Fluid flow physics in plants needs to be understood due to their complexity. These systems are not only multi-species, multi-scale, and multi-physics in nature but also involve intricate fluid/bio-structure interactions, highlighting the interdisciplinary nature of this research. Fluid flow hydrodynamics play a crucial role in plants by enabling water, nutrients, and hormones to transport throughout their tissues, essential for growth, survival, and reproduction on planet Earth and in outer space missions. The process of water movement through a plant, known as transpiration, relies on water molecules' cohesive and adhesive properties, creating a continuous column of water from the roots to the leaves. This movement is driven by a combination of capillary action, root pressure, and transpiration pull, with water evaporating from the stomata in the leaves. Additionally, the flow of phloem sap, which distributes sugars and other organic molecules from photosynthetic tissues to non-photosynthetic parts of the plant, is regulated by pressure differences in the plant's vascular system. Moreover, fluid flow aerodynamics also has a vital role in plants, for example, by transporting leaves and pollen particles from one vegetation region into another, by reducing overall carbon footprints, and by the impact on micro-climate, e.g., urban heat waves. Therefore, a comprehensive understanding of fluid flow dynamics in plants is not just beneficial but fundamental to advancing our knowledge in this field and potentially making discoveries. This special collection of articles presents state-of-the-art research in fluid flow dynamics and plants. The investigations made by the authors of the papers cover both experimental and computational studies around a range of plant applications, including hydrodynamics and aerodynamics flows. This unique topic has the potential to significantly advance our understanding of plant flow-biology and inspire new applications. A summary of the papers appearing in the special collection is presented below.
Padhi et al.1 explored the behavior of Brassica juncea plant roots under various hydroponic flow configurations to address food security challenges. Different flow setups were tested to analyze their effects on root growth and internal stress, including continuous flow, flow/no-flow (F/NF), and no-flow/flow (NF/F). Results showed continuous flow increased cortical cell development, protecting the vascular bundle from stress. However, periodic flow (F/NF and NF/F) with lower average power led to longer root lengths and more efficient nitrogen uptake compared to continuous flow. This suggests that F/NF flow configurations could be more cost-effective and promote better root growth in hydroponic systems.
Zhang et al.2 proposed a new computational fluid dynamics (CFD) model that combines a drift flux model with a vegetation source term and an enhanced turbulence model to simulate sediment-laden flows in vegetated areas. The model was validated using experimental data, and the study examined how factors like vorticity, vertical velocity, Reynolds stress, and turbulent kinetic energy (TKE) influence sediment distribution. The results showed that at the vegetation canopy, vorticity correlates with suspended sediment concentration (SSC), while above the canopy, vertical velocity, Reynolds stress, and TKE positively correlate with SSC. Below the canopy, these correlations are negative. Overall, Reynolds stress and TKE showed a stronger connection to sediment movement than vorticity and vertical velocity.
Zhang et al.3 showed that vortices generated by the interaction of in-stream vegetation with surrounding flows play a crucial role in shaping hydro-geomorphodynamics in water systems. Their research shows that elongating vegetation patches in the middle of a channel creates complex wake flow patterns, mainly due to the formation of patch-edge Kelvin–Helmholtz (KH) vortices. They demonstrated that KH vortices enhance wake mixing, evidenced by higher steady wake velocity, shorter wake length, and reduced energy of von Karman vortices. By quantifying these effects, their work highlights how vegetation-induced vortex interactions regulate mixing processes, providing valuable insights for future environmental flow management.
Buono et al.,4 through flume experimental measurements, quantified the drag coefficient (Cd) for a rigid, uniformly distributed rod canopy in a sloping channel following a dam collapse. The experiments measured water surface profiles and drag using load cells under different slopes and water depths. Using a diffusive wave approximation, the Saint–Venant equation (SVE) was applied to analyze front speed. A significantly reduced Cd of 0.4 was observed near the advancing wavefront compared to steady uniform flow cases. This suggests that transient flow disturbances and increased air entrainment in the wavefront reduce drag more than traditional sheltering effects in uniform flows.
