper regions (towards $r/r_0\approx 0$), reflecting lower mass retention compared to the base. This effect can be attributed to a capillary pinch that moves liquid from the center to the edges before settling under gravity. The curves show that although the drop remains anchored to the substrate for most of the drying process, it eventually moves towards the lower region. Despite the complex dynamics, the drop maintains its asymmetric shape throughout the drying process. The gradual height change across the profile indicates uniform and controlled evaporation. Figure 5b panel III shows that vertical droplets at 40% relative humidity exhibit a height profile similar to those dried at 20% relative humidity, with progressive flattening and extension.

Figure 6a panel I illustrates the pattern formation process in a pendant drop of fertilizer at 20% relative humidity. In the early stages (t = 1470 s and 2040 s), the drop is nearly perfectly circular, with clear edges and a homogeneous distribution of solute. At this point, surface evaporation is concentrating the solutes, but it has not yet reached the degree necessary for visible nucleation of solids. As evaporation progresses (t = 2160 s to 2220 s), minor changes in homogeneity occur, with small aggregates appearing, indicating the onset of nucleation where local solute concentrations reach saturation. This process intensifies between t = 3900 s and 4500 s, leading to the formation of elongated crystals and some amorphous structures. This phase results from a complex interaction between solute diffusion towards high-concentration areas and solvent migration towards less saturated areas, exacerbated by the continuous reduction in liquid volume. In the final stages (t = 7140 s to 8754 s), the droplet exhibits a dense, highly organized structure of crystals and solid aggregates, culminating in a final morphology that combines large crystals, amorphous structures, and fibrous networks. At 40% relative humidity (Figure 6b panel I), the drying process shows liquid retention due to the fibrous nature of the material, similar to the behavior observed in sessile drops at this humidity. This retention leads to regions where structures remain partially hydrated.

Figure 6a panel II shows a sequence of lateral images capturing the drying process of a pendant drop. Initially, the drop appears with a hemispherical shape due to strong surface tension keeping the liquid compact. Over time (up to t = 1650 s), the drop elongates and its volume decreases due to solvent evaporation. This transition increases solute concentration within the droplet. As evaporation continues, internal dynamics become more complex, and gravity causes the droplet to lose its anchorage and shrink radially (t = 1950 s). By t = 2250 s, most of the liquid has evaporated, leaving a thin deposit. Similar patterns are observed at 40% relative humidity (Figure 6b panel II), consistent with those seen at 20% relative humidity.

Figure 6a panel III presents a plot of the normalized height profile ($h/h_0)$ of a pendant drop as a function of the normalized radius ($r/r_0$). Initially, the profiles are tall and wide, indicating that the droplet retains most of its original volume and maintains a spherical shape, with effective surface tension countering gravitational deformation. As evaporation progresses, the profiles flatten, indicating symmetrical thinning. The height reduction towards the ends shows that surface tension can no longer effectively counteract gravity, and the remaining mass redistributes towards the center, forming a narrower profile. The curves demonstrate that the drop maintains profile symmetry throughout drying, despite rapid radius reduction in the final evaporation stage. The smooth height transitions indicate stable evaporation. Figure 6b panel III shows that pendant droplets at 40% relative humidity exhibit height profiles similar to those dried at 20% relative humidity, with progressive flattening and extension.

Figure 7 shows the relative evaporation time for each evaporation configuration. We observe that the sessile configuration has the highest relative evaporation time, with an average value close to 5.8, followed by the vertical configuration with an average around 3, and finally, the pendant configuration shows the lowest relative evaporation time, with an average close to 1.6. The sessile configuration might be more sensitive to relative humidity due to the air boundary layer that forms around the droplet. This boundary layer acts as a barrier to the diffusion of water vapor, and its effectiveness is directly related to the relative humidity of the surrounding air. The higher the relative humidity, the more saturated the air is with water vapor, and the less efficient the diffusion of vapor from the droplet into the air. In contrast, in the pendant configuration, the boundary layer is thinner and constantly disturbed by the airflow around the droplet. This is because the droplet is more exposed to air on all sides and is in less contact with a solid surface. The constant disturbance of the boundary layer facilitates the renewal of air in contact with the droplet’s surface, which means that water vapor is removed more quickly and replaced by drier air. This makes the evaporation process less dependent on the ambient relative humidity since even if the air is more saturated, the dynamic boundary layer allows for efficient diffusion of water vapor into the environment.

