Transport of plant growth promoting bacteria (Azospirillum brasilense) in sand under transient water flow: effect of inoculation regime

Highlights

Time dependent deposition of two Azospirillum brasilense strains in sand quantified.

Three inclusions regimes examined: surface, subsurface and premixed.

For surface and subsurface the bacteria accumulated near the point source and remained stagnant in the premixed.

The attachment/detachment numerical model found adequate to describe the time dependent deposition profiles of the bacteria.

Abstract

Azospirillum brasilense strains Sp7 and Cd are commonly employed plant growth-promoting bacteria (PGPB) that produce phytohormones and fix nitrogen. The two basic methods of PGPB soil inoculation are direct mixing with the soil and irrigation with liquid inoculants. The integration of drip irrigation with delivering plant growth-promoting bacteria in desert areas with sandy soil is becoming more common. With the drip irrigation system, the mobility of PGPB in the sandy soil determines the range of root zone inoculation. Therefore, we examined the transport and fate of PGPB under transient water flow conditions in a 30-cm high segmented sand column with three sand-inoculation regimes: (1) surface irrigation, (2) subsurface irrigation, and (3) sand premixing. The water, bromide, and bacterial distribution in the sand profile was measured at 2 and 48 h after irrigation. The measured data were described using the attachment/detachment numerical model using the HYDRUS 2/3D code. Results showed that even though A. brasilense Sp7 and Cd exhibit similar hydrophilicities and zeta potentials, their deposition in the sand profile differs. Strain Cd consists of smaller cells that undergo less adsorption and less straining than strain Sp7, and the former’s vertical movement therefore reaches greater depths under surface- and subsurface-inoculation regimes. Nevertheless, most of the PGPB accumulated near the water source. In the sand-premixing inoculation regime, the bacteria barely moved at all. Overall, when the target root zone was deep, subsurface-irrigation inoculation worked better than the other two inoculation regimes, because it was more likely to deliver large amounts of PGPB to the root zone. Furthermore, the first-order attachment model optimized two parameters (first-order attachment coefficient and die-off rate) and well simulated the bacterial vertical movement in the surface- and subsurface-inoculation regimes (R² > 0.91).

Introduction

Plant growth-promoting bacteria (PGPB) are functioning in nitrogen fixation, phosphorus solubilization, potassium solubilization, stress tolerance, and plant-pathogen antagonism (Bashan 1998; Compant et al. 2005; Zamioudis and Pieterse 2012; Olanrewaju et al. 2017). The application of PGPB to different crops can increase yield and decrease the need for conventional chemical fertilization, as shown by various research experiments in the last 40 years (Adesemoye et al. 2009; Bashan et al. 2014). For example, inoculation of an Azospirillum sp. increased maize yield by an average of 10% (Díaz-Zorita et al. 2015); and inoculation of an Azotobacter sp. increased the yield of various crops by an average 34.4% (Schmidt and Gaudin 2018). Interest from farmers and researchers in minimizing chemical fertilizer use and increasing crop yields has propelled the utilization of this bacterium, especially in desert areas with sandy soil (Galindo et al. 2022; Hungria et al. 2022). Globally, sandy soils encompass an area ranging from 5 to 14 million square kilometers, yet the extent of food production on these soils is confined to merely 325,000 square kilometers (Bockheim 2024). Therefore, the use of PGPB in sandy soil for fertility improvement has great potential. Furthermore, Quartz sand is often used as a soilless media in plant nurseries under controlled experimental environment (Bashan and Levanony 1988). Therefore, studying the inoculation of sand by PGPB is relevant for these agricultural systems.

It is critical to ensure that PGPB are effectively introduced into the root zone (Bashan et al. 2014). The most used method is seed inoculation (Di Salvo et al. 2018), which is both simple and economical (Bashan 1998). Seedling root (Aslantaş et al. 2007), leaf spray (Bashan and de-Bashan 2002; Bejarano et al. 2017), soil surface spray (Efthimiadou et al. 2020), soil mixing (Remans et al. 2008) inoculation have been used as well. Although all these inoculation methods are simple, they are limited to one-time use. With the development of irrigation systems, soil inoculation through sprinkling irrigation, surface and subsurface drip irrigation has garnered much attention (Janat and Kurdali 2008; Simões et al. 2019; Stegelmeier et al. 2022). An advantage of irrigation inoculation is that the PGPB can be repeatedly applied during the growing season. Some studies have shown that surface-irrigated bacteria accumulate in the topsoil layers (Huysman and Verstraete 1993; Haller et al. 2016), whereas subsurface drip irrigation can deliver bacteria to the active root zone (Trooien et al. 2000; Kouznetsov et al. 2004; Reyes Esteves et al. 2022). Additionally, the inoculated bacteria may move to deeper soil layers under the influence of drip irrigation water or rainfall (Soltani Tehrani et al. 2023). To improve the efficiency and accuracy of PGPB inoculation through drip irrigation, one must determine the transport and retention characteristics of the inoculated bacteria in the soil.

The bacterial transport and retention in porous media are affected by three main factors: (i) the bacterial cell envelope properties, (ii) the porous medium properties, and (iii) the liquid-phase properties (Bradford et al. 2013; Yang et al. 2021; Chen et al. 2023). Bacterial properties affecting transport include surface charge and hydrophobicity, shape and size, surface macromolecular composition, chemotaxis and haptotaxis, physiological state, and cell concentration (Engström et al. 2015). Porous medium properties include particle size and surface properties, mineral type and content and organic matter content (Zhong et al. 2017). Liquid-phase properties include the water content, solution pH, temperature, ion concentration and composition, viscosity, and surface tension (Zhong et al. 2017; Rusconi et al. 2014). Bacterial deposition in soil or sand is commonly classified as occurring through adsorption and straining (Engström et al. 2015). Adsorption is the phenomenon that bacteria adsorbed on soil or sand particle surface under the combination of van der Waals attraction force, double-layer repulsion force and acid–base interactions (hydrophobic force); (van Oss 1989; Oss 1997). Straining is commonly related to physical properties, such as bacterial size and soil pore size distribution (Gannon et al. 1991; Huysman and Verstraete 1993; Bradford et al. 2006).