Guha et al.5 explored the relationship between the electrical potential in plant tissues and the electrokinetics of fluid flow, which is influenced by circadian rhythms. Experiments on water hyacinth stems showed a cyclic variation in streaming potential corresponding to these biological rhythms. Further experiments on Dracaena sanderiana stem segments examined how streaming potential varied with different flow rates and electrolyte properties, such as ionic strength, species, and pH. The results by Guha et al.5 align with electrokinetic principles, thus enhancing our understanding of how diurnal cycles and fluid flow dynamics influence plant hydraulics and electrical potentials.
To address the issue of lubricating oil creep loss in aerospace equipment, Zhang et al.6 designed a biomimetic structure inspired by the Nepenthes pitcher plant's peristome region. This is by combining a wetting gradient and geometric diversion pattern. Simulations of two-phase flow were conducted to study droplet transport on this structure. The structure was then fabricated on a titanium surface using hydrothermal deposition and laser etching, and droplet movement was observed. Superhydrophilic regions had a contact angle of 0°, while superhydrophobic regions had a 159° angle. The transport efficiency decreased with greater curvature but improved with increased spacing between structural units. The biomimetic structure enabled adequate water and oil directional transport, with transport rates influenced by structural parameters and droplet viscosity.
Wu et al.7 developed a fog droplet distribution model based on a 3D motion model of droplets, combined with particle size distribution and a 2D normal distribution function. In plant protection operations, the distribution of droplets significantly affects the atomization effect. This study by Wu et al.7 analyzed how the initial incidence angle and wind speed influence droplet distribution. Simulations of droplet distribution were validated with experimental data. The optimal conditions were identified as an initial incidence angle of 17°, yielding a minimal slope and a high coefficient of determination (0.9622) with a 3.12% error, and a wind speed of 0.1 m/s with a 0.9782 determination coefficient and 4.61% error. The model effectively improved droplet distribution uniformity, providing a theoretical foundation for optimizing operational parameters.
Yang et al.8 proposed an analytical solution to predict lateral velocity distribution in meandering compound channels, which is crucial for understanding flood discharge and sediment transport. These channels with vegetated floodplains, common in natural rivers, usually exhibit complex hydraulic behavior and sediment transport processes. Based on depth-averaged Navier–Stokes and continuity equations, the newly developed model incorporates factors like bed friction, vegetation drag, transverse turbulence, and secondary flows. Validated by experimental data, the model accurately predicts the velocity distribution. The study by Yang et al.8 shows that secondary current coefficients and dimensionless eddy viscosity substantially impact velocity profiles more than vegetation drag. Their model thus provides a handy tool for analyzing flow in vegetated, curved river channels.
Lin et al.9 examined the impact of branch angle on the wind resistance of sympodial trees, focusing on their aerodynamic behavior under controlled wind conditions. Their study reveals that, as wind speed rises, trees experience unstable oscillations and increased drag due to irregular leaf vibrations. Trees with larger branch angles show higher drag at wind speeds below 20 m/s but demonstrate better reconfiguration, allowing them to withstand stronger winds. The research proposes a wavy streamlining reconfiguration process for these trees and finds that their structure acts as a high-frequency filter, dissipating branch vibration energy. These insights are valuable for understanding tree aerodynamics and selecting wind-resistant urban trees.
Saini et al.10 investigated fluid flows traversing porous media of varying viscosities, particularly relevant in oil extraction applications from reservoirs. The authors studied the fluid flow of a Newtonian fluid between two non-Newtonian Jeffreys fluids with temperature-dependent viscosity in a composite vertical channel. Their framework includes three regions: the intermediate region for Newtonian fluid flow and the outer layers for Jeffreys fluids within a porous medium. The Brinkman–Forchheimer equation governs the flow dynamics for both low and high permeabilities, leading to a nonlinear system requiring advanced mathematical analysis techniques. Regular and singular perturbation methods are applied to derive asymptotic expressions for velocity profiles across the regions. Key hydrodynamic quantities like flow rate and wall shear stresses are calculated based on these profiles, with graphical analysis revealing relationships with parameters such as Grashof and Forchheimer numbers. Notably, a pronounced velocity profile occurs when the permeability is high, and the viscosity parameter of the Newtonian region is lower than that of the surrounding Jeffreys fluid due to a more significant viscosity reduction in the Jeffreys fluid as temperature increases.