Figure 8 illustrates the effect of initial droplet volume on the drying patterns of fertilizer droplets at 20% relative humidity (RH) across three different configurations: sessile, vertical, and pendant. In the sessile configuration, droplets with volumes of 3 μL, 6 μL, 9 μL, 12 μL, and 15 μL exhibit consistent morphological characteristics. Each pair of images for these volumes shows patterns that include elongated crystalline structures and fibrous regions. The left half of each image typically displays elongated crystalline structures, while the right half shows a more fibrous pattern. In this configuration, two different types of patterns prevail regardless of the volume. For the vertical configuration, the drying patterns also remain consistent across the range of volumes. The images reveal a gradient of crystal density from the top to the bottom of the droplet, reflecting the influence of gravity on solute distribution during evaporation. As the volume increases, the shape factor, defined as the ratio of the droplet height to its base diameter, also increases. This shape factor reaches a maximum value of $\gamma$ = 1.2 in 15 μL droplets and a minimum value of $\gamma$ = 1 in 3 μL drops. This change suggests that gravity significantly impacts the drying dynamics, causing more pronounced solute movement and aggregation in larger droplets. In the pendant configuration, the patterns again show consistent morphological characteristics across different volumes. The images reveal that the fibrous structures are prominently present, with larger droplets exhibiting more extensive and interconnected crystalline networks. The uniformity in pattern formation despite varying volumes indicates a robust drying process influenced by the pendant configuration.

Figure 9 presents the fertilizer deposits generated in three different configurations (sessile, vertical, and pendant) under an intermediate vapor pressure (RH = 40%). For the sessile droplets, the deposits exhibit distinct regions of elongated crystals surrounded by amorphous aggregates and fibrous structures. The size of the crystalline region increases with the initial droplet volume. The consistency in the appearance of these crystalline structures across different volumes suggests a robust crystallization process influenced by the sessile configuration and intermediate humidity conditions. The elongated crystals form prominent patterns, indicating strong directional growth facilitated by the sessile droplet’s evaporation dynamics. In the vertical configuration, the drying process results in a clear separation between a high-mass-concentration region at the bottom of the deposit and a low-concentration region at the top. The high-concentration area features intricate interlocked hydrated crystalline structures, surrounded by small hydrated crystals. These crystals exhibit elongated forms with indistinct contours, mixed with amorphous and fibrous structures. This separation indicates a pronounced influence of gravity on solute distribution during drying, leading to the formation of dense crystalline networks at the lower part of the droplet. The low-density region at the top displays small, dispersed aggregates, further emphasizing the gravity-driven solute gradient. For the pendant droplets, the predominant feature across all volumes is the formation of fibrous structures. These structures consist of aggregates that may or may not be hydrated, independent of the initial droplet volume. The uniformity in the fibrous structures across different volumes suggests that the pendant configuration leads to consistent drying patterns under intermediate humidity. Gravity plays a significant role in shaping the final deposit morphology, promoting the formation of fibrous networks as the droplet dries.

To quantify the heterogeneity of the mass distribution of fertilizer deposits, we carried out a Gray Level Co-occurrence Matrix (GLCM) entropy-based texture analysis. Figure 10 presents the entropy values of dried fertilizer droplets over a wide range of initial drop volumes (3 μL to 15 μL) in three different configurations: sessile, vertical, and pendant, at 20% relative humidity (RH). The results in Figure 10 show that, regardless of the initial droplet volume and configuration, there are no significant differences in the entropy values of the deposits produced at 20% RH. The entropy values remain relatively constant, suggesting that the initial droplet volume and the configuration used do not significantly influence the heterogeneity of the mass distribution in these deposits. This consistency indicates a stable pattern formation process under these drying conditions.

Figure 11 compares the entropy values of fertilizer deposits generated at 40% RH across different initial droplet volumes and configurations. The analysis reveals significant differences in the heterogeneity between deposits produced with low initial droplet volumes (3–6 μL) across different configurations. For these small volumes, sessile droplets exhibit higher entropy values, indicating more complex and disordered patterns, while vertical droplets show lower entropy values, suggesting simpler and more uniform patterns. For higher initial droplet volumes (9–15 μL), the entropy values of sessile and pendant droplet deposits do not show significant differences, indicating similar pattern complexity and heterogeneity. However, significant differences are observed when comparing these two configurations with the vertical droplets. Vertical droplets consistently show lower entropy values, reflecting less complex mass distributions compared to sessile and pendant droplets.