Azospirillum brasilense is one of the most studied PGPB and is most applied to cereal grains (e.g., maize, millet, rice, wheat, and sorghum) (Bashan 1999; Lucy et al. 2004; Bashan and de- Bashan 2015; Cassán and Diaz-Zorita 2016; Cassán et al. 2020). Azospirillum brasilense is gram-negative bacteria. Strain Sp7 and Cd are two closely related strains of A. brasilense, with strain Cd initially isolated from plant roots that had been inoculated with strain Sp7 (Tarrand et al. 1978). Laboratory and field experiments with PGPB employed inoculation through ploughing, surface or subsurface irrigation. However, the comparison of bacterial transport and retention characteristics between different soil inoculation regimes is still lacking. Understanding the transport and retention of PGPB under different soil inoculation regimes is essential for effectively delivering PGPB to the active root zone to maximize their beneficial effects. We hypothesized that different inoculation regimes would affect the transport, retention, and survival characteristics of PGPB under transient unsaturated water flow. Therefore, the main objective of this study is to quantify the influence of three PGPB inoculation regimes on their transport and retention in the sand profile under transient unsaturated water flow. Two strains of Azospirillum brasilense were employed - Sp7 and Cd. The surface characteristics and dimensions of the two strains was measured. The three-inoculation regimes employed were: (i) surface irrigation (ii) subsurface irrigation, and (iii) sand premixing. The transport and retention characteristics were quantified from the bacterial distribution in the sand profile following 2 and 48 h from the time of application. The validity of the attachment\detachment numerical model to describe the measured time-depended profiles was evaluated and the model optimized parameter used to interpret the results. Manny studies (e.g. Schinner et al. 2010; Wang et al. 2011; Chen and Walker 2012; Bradford et al. 2013; Wang et al. 2013; Sasidharan et al. 2016; Suliman et al. 2017; He et al. 2018; Yang and van Elsas 2018; Le et al. 2023) that explore the transport characteristics of various bacteria have employed quartz sand to provide a uniform and homogeneous prose medium for controlled and repeatable experimental conditions. Using sand rather than naturally occurring soils enable the validation of numerical models, which may be further developed for naturally occurring soil, considering other environmental conditions of the solid and liquids properties.

Materials and methods

Soil

Fine quartz sand was used in all experiments. The sand originated from the Negev desert in Israel was purchased from Yehu Clays Ltd. The mineralogical composition was close to pure quartz with traces of ferrous minerals (Mishurov et al. 2008). It composed SiO₂ (94.7%), Al₂O₃ (1.6%), Fe₂O₃ (0.37%), CaO (0.7%), MgO (0.09%), Na₂O (0.7%), K₂O (0.6%). The particle-size distribution of the fine sand was measured using laser diffraction (Mastersizer 2000, Malvern Instruments Ltd., UK). The cumulative percentages of grain sizes are shown in Figs. 1, 2(a). The saturated hydraulic conductivity of sand (16 cm h^− 1) was measured by falling-head method using a KSAT apparatus (METER Group AG, Germany). The bulk density of the find sand was1.47 g cm^− 3, and the specific surface area was 0.17 m² g^− 1.

Fig. 1

Fluorescence microscope pictures of (a) A. brasilense Sp7 and (b) A. brasilense Cd

Fig. 2

(a) Particle size distribution of sand; (b) Water-retention curve of the quartz sand used in the study (water content –bottom x axis; capillary pressure – left y axis). Effect of cell size on straining in sand (bacterial size –top x axis; percentage of pore space in which straining can occur (P) – right y axis)

The water-retention curves of sand were measured by tension table (EcoTech, Germany). The van Genuchten model (Van Genuchten 1980), Eq. 1, was fitted to the measured-water retention curve.

$${S}_{e}=\frac{\theta -{\theta }_{r}}{{\theta }_{s}-{\theta }_{r}}=\frac{1}{{\left[1+{\left(\alpha {\Psi }\right)}^{n}\right]}^{m}}$$

(1)

where, S_e is the effective saturation, θ is the water content (cm³ cm^− 3), θ_r and θ_s is the residual water content and saturated water content (cm³ cm^− 3), respectively. $\varPsi$ is pressure head (cm), α is a scale parameter inversely proportional to mean pore diameter (cm^− 1), n and m are the shape parameters of soil water characteristic, m = 1 − 1/n, 0 < m < 1. The van Genuchten model parameters are listed in Table 1.