Wang et al.11 showed that there is an urgent need to accurately predict bed-load transport rates in vegetated river ecosystems to aid restoration efforts. To address this bottleneck, they developed a new model to estimate the effective shear stress on the riverbed based on the energy equation and the relationship between energy loss in mean flow and turbulence caused by emergent vegetation. The model was used to evaluate the Meyer–Peter–Müller (MPM) formula's performance in predicting bed-load transport rates in vegetated flows by comparing it with experimental data from the literature. Findings indicated that the MPM formula often overestimates bed-load transport rates when the dimensionless effective shear stress is below one and underestimates them when it exceeds one, suggesting vegetation enhances and reduces sediment transport depending on shear stress levels. To improve accuracy, the coefficients of the MPM formula were modified using extensive experimental data, resulting in a new predictive formula that outperforms existing equations and effectively predicts bed-load transport rates, even for umbrella-like vegetation.
Liu et al.12 studied the impact of heterogeneous vegetation patches on turbulence characteristics in water flow, specifically focusing on the effects of alternating sparse and dense patches. Numerical simulations of various vegetation scenarios were compared with those of homogeneous vegetation. The findings indicate that heterogeneous arrangements significantly alter flow velocity distributions in both the vegetation zone and the main channel, enhancing material exchange between these areas. The impact of vegetation density differences on the main channel increases with more significant density variations but remains limited to within 10% of the vegetation width. Additionally, the study by Liu et al.12 finds that using mid-height data to represent the entire cross section of heterogeneous vegetation can lead to a maximum error of up to 11%.
Boukor et al.13 examined the aerodynamic behavior of an idealized plant leaf modeled as a flexible, thin, rectangular plate clamped at its midpoint and oriented perpendicular to airflow. They showed that the flexibility of the structure provides an advantage at moderate flow speeds, allowing for significant drag reduction through elastic reconfiguration. However, dynamic instability can induce flow-induced vibrations at higher flow speeds that limit this reduction. Employing wind tunnel experiments, they quantified a critical Cauchy number below which static reconfiguration is possible, leading to drag reduction, and above which dynamic instability results in significant fluctuating loads. They explained how the mass number influenced the critical velocity and established optimal flexibility to facilitate this drag reduction while avoiding instability. The study also notes ambiguity in attributing the vibrations to flutter instability, vortex-induced vibration, or a combination of both.
Valdés-Parada and Sánchez-Vargas14 focused on the transport and adsorption of airborne chemical species in tree crowns, a process crucial for various environmental impacts. Recognizing the complexity of this multiphase and multiscale phenomenon, the researchers developed an upscaled model for momentum transport and species adsorption in tree crowns using the method of volume averaging. The model's average chemical species concentration predictions were validated against direct numerical simulations, showing excellent agreement with a relative per cent difference of less than 1%.
Sevanto15 developed hydrodynamic models that analyze flow through sieve plates. Investigating sieve plate resistance is a crucial factor in understanding the efficiency of carbohydrate transport in tree phloem. The total resistance of a sieve plate is derived by summing the resistances of each pore. The researchers constructed an experimental setup using polyvinyl chloride (PVC) piping and plastic straws that mimic phloem sieve tubes to validate their new model. They measured flow rates and calculated flow resistance across Reynolds numbers between 0.5 and 300. Their findings indicate that existing models may significantly overestimate flow resistance due to sieve plates and suggest that formulations for perforated plates may more accurately represent this resistance.
Phan et al.16 explored the relationship between fractal geometry and dynamic processes in fractional continuous models, specifically during phase transitions like thermal melting and hydrodynamic void collapse. The authors present general analytical expressions to estimate vanishing times, which depend on the fractal nature of the space. Their research mainly focuses on natural soils, which have fractal characteristics vital for plant growth, and investigates the phenomenon of cavity shrinkage in incompressible fluids. The authors demonstrate how a minimal collapsing time can arise from a complex interaction between fluid viscosity and the surface fractal dimension through numerical simulations that extend beyond the inviscid limit.
The above research studies present new findings and scientific challenges that will stimulate further research to deepen our knowledge of fluid flow dynamics and plants.
The guest editors would like to thank the editorial board of Physics of Fluids, especially the Editor-in-Chief Professor Alan Jeffrey Giacomin, the Journal's Managers, and the AIP staff for their assistance and support in publishing and promoting this Special Collection.