To gain deeper insights into the influence of surfactant additives on the quality of sessile fertilizer droplet coatings, we investigated the impact of sorbitol on these coatings. Figure 12 presents the deposit patterns (a) and their corresponding three-dimensional representations (b) generated with varying concentrations of sorbitol. At low concentrations (0.01–0.1%), sorbitol hinders aggregate formation within the central region of the deposit, allowing the fibrous structure to pervade the coating, as evidenced by the green regions in the three-dimensional projections. Starting at a 10% sorbitol concentration, a morphological transition is apparent, characterized by the emergence of small dispersed aggregates within the deposit, identified by the sky blue regions in the three-dimensional projections. Notably, the size of these aggregates diminishes as the sorbitol concentration increases. These findings suggest that sorbitol serves as a modulating agent, influencing salt aggregation and subsequent mass transport mechanisms during the drying process.

Figure 13 quantifies the heterogeneity of the mass distribution of fertilizer deposits with different sorbitol concentrations through GLCM entropy-based texture analysis. The results indicate that configurational entropy decreases exponentially as a function of sorbitol concentration. The maximum entropy value, approximately 8.5, is observed at ${\varphi }_s$ = 0.01%, whereas the minimum value, around 7.0, occurs at ${\varphi }_s$ = 40%. This behavior suggests an inverse relationship between sorbitol concentration and the heterogeneity in the mass distribution of fertilizer deposits.

Last, but not least, Figure 14 presents a comparison of foliar fertilizer deposition patterns on Coffea Arabica leaves under three application configurations (sessile, vertical, and pendant) and two relative humidity conditions (20% and 40% RH). In all configurations and humidity conditions, structures consistent with those observed on the PMMA substrate were found. The deposition patterns at 20% RH show fibrous structures in the sessile configuration, a higher concentration of deposits at the bottom in the vertical configuration, and homogeneous patterns in the pendant configuration. At 40% RH, the structures in the sessile configuration are a mixture of fibrous and amorphous, while in the vertical configuration, the deposits are dense in the upper part but hydrated in the lower part, and in the pendant configuration, scattered crystalline structures are observed. These observations validate the applicability of our initial findings regarding the effect of droplet configuration and humidity conditions on nutrient distribution in foliar applications on real leaves.

4. Discussion

The present study has provided a detailed view of the formation of fertilizer deposits in three different configurations: sessile, vertical, and pendant, as well as their response to factors such as initial droplet volume, vapor pressure, and the presence of sorbitol. The results reveal two types of deposits in the sessile droplets, with well-defined crystals and fibrous structures. In the case of vertical drops, two distinct regions are observed, one with fibrous structures at the bottom and small crystal clusters at the top. In contrast, the pendant drops show a predominance of intertwined large crystals with peripheral fibrous structures. Furthermore, the force of gravity has been shown to play a fundamental role in the morphology of deposits, evidenced by changes in the droplet shape factor.

Investigating the distribution of fertilizer aggregates on plant leaves is essential, as it can significantly impact nutrient absorption [37]. Within a cycle of re-wetting and foliar fertilizer absorption [38], a homogeneous distribution of fertilizer can lead to more uniform and efficient nutrient uptake by the plant. Conversely, in a heterogeneous distribution, areas with high fertilizer concentration can only release nutrients when sufficiently hydrated. Additionally, high-concentration areas may increase the risk of phytotoxicity, killing leaf cells. In this context, the incorporation of sorbitol as a surfactant can provide additional benefits in fertilizer application, improving the uniformity of nutrient distribution.

A significant finding emerges from the influence of vapor pressure on deposit formation. The high vapor pressure (60% HR) in fertilizer droplets precludes deposit generation within 72 h, while intermediate (40% HR) and low (20% HR) vapor pressure conditions result in deposit formation. The relative evaporation times of each configuration elucidate drying dynamics. Sessile droplets have the longest evaporation times, while vertical and pendant droplets, influenced by gravity, show intermediate and the fastest evaporation times. These observations contrast with the findings of Mondal et al. [17], which indicate that droplets in vertical configurations exhibit the longest evaporation times due to gravitational effects, whereas our results show that sessile droplets have the longest evaporation times. This discrepancy highlights the unique drying behavior of droplets with varying chemical compositions under different vapor pressures. As Andalib et al. [39] have observed, the evaporation rate diminishes as the relative humidity rises, which supports our findings on the role of humidity in evaporation dynamics. Therefore, in the application of foliar fertilizers, it is important to maintain relative humidity levels of at least 40%. First, this ensures that evaporation is rapid enough to prevent droplets from remaining in a liquid state for too long, which could lead to nutrient loss due to runoff during the condensation cycle. Second, this humidity level facilitates the formation of well-distributed deposits on the leaves.