Table 1 Total surface free energy SFE (γ_T), dispersive (γ_d) and polar (γ_p) components (mJ m^− 2) for water, diiodomethane and formamide at 25 ℃

Cell culture and observation

A. brasilense strains Cd and Sp7 were cultivated in sterile 250 mL Erlenmeyer flasks containing 100 mL Luria Broth growth medium and 50 µg ml^− 1 ampicillin until late log phase (∼ 24 h at 30 °C, on an orbital shaker at 150 rpm). The bacterial culture was concentrated by centrifugation (5000 x g for 10 min at 4 °C). The supernatant was removed, and the cells resuspended in 40 ml of 20 mM KCl. This washing process was repeated three times. The final bacterial suspension was diluted with 20 mM KCl until the optical density at 600 nm (OD₆₀₀) ∼ 1 (strain Sp7 ∼ 1.2 × 10⁸ CFU ml^− 1; strain Cd ∼ 5 × 10⁸ CFU ml^− 1); this was the standard suspension used for all experiments unless noted otherwise. For observation, bacteria were dyed with BacLight LIVE/DEAD bacterial viability kit (Molecular Probes, Eugene, OR, USA) according to the manufacture protocol: (1) add 3 µL of the dye mixture (Component A and Component B of LIVE/DEAD bacterial viability kit) for each mL of the bacterial suspension; (2) mix thoroughly and incubate at room temperature in the dark for 15 min. The dyed bacteria suspension was viewed under a fluorescence microscope (Olympus, Japan). The excitation-emission wavelength combination of the filter enables blue light excitation in a narrow wavelength range of 475–490 nm and green fluorescence detection in the range of 505–535 nm. The bacterial size was determined based on the fluorescence microscope pictures (10 replicates) using 20 μm scale bar. The wet weight of rod-shaped cells was calculated according to Eq. 2 (Baldwin et al. 1988). The wet weight of bacteria was calculated assuming the density of bacteria ρ is 1.1 g cm^− 3 (e.g. Loferer-Krößbacher et al. 1998).

$$W=\left[\frac{\pi {D}^{2}\left(L-D\right)}{4}+\frac{\pi {D}^{3}}{6}\right]\cdot \rho$$

(2)

where, L (cm) is bacterial length, D (cm) is bacterial width and W is bacterial wet weight (g).

For bacterial enumeration, the drop plate viable counting method was used. Ten-fold serial dilutions were placed in a clear 96-well plate; 20 µl of sample was transferred into 180 µl sterile PBS (pH 7.4) and mixed. Four replicates of 10-µl aliquots from selected dilutions were spotted onto agar plates (Herigstad et al. 2001). Plates were dried under sterile air, sealed, and incubated at 30 ºC for 36 h. The number of bacteria per milliliter of one sample was calculated by dividing the number of colonies by the dilution factor and spot volume. When using the drop plate viable counting method, bacteria can exist in a viable but non-culturable (VBNC) state. To address this, we calibrated bacterial enumeration from culturable techniques using microscopy methods in the following batch adsorption experiment. The results showed that the adsorption isotherm obtained from culturable techniques and microscopy methods were very similar.

Contact angle and surface free energy

A 10-ml aliquot of bacterial suspension (OD₆₀₀ ∼ 1.8) was filtered through a 0.45 μm cellulose membrane filter using vacuum filtration to form a cell lawn (Gallardo-Moreno et al. 2011). The cell lawn was dried in a desiccator for 1 h. The drying time needed to reach the “plateau contact angle” (Gallardo-Moreno et al. 2011) was determined in a preliminary experiment.

The contact angle was measured by the sessile drop method using an optical contact angle (OCA) device (Dataphysics Co., Germany). All contact angles were measured against two polar (water θ^W and formamide θ^F) and one nonpolar (diiodomethane θ^D) wetting liquid. The contact angle measurement was time dependent. Here, the initial contact angle (measured at t = 0.5 s) was used to calculate surface energy by solving Eq. 3 for the three liquids, based on the method by Wu (1973). The calculation was done with OCA Software SCA20 (Dataphysics). Total surface energy, and dispersive and polar components of the surface free energy for the three liquids are presented in Table 2.

$${\gamma }_{l}\left(1+ \text{cos}\theta \right)= 4 \left(\frac{{\gamma }_{s}^{d}{\gamma }_{l}^{d}}{{\gamma }_{s}^{d}+{\gamma }_{l}^{d}}+ \frac{{\gamma }_{s}^{p}{\gamma }_{l}^{p}}{{\gamma }_{s}^{p}+{\gamma }_{l}^{p}}\right)$$

(3)

where ${\gamma }_{l}$ is the wetting liquid’s surface free energy (mJ m^− 2); ${\gamma }_{s}^{d}$ and ${\gamma }_{s}^{p}$ are the dispersion and polar components of the solid’s surface energy, respectively (mJ m^− 2); ${\gamma }_{l}^{d}$ and ${\gamma }_{l}^{p}$ are the dispersion and polar components of the wetting liquid’s surface energy, respectively (mJ m^− 2).

Table 2 Contact angles, surface energy components, BATH and zeta potential of of A. brasilense Sp7 and Cd

Bacterial adhesion to hydrocarbons

Hydrophobicity of A. brasilense strains Sp7 and Cd was measured using the bacterial adhesion to hydrocarbons (BATH) assay (Rosenberg et al. 1980). Bacterial pellets were resuspended in 50 ml phosphate–urea–magnesium sulfate (PUM) buffer (17 g l^− 1 K₂HPO₄, 7.26 g l^− 1 KH₂PO₄, 1.8 g l^− 1 urea and 0.2 g l^− 1 MgSO₄·7H₂O, pH 7.1). The bacterial suspension was allowed to settle for 30 min, and the well-dispersed cells were collected from the upper layer and diluted in PUM buffer to an OD₆₀₀ ∼ 0.5. A 5-ml aliquot of this bacterial suspension and 1 ml of n-hexadecane (Sigma Aldrich, USA) were added together to a 20-ml glass tube and mixed by vortexing for 2 min. The mixture was allowed to separate for 15 min after vortexing. The concentration of residual bacteria in the aqueous phase was measured at OD₆₀₀. Each sample was replicated three times with three technical repeats per biological replicate.

