The Boundary Layer over a Populus Leaf

Air flow over a Populus leaf was investigated using a hot-wireanemometer. When the air flow in the wind tunnel was laminar,the boundary layer was often turbulent at a wind speed of only1.5 m s^–1, particularly when encouraged by uneven topographyand roughness of the surface, as on the lower side of the leaf.The smoother upper surface behaved in a similar way to a flatplate when at low wind speeds, and the profiles of wind speedcould be shown to be equivalent to those expected from laminarboundary layer theory. Nevertheless, the boundary layer becameturbulent at Reynolds numbers much lower than those requiredto cause the transition to turbulence in a flat plate. Turbulentair flow in the wind tunnel greatly increased boundary layerturbulence but had only a small effect on evaporation from amodel of the leaf. The evaporation rates observed were 2.5 timeshigher than expected from theory, irrespective of the turbulenceregime.     

The turbulent boundary layer over a flapping Populus leaf

Abstract The air-flow regime over a Populus leaf was investigated using a constant temperature hot-film sensor which could be glued on the abaxial surface. The leaf was exposed to a laminar or turbulent flow of air in a wind-tunnel, while being free to undergo normal motion. In the laminar air-flow the boundary layer remained laminar, despite the fluttering of the leaf, until a Reynolds number of 2.3 × 10⁴ was reached. When the air incident on the leaf was made turbulent, to resemble natural conditions, the boundary layer became turbulent at a Reynolds number of 0.4 × 10⁴. The experiments suggest that the boundary layers over leaves are always turbulent in the natural wind.     

Quaking and Gas Exchange in Leaves of Cottonwood (Populus deltoides, Marsh.)

Cottonwood (Populus deltoides, Marsh.) leaves are amphistomatous and have an adaptation in their petiole which allows them to oscillate in wind. A possible function of these oscillations in enhancing gas exchange was studied.

Cottonwood leaves were found to oscillate in the presence of wind velocities frequently encountered in nature. A pressure differential across the leaf was shown to result in bulk flow of air through that leaf. Oscillating a cottonwood leaf at frequencies found to occur in nature was found to increase the rate of O₂ flux through the leaf. The measured changes in boundary layer resistances during oscillations were found to be insufficient to account for the increased O₂ flux. Thus, the bulk flow of air through an oscillating cottonwood leaf results in a decreased total resistance which is typically 25% less than that of a still leaf.

     

Boundary Layer Resistance and Temperature Distribution on Still and Flapping Leaves: II. Field Experiments

The forced convection of heat from reed (Phragmites communis) leaves was observed in their natural environment. The leaves were painted with liquid crystals, which displayed or indicated their temperature without any interference with natural air flow. Temperature differences as large as 15 C were observed between the leading and trailing edges of the nontranspiring, painted leaves. The turbulence of the natural wind decreased the boundary layer resistance around the leaf to about 40% of the resistance in a laminar steady wind.     

Mutual diffusional interference between adjacent stomata of a leaf

The mutual diffusional interference between adjacent stomata in laminar flow over a leaf is shown to play a decisive role in determining overall transpiration. The magnitude of this interference varies with the interaction of the vapor diffusional shells forming above each stoma and the air flow over the leaf. The interference decreases with increasing incident radiation and wind velocity. The effect of interference on the stomatal resistance to diffusion plays a major role in the overall variations in transpiration.     

Buoyancy effect on forced convection in the leaf boundary layer

Abstract. Mixed convection (forced convection plus free convection) in the leaf boundary layer was examined by air flow visualization and by evaluation of the boundary layer conductance at different leaf-air temperature differences ( T _L- T _A) under low wind velocities. The visualized air flow was found to become more unstable and buoyant at higher T _L- T _A. An ascending longitudinal plume was induced along the upper surface, and the air flow along the lower surface ascended after passing the trailing leaf edge. The air flow modified by buoyancy was considered to result in an increase in boundary layer conductance ( G _A) for mixed convection, which became higher with higher T _L- T _A as compared with the conductance for pure forced convection without buoyancy. This increase in G _A appeared larger at larger Grashof number (Gr) and at smaller Reynolds number (Re). The dependences of buoyancy effect on Gr and Re were related to 'edge-effects'.     

Leaf Temperatures in a Gas Exchange Chamber and in the Open Air

Leaf temperatures in a Koch fully climatized gas-exchange chamberas designed by Siemens and in a similarly equipped open-airreference were measured with horizontally and vertically insertedthermocouples on Nerium oleander L. On a sunny day with onlylittle air movement and an average air temperature of 20.4 °C,leaf over-temperatures in the gas-exchange chamber were loweron average by 2.2 K. The extent of reduction of over-temperaturein the chamber is determined by the reduced global radiationin the chamber and the differences of wind velocities in chamberand reference. Differences in the ventilation intensity in thechamber have no demonstrable influence on the leaf over-temperatures.The over-temperatures of the reference leaves, on the otherhand, depend to a large degree on air velocity. The changedradiation and air flow conditions in the chamber as comparedwith open-air conditions have consequences for the physiologicalreactions of the enclosed plant and must be taken into accountwhen comparing results from gas-exchange measurements with open-airconditions. For further improvements of gas-exchange measurementequipment, air flow conditions and radiation quantity and qualitymight be starting points     

Effects of airflow and liquid temperature on ammonia mass transfer above an emission surface: Experimental study on emission rate

The present study performed a series of experiments in a wind tunnel to investigate the impact of velocity, turbulence intensity and liquid–air temperature difference on ammonia emission rates. Decreasing velocity, turbulence intensity and liquid temperature are shown to reduce the ammonia emission rates. The emission rates are more sensitive to the change of velocity at a low velocity compared to change of velocity at a higher velocity range, which corresponds with the conclusion that the boundary layer thickness of velocity increases sharply when velocity is changed from 0.2 m/s to 0.1 m/s. In addition, the emission rates are more sensitive to the change of temperature at a higher temperature than at a lower liquid temperature range. The influence of velocity and liquid–air temperature difference on boundary layer thickness is also analyzed. The relationship between the emission rate and boundary layer thickness is presented.     

Soil CO2 efflux in a beech forest: comparison of two closed