The analysis of deposition patterns revealed that the Critical Relative Humidity (CRH) of the possible compounds in Bayfolan^® Forte exerts a significant influence on the morphology of deposits formed during the evaporation of fertilizer droplets. The CRH of blended or compound fertilizers often falls below the average CRH of their individual components. The extent of this reduction can be quite substantial in certain instances. One notable example is a mixture of ammonium nitrate (CRH: 59.4%) and urea (CRH: 72.5%), which shows a marked decrease in CRH (18.1%), leading to rapid moisture absorption. This hygroscopic capacity retards the evaporation process, facilitating the formation of deposits with a hydrated and fibrous structure. Conversely, compounds with high CRH, such as ammonium sulfate (CRH: 79.2%), potassium chloride (CRH: 84.0%), and monocalcium phosphate (CRH: 93.6%), do not absorb water at low to intermediate relative humidity levels (below 50% RH). This limited hygroscopic behavior allows evaporation to occur relatively quickly and moderately, resulting in more defined and less dispersed deposition patterns. Additionally, under conditions of high relative humidity (above 60% RH), no deposits were observed due to the significant moisture absorption by these compounds, which prevents adequate evaporation for visible deposit formation.

This study investigates the impact of sorbitol on the coating quality of fertilizer sessile droplets. The findings suggest sorbitol’s potential role in modulating salt aggregation, thereby influencing deposit morphology. This aligns with prior research demonstrating sorbitol’s capability to facilitate the transport of macro- and micronutrients in organic fertilizer through the phloem [5]. Furthermore, the heterogeneity of the mass distribution has been evaluated through texture analysis, finding consistency in the entropy of the deposits, regardless of the configuration and the initial volume of the drop, except for vertical deposits. Additionally, the entropy of GLCM as a function of sorbitol concentration reveals an exponential relationship between sorbitol concentration and heterogeneity. These discoveries, in line with previous research in the field of material chemistry and nanotechnology, underline the importance of sorbitol as a key modulating agent [40,41], opening new perspectives for the design and optimization of controlled release systems and applications in precision agriculture.

The study has several notable strengths. First, it provides a detailed characterization of pattern formation in fertilizer deposits, investigating multiple configurations and initial droplet volumes. This provides a complete view of how these factors influence the morphology of the deposits. Additionally, quantification of mass distribution heterogeneity using GLCM entropy-based texture analysis adds a valuable quantitative approach to the research. The consistency of the results across different configurations and initial droplet volumes, as well as the exploration of the influence of vapor pressure and surfactants, contribute significantly to the understanding of this process.

Despite its strengths, the study presents some limitations. The influence of temperature and its interaction with relative humidity were not fully explored. Additionally, while the study investigated the effect of sorbitol as a surfactant, it would be valuable to examine other surfactants and additives to gain a more complete understanding of their impact on deposit morphology. Chemical analyses to identify the precise composition of the deposits and their relationship to sorbitol concentration could further enhance the findings. Moreover, the study did not investigate Marangoni flows, which are known to significantly influence the dynamics of droplet evaporation and could affect the distribution and uniformity of the foliar fertilizer coatings. Future studies should consider these factors to provide a more comprehensive understanding of surface coating with foliar fertilizers.

In the future, it would be interesting to expand the research to further explore the influence of temperature and temperature–moisture interaction on pattern formation in fertilizer deposits. Furthermore, the practical application of these findings could be investigated in the agricultural industry, which could contribute to improving the efficiency of fertilizer application and ultimately sustainable agriculture. Further studies on other surfactants and additives and their effects on deposit morphology would provide a deeper understanding of the modulation of deposit characteristics. Finally, identifying the precise chemical composition of the deposits and their relationship with surfactants could open new avenues of research to optimize the quality of fertilizer coatings.

5. Conclusions

This study has comprehensively investigated the formation of fertilizer deposits in sessile, vertical, and pendant configurations, evaluating factors such as initial droplet volume, vapor pressure, and the presence of sorbitol. The results reveal distinctive patterns in the morphology of the deposits, highlighting the significant influence of gravity on the shape and distribution of the droplets. Furthermore, the critical importance of vapor pressure in the formation of these deposits has been demonstrated, with significant implications for surface coating. Additionally, sorbitol was found to modulate salt aggregation, significantly affecting the heterogeneity and final morphology of the deposits.

These findings provide valuable insights into optimizing fertilizer deposition processes and enhancing nutrient delivery for plant growth and development. Future research should explore the effects of other surfactants and temperature variations to further improve precision agriculture practices.