Zeta potential

Bacterial cell pellets were resuspended in 20 mM KCl and diluted to OD₆₀₀ ∼ 1. The zeta potential of the bacterial suspension was measured by Zeta Potential Analyzer (NanoBrook 90Plus PALS, Brookhaven Instruments, USA). Each sample was analyzed for two cycles in five repetitions.

Batch adsorption experiment

A. brasilense strains Sp7 and Cd were suspended in PBS (pH 7.4) and diluted to 10 different concentrations (OD₆₀₀ ranging from 0 to 1). In a 50-ml centrifuge tube, 3 g of sand was mixed with 30 ml bacterial suspension and shaken on an orbital shaker at 150 rpm at 25 °C for 1 h. The sand was then allowed to settle for 10 min and 10 ml supernatant was collected for bacterial enumeration by viable counting method (Mills et al. 1994). The number of adsorbed bacteria was calculated by subtracting the number of unattached bacteria from the total applied number of bacteria. Each concentration was replicated three times, with four technical repeats per biological replicate.

The Langmuir model (Eq. 4) and the Freundlich model (Eq. 5) were fitted to the measure bacterial adsorption isotherms.

$$Qe=\frac{{Q}_{max}\cdot k\cdot Ce}{1+k\cdot Ce}$$

(4)

$$Qe=m{Ce}^{n}$$

(5)

where Q_e is the number of bacteria adsorbed to the sand (cell g^− 1), C_e is the equilibrium concentration of non-adsorbed bacteria (cell ml^− 1), Q_max is the maximum adsorption capacity (monolayer capacity) (cell g^− 1), and k is the Langmuir adsorption constant (cm³ cell^− 1) which is related to the bonding energy of adsorption; for Freundlich model, n is a constant and m [(cell g^− 1) (cell ml^− 1)⁻ⁿ] is a constant related to the adsorption capacity.

Transport experiments

A 30-cm PVC tube (O.D.=27 mm; I.D.=20 mm) comprised of 1-cm long segments, sterilized and reconstructed into a 30-cm long segmented column (30 × 1 cm segments) held together using transparent adhesive tape. A wire mesh (diameter 1 mm) and polyester filter (thickness 2 mm, pore diameter 500 μm) were incorporated to the bottom of the column to prevent sand loss but allow air escape. The column was packed with wet sand (gravimetric water content 10%) to a bulk density of 1.47 g cm^− 3. Most of the material and equipment used in this experiment, including sand, columns, solutions, and labware, were sterilized by autoclaving (121 ºC for 20 min). Non-autoclavable equipment (e.g., pump tubes) was sterilized by washing with 70% ethanol.

Three different treatments applied in this transport experiments are: (1) surface irrigation with bacterial suspension; (2) subsurface irrigation (at 15-cm depth) with bacterial suspension; (3) bacterial suspension homogeneously mixed with the sand, followed by surface irrigation with double-distilled water (DDW). The irrigation water flow rate was 0.25 ml min^− 1 and the irrigation event took place 40 min (10 mL bacterial suspension in total). To standardize the bacterial count across all treatments, 10 mL of bacterial suspension was used in the premixing method. To achieve an initial water content of 10% in all sand columns, an additional 4 mL of DDW was added to the 10 mL of bacterial suspension before mixing it with the sand. A sterile environment was maintained during this experiment by covering the irrigation system with a sterilized plastic bag. For each treatment, two independent columns were prepared and irrigated. Each column was cut into 15 segments 2 h and 48 h after the end of irrigation. The sand from each segment was removed and divided into two portions. One portion was stored in a sealed glass vial for measurement of gravimetric water content and the other portion was placed in a 50-ml centrifuge tube and mixed with PBS (1:10 w/v). The tubes were shaken for 1 h on an orbital shaker at 140 rpm at 4 °C. The sand was allowed to settle for 2–3 min after shaking, and 10 ml supernatant was collected for bacterial enumeration with the viable counting method. A similar irrigation/inoculation experiment was performed with 300 ppm potassium bromide as the tracer instead of bacteria. The initial bromide concentration in the sand for the surface and subsurface was zero. For the premix regime, the initial bromide concentration was 0.5 mg cm^− 3. The concentration of bromide was determined by ion chromatography (Metrohm AG, Switzerland) (Dahan and Ronen 2001). The water content, bromide concentration and bacterial counts in the sand profile were plotted as a function of depth. Mass balances were calculated for the water, bromide, and number of bacteria recovered from each section of the segmented column. For water distribution, the water-content values were averaged from all the columns. For bromide distribution, the values of two replicates were averaged. For bacterial distribution, each sample comprised three biological replicates (independent column experiments) with four technical repeats per biological replicate.

Modeling approach

One-dimensional (1D) uniform water flow in a vertical soil column under variably saturated conditions follows the Richards equation (Richards 1931):

$$\frac{\partial \theta }{\partial t}=\frac{\partial }{\partial z}\left[K\left(\frac{\partial h}{\partial z}+1\right)\right]+{S}_{w}$$

(6)

where $\theta$ is the volumetric water content (cm³cm^− 3), $t$is time (h), $z$is the spatial coordinate (cm), $h$ is the soil water potential (cm), ${S}_{w}$ is the sink term which represents the volume of water removed per unit time from a unit volume of soil (h^− 1), and $K$ is the unsaturated hydraulic conductivity (cm h^− 1). The unsaturated hydraulic conductivity $K$ described by the relationship between $\theta$ and $h$ in van Genuchten model was expressed as (van Genuchten 1980):

$$K\left(\theta \right)={K}_{s}{{S}_{e}}^{\frac{1}{2}}{\left[1-{\left(1-{{S}_{e}}^{\frac{1}{m}}\right)}^{m}\right]}^{2}$$

(7)

where ${K}_{s}$ is saturated hydraulic conductivity (cm h^− 1).

The convection–dispersion equation (CDE) describing non-reactive tracer (e.g., bromide) transport can be written as:

$$\frac{\partial C}{\partial t}=D\frac{{\partial }^{2}C}{{\partial z}^{2}}-v\frac{\partial C}{\partial z}$$

(8)

where $C$ is the solute concentration (mg cm^− 3) in the aqueous phase, t is time (h), D is the dispersion coefficient (cm² h^− 1), and v is the pore-water velocity (cm h^− 1). Here, dispersion includes the combined effect of mechanical dispersion and diffusion.

For bacterial transport, attachment/detachment model was applied as follows:

$$\frac{\partial \theta C}{\partial t}+{\rho }_{b}\frac{\partial S}{\partial t}=\frac{\partial }{\partial x}\left(\theta D\frac{\partial C }{\partial x}\right)-\frac{\partial q C}{\partial x}-{\mu }_{w}\theta C-{\mu }_{s}{\rho }_{b}S$$

(9)

where θ is the volumetric water content; ${\rho }_{b}$ is the soil bulk density (g cm^− 3); t is the time (h); q is the flow rate (cm h^− 1); $x$ is the spatial coordinates (cm); $D$is the dispersion coefficient (cm² h^− 1); C is the concentration of bacteria in the aqueous phase (CFU cm^− 3); S is the solid-phase concentrations associated with adsorption site (CFU g^− 1); ${\mu }_{s}$ is the die-off rate of the bacteria (h^− 1) in solid phase; ${\mu }_{w}$ is the die-off rate of the bacteria (h^− 1) in solid phase. It should be note here, we cannot distinguish that the bacteria death happened at the liquid or solid phase. Therefore, we only used one parameter ${\mu }_{s}$ to represent bacterial death, non-recovered bacteria, and bacteria with VBNC state. Since fitting bacterial retention profiles was more difficult than fitting traditional bacterial breakthrough curves (Chen et al. 2024), here we only applied one site model, and the mass transfer between the aqueous and solid phase was described as:

$${\rho }_{b}\frac{\partial S}{\partial t}=\theta {\psi }_{t}{k}_{a}C-{k}_{d}{\rho }_{b}S$$

(10)

where ${k}_{a}$ is the first-order attachment coefficient (h^− 1); ${k}_{d}$ is the first-order detachment coefficient (h^− 1); and ${\psi }_{t}$ is a dimensionless colloid retention function that accounts for time-dependent deposition. To minimize the fitting of non-unique parameters, ${\psi }_{t}$ was set to 1 and ${k}_{d}$ to 0, implying no time-dependent deposition and no detachment. For water flow, the upper boundary was set as the atmospheric boundary, the lower boundary was set as the seepage face, and the boundary of the dripper was set as variable flux. The van Genuchten parameters and the longitudinal dispersivity (cm) were optimized from the fitting of the water- and bromide-distribution profiles. The transverse dispersivity (cm) was set to 10% of the longitudinal dispersivity (Hu et al. 2017). The measured and optimized soil hydraulic and solute transport parameters are listed in Table 3. The parameters ${k}_{a}$ and ${\mu }_{s}$ were optimized for all three inoculation regimes. The initial conditions for bacterial transport were zero for surface and subsurface and total concentration for the premixed treatments. The upper or middle boundary conditions are assigned as flux concentration for all treatments. The lower boundary condition is assigned as zero gradient.

Table 3 The van Genuchten model optimized parameters and the parameters in Eq. 11

The above water flow, solute and bacterial transport equations were solved numerically using the HYDRUS 2/3D (Šimůnek et al. 2008) to enable the description of the subsurface fluxes.

Statistical analysis

The difference of recovery between 2 and 48 h was assessed by one-way analysis of variance (ANOVA) followed by Tukey’s post hoc test and conducted by SigmaPlot 12.0. The standard error of the optimized parameters is calculated by the HYDRUS code and presented in Table 4.

Table 4 Optimization parameters for the Langmuir and Freundlich models from the measured adsorption isotherms for A. brasilense Sp7 and Cd

Results and discussion

Bacterial surface properties and sand properties

From the fluorescence microscope images presented in Fig. 1 morphology of the cells is varied. The late-log-phase A. brasilense Sp7 is rod-shaped with a width of 0.9 ± 0.1 μm and a length of 6.7 ± 1.7 μm; A. brasilense Cd is rod-shaped with a width of 0.7 ± 0.1 μm and a length of 2 ± 0.5 μm.

Cell-surface properties (Table 5), such as hydrophobicity and zeta potential, can affect the transport and retention characteristics of bacteria through the soil (Gannon et al. 1991). In our study, three quantities were used to quantify cell-surface hydrophobicity. First, contact angles of the two strains with water were around 40° and similar, indicating the strains’ pronounced hydrophilicity. Second, the hydrophilic nature of both strains was also reflected by the surface free energy. The literature reports that the total surface free energy of 10 species of bacteria ranged from 33 to 65 mJ m^− 2 (Busscher et al. 1984; Zhang et al. 2015). The value of the total surface free energy of strain Sp7 in our study was 56.15 mJ m^− 2 as reported by Jacobs et al. (2007). The ratio between the dispersive and polar parts can be used to predict the adhesion between liquid and solid phase, with more similar ratios meaning that more interactions are possible between the two phases (Wu 1973). The two A. brasilense strains had a larger polar than dispersive part (Table 6), similar as water, implying their good affinity to water and bad affinity to a hydrophobic surface. Third, BATH values of strain Sp7 and Cd were small relative to various bacterial BATH values reported in the literature, indicating that both strains can be considered highly hydrophilic (Collado et al. 2008). The BATH value of strain Sp7 determined by Jacobs et al. (2007) was 9–14% higher than the value obtained in our experiment. The discrepancy may stem from the different growth stages of the bacteria or population heterogeneity (Dufrêne and Rouxhet 1996). Burdman et al. (2001) characterized the major outer membrane proteins of A. brasilense Sp7 and Cd and found that they were similar; these proteins are believed to play a major role in bacteria’s affinity to plant roots (Dufrêne and Rouxhet 1996). Overall, the three cell surface quantities showed that strains Sp7 and Cd have similar surface characteristics but different size and dimensions.

The zeta potential value of the two strains was similar and close to the zeta potential (-15 mV in 10 mM NaCl) of A. brasilense Sp7 reported by Jacobs et al. (2007). The zeta potential value of clean quartz sand is about − 40mV (Dong et al. 2014). Higher (absolute) value of zeta potential for bacteria or sand implies stronger electrostatic repulsive force between them (Schinner et al. 2010).

Figure 2(b) shows the measured soil water-retention curve of the quartz sand. Straining is closely related to both sand properties and bacterial cell size. Sands are assumed to contain some cylindrical and tortuous capillaries and the critical straining pore diameter R can be related to a critical capillary pressure for straining according to Laplace’s equation (Laplace 1807). The percentage of pore space in which straining may occur (P) was calculated according to Eq. 11 (Bradford et al. 2006).

$$P=\left(1-{S}_{r}\right){[1+{\left(\frac{2\sigma {\upalpha }}{\rho gR}\right)}^{n}]}^{-m}+{S}_{r}$$

(11)

where θ_r, θ_s α,m, and n are van Genuchten model parameters; S_r is residual water saturation (0.0467), which is calculated by dividing θ_r by θ_s; σ is the surface tension; R is the critical straining pore diameters for A. brasilense strain Sp7 or Cd (Table 3). Here we used the length of bacteria as R.

Table 5 Measured and optimized soil hydraulic and solute transport parameters

According to this equation, the P values of strains Sp7 and Cd in this experiment means that straining of Sp7 and Cd may occurr in 11% and 5% of the pores, respectively.

Straining is an important mechanism for bacterial retention, and as already noted, it is greatly affected by bacterial cell size and soil pore-size distribution. Bradford et al. (2006) calculated the percentage of pore space in which straining of microorganisms can occur (P) with 12 different soil textures; P values ranged from 10.5 to 86.2%. The P values of the two A. brasilense strains in our sand (11% and 5%) were similar to those of bacteria in sand determined by Bradford et al. (2006). Compared to strain Cd, A. brasilense Sp7 showed higher probability of straining due to its larger size. Bacterial cell size typically ranges from 0.2 μm to several micrometers (Marshall 1985). In this sand, within this range, the effect of cell size on the P value is small (Fig. 2(b). Therefore, in theory, bacterial straining should be small. However, if bacteria form aggregates due to environmental pressure, straining may increase greatly. Burdman et al. (1998, 2000) studied the aggregation of A. brasilense Sp7 and Cd and found that A. brasilense Sp7 aggregated almost three times as much as A. brasilense Cd. The higher aggregation of A. brasilense Sp7 may result in more straining. Therefore, considering both aspects (cell size and bacterial aggregation), A. brasilense Sp7 was subjected to more straining than A. brasilense Cd in the sand.

Adsorption isotherms

Bacteria are usually treated as living colloidal systems and the behavior of bacteria on sand surface is analyzed by adsorption isotherms (Marshall 1976). The measured adsorption isotherms of A. brasilense Sp7 and Cd s are presented in Fig. 3. The wet weight of A. brasilense Sp7 and Cd as calculated by Eq. 2 is 4.6 × 10^− 12 g and 0.73 × 10^− 12 g, respectively. Considering the wet weight can directly reflect the biomass, we plotted the adsorption isotherms in units of weight concentration in Fig. 3. The Langmuir (Eq. 4) was fitted to the measured adsorption isotherms, and the optimized models’ parameters are listed in Table 6.

Table 6 Optimized parameters for first-order attachment model fitting and recovery

Fig. 3

Adsorption isotherms of A. brasilense Sp7 and Cd on quartz sand

The Langmuir adsorption isotherm is commonly used to describe adsorption isotherms in many systems. The Langmuir adsorption constant $k$ usually represents the adsorption free energy. Nevertheless, it should be noted here that the basic assumptions for Langmuir adsorption are equivalent adsorption sites, non-interacting adsorbate molecules and monolayer adsorption (Latour 2015). Because bacteria do not meet these prerequisites, the Langmuir adsorption constant can only be used to characterize the shape of the adsorption isotherm, rather than representing the adsorption free energy. In Fig. 3, the ${Q}_{max}$of strain Sp7 was much higher than that of Cd.

For Freundlich adsorption isotherm, the parameter $m$ is related to the adsorption capacity of adsorbent for the adsorbate and $n$ is related with adsorption intensity (Zhong et al. 2015; San Martín et al. 2020). In Fig. 3, strain Sp7 had higher $m$ and $n$ than strain Cd, implying strain Sp7 always had higher adsorption capacity and adsorption intensity on sand. Comparing two models, the Freundlich model fitted curve is very close to the Langmuir model fitted curves.

In previous studies, the adsorption of A. brasilense Sp7 and Cd was generally determined with adhesion tests, which usually tested only one bacterial concentration. The reported adsorption of strain Sp7 on sand (7 × 10⁶ CFU g^− 1) was 54.7% (Jacobs et al. 2007) and the adsorption of strain Cd on sand (2 × 10⁶ CFU g^− 1) was 28.3% (Bashan and Levanony 1988). Overall, the conclusion in our study is consistent with previous study: at similar weight concentration, strain Sp7 absorbs more on sand.

Deposition in the sand profile

Three different inoculation regimes (surface, subsurface, and premixed) were applied in the transport experiments (Figs. 4 and 5). In Fig. 4a, since the surface and premixed regimes applied with the same volume of irrigation water on the sand surface, water content distribution was similar, whereas the subsurface irrigation resulted in higher water content in the lower part of the sand column. The bromide distribution under the three regimes is shown in Fig. 4b. For surface irrigation, bromide reached 20 cm depth; for subsurface irrigation, bromide was distributed at 9–29 cm depth and exhibiting a maximum at 16 cm. For the premixed regime, bromide displacement from the upper 10 cm and distributed at 12–30 cm depth. Comparing water and bromide distribution after 2 h and 48 h, the latter showed slightly deeper infiltration after 48 h, but the difference was not significant (P > 0.05). The recovery of water ranged from ∼ 98.5 to 100.5% and the recovery of bromide ranged from ∼ 94.5 to 101.5%.

Fig. 4

(a) Water content (cm³ cm^− 3) and (b) bromide concentration with three different application methods (surface irrigation [top], subsurface irrigation [middle] and premixed [mixed]) as a function of soil depth (cm) (the unit is mg Br per cm³ water)

Fig. 5

Abundance of A. brasilense Sp7 (a) and Cd (b) with three different application methods (surface irrigation [top], subsurface irrigation [middle] and premixed [mixed]) as a function of soil depth (cm) in units of log CFU cm^− 3. (the unit is CFU per cm3 water)

The two strains distribution with different inoculation regimes are presented in Fig. 5. It should be noted that the bacterial abundance is presented on the log scale, hence, most of bacteria are accumulating near the water source in the surface and subsurface irrigation regimes. Specifically, with surface irrigation, most bacteria accumulated on the sand surface (0–5 cm); with subsurface irrigation, most bacteria accumulated near the water source (14–20 cm); with the premixed method, the bacteria barely moved, but showed an obvious decrease in abundance relative to the initial abundance. The phenomenon that a great number of bacteria retained near the water source agreed with previous studies (Huysman and Verstraete 1993; Kouznetsov et al. 2004; Haller et al. 2016).

When inoculating plants with shallow root systems (e.g., seedlings), surface drip irrigation inoculation may be useful because the PGPB can move more deeply with the roots as they grow (Bashan and Levanony 1987). For plants with deep root zones, the PGPB cannot move downward with the help of the roots and therefore, subsurface drip irrigation inoculation has an advantage over surface inoculation. Regarding inoculation by the premixing method, the applied drip irrigation water hardly affected bacterial movement. Three explanations are suggested: one is that with the same total number of inoculated bacteria, the real concentration of the premixed bacteria was lower than that using point source inoculation, and therefore in the former case, low-concentration bacteria are more likely to attach to soil or sand particles as indicated by the adsorption isotherm (Fig. 3); a second explanation is that, during the premixing process, the water content is relatively low, and therefore bacteria may be captured by the thin water films and form irreversible adsorption (Gargiulo et al. 2008; Shang et al. 2008; Flury and Aramrak 2017); a third explanation is that, some bacteria may be damaged during the premixing process and damaged bacteria may have higher affinity to sand than live bacteria (Foladori et al. 2015).

Comparing the movement of two strains, A. brasilense strain Cd showed deeper movement than strain Sp7. Specifically, small cell size and low adsorption of strain Cd resulted in higher bacterial movement. The differences between the two strains at 2 and 48 h can yield some insights into the redistribution in the sand profile following their application. Under surface inoculation regime after 48 h, strain Cd that penetrated deepest into the sand arrived at a depth of about 18 cm; under subsurface inoculation regime, the deepest-penetrating strain Cd moved 8 cm further down after 48 h compared to its depth at 2 h. In contrast, strain Sp7 did not show noticeable movement after 48 h compared to its depth at 2 h. The mechanism of bacterial movement in porous media under water flow includes advection, mechanical dispersion, diffusion, and bacterial motility (Bradford et al. 2013; Creppy et al. 2019). In our experiment, mechanical dispersion can be neglected, because the water flow velocity was small (Unice and Logan 2000); bacterial motility can also be neglected, because no nutrients gradient existed in the column (de Anna et al. 2021). Diffusion, however, may be more significant when the water content is higher as indicated by the subsurface treatment (Schelde et al. 2002). Advection during the application period may be another mechanism that resulted in different redistribution behaviors for strain Sp7 and Cd between 2 and 48 h.

Bacterial recovery (Table 6) implied on irreversible adsorption and the growth/death of PGPB to some extent. Comparing the three irrigation regimes, recovery of bacteria under the premixed inoculation regime was markedly lower than that from the surface and subsurface inoculation regimes. One explanation may be that the mixing process kills some bacteria. Another explanation may be, during the premixing process, the water content of premixed inoculation regime (10%) is low than those of surface and subsurface inoculation regime (10% + irrigated water), and therefore resulted in more irreversible adsorption (Shang et al. 2008). Overall, the recovery at 2 and 48 h was not significantly different (P > 0.05). In some cases, the recovery at 48 h was higher than at 2 h, implying some bacterial growth. Although no nutrients were added to the sand, live bacteria can use compounds of dead cells as energy and nutrient sources (Schink et al. 2019). Previous studies (Sangeetha and Stella 2012; Bashan and de-Bashan 2015) have shown that application of PGPB to soil without a proper carrier result in a quick decline in their population; meanwhile, surrounding environmental conditions (water, nutrients, pH, temperature, etc.) and other soil’s microbiome (e.g., other bacteria, fungi, archaea, protozoa) also greatly affected the inoculation and survival of PGPB (Yaghoubi Khanghahi et al. 2021; de-Bashan and Nannipieri 2024). Therefore, inoculating bacteria into the nutrient-rich root zone, and repeat inoculations, are both recommended under field conditions.

Model evaluation

The water content and bromide modeling were performed separately from the bacterial modeling. The optimized values (Table 3) for hydraulic properties (${\upalpha } \text{a}\text{n}\text{d} \text{n})$ and solute transport (dispersivity) were then employed as fixed values in the bacterial modeling. The fitted deposition curves of water content (0.94 > R² > 0.83) and bromide (R² > 0.97) exhibited high adequacy describing the measured profiles. For water content distribution, we optimized two parameters: α and n. Some difference in α and n values can be observed among the three irrigation methods. This might be because the inoculated PGPB affects the soil hydraulic properties. In addition, although value Ks was fixed, the inoculated PGPB may affect saturated hydraulic conductivity as well (Volk et al. 2016). Furthermore, the optimized longitudinal dispersivity for subsurface irrigation was higher than for the other two methods, which may be related with the backflow and different velocity distribution of subsurface irrigation (Vanderborght and Vereecken 2007).

In the first-order attachment model, we only used one parameter ${\mu }_{s}$ to represent bacteria death at all interfaces and non-recovered bacteria. Considering the bacterial recovery at 2 h and 48 h is similar and the unit of the parameter µ_s is reciprocal of time, we optimized two parameters (K_a and µ_s) and fitted the deposition files at 2 h and 48 h separately. The figures show the fitted results after optimizing the two parameters (Fig. 5; Table 6).

Regarding the parameter µs, this not only reflects bacterial growth and death, but also includes the non-recovered bacteria (irreversible adsorption) during extraction. We plotted Y (non-recovered bacteria) against X (µ_s × time) in Fig. 6, showing a linear relationship. This means that in this model, the parameter µ_s can be used to adjust the mass balance and then it helps to compare the attachment coefficient.

Fig. 6

Linear correlation between non-recovered bacteria and the product of µs and time

The attachment/detachment model has been used in three main modes: first-order attachment model (one site, no blocking), Langmuirian blocking model (one site, Langmuirian blocking), and two-site model (Gargiulo et al. 2008). For the Langmuirian blocking model and two-site model, more than three parameters are commonly optimized. These models are commonly used when modeling the breakthrough curve and deposition curve simultaneously. In our experiment, only deposition profiles were considered, and we found the first-order attachment model more suitable.

Regarding the first-order attachment coefficient (K_a), strain Cd showed higher K_a values for surface and subsurface inoculation regimes than strain Sp7, which agrees with the lower adsorption obtained in the adsorption isotherms (Fig. 3) and deeper vertical movement (Fig. 5). For the premixed inoculation, because the bacteria barely move and the recovery was low, the K_a value was not reliable. Comparing surface inoculation, the subsurface irrigation had a relatively higher K_a. The reason may be that the bacterial movement for subsurface irrigation was two directions (upward and downward), and the pore water velocity was lower. Thus, the advection flux of bacterial transport was smaller than that of surface inoculation.

Previous studies that modeled bacterial BTCs and deposition profiles simultaneously using the attachment/detachment model generally showed a very good fitting, with R² ranging from 0.74 to 0.99 (e.g., Gargiulo et al. 2007; Bradford et al. 2013; Firouzi et al. 2015; Sepehrnia et al. 2018). Nevertheless, comparing the fit of the BTC and deposition profile, it was always more difficult to show good description with the latter because of the difficulty in recovering all the bacteria from the sand (Chen et al. 2024). Therefore, the goodness of fit in our experiment is acceptable. Overall, under the condition of the current experimental we consider the first-order attachment model to be a feasible and applicable model for evaluation of the bacteria’s vertical movement following its application.

Conclusion

We investigated the surface properties of A. brasilense Sp7 and Cd and their vertical movement under transient water flow at three inoculation regimes: surface irrigation, subsurface irrigation, and sand premixing. A. brasilense Sp7 and Cd exhibited similar surface properties (hydrophilicity and zeta potential). As A. brasilense Cd had a smaller cell size, and showed less adsorption, and less straining than A. brasilense Sp7, its vertical movement after 48 h reached a significantly (P < 0.05) greater depth under surface and subsurface irrigation. Overall, for surface/subsurface drip irrigation inoculation, a large amount of PGPB still accumulated near the inoculation source (within 5 cm), irrelevant of bacterium type and in agreement with the literature. With premixing inoculation, most of the bacteria scarcely moved. Based on these results, we recommend using subsurface irrigation to deliver PGPB to the root zone, to improve inoculation success rate. In addition, bacterial distribution in the sand profiles was well described using the first-order attachment model. Therefore, the attachment/detachment model is expected to be useful in simulating PGPB transport under field conditions when the first-order attachment coefficient and die-off rate of bacteria are known. The results of this study offer new insights into the inoculation of PGPB using drip irrigation systems in sand. It is important to note that the adsorption of bacteria by quartz sand is significantly lower than that by clay and organic matter. Consequently, the conclusions drawn from this study may be limited in applicability to clay-rich soils and soils with high organic matter content. Therefore, further experiments in various naturally occurring soil types are necessary to adjust and refine the model for application in more complex soil systems. Nevertheless, it may be applicable to plants nurseries where soilless media such as sand are employed as a growing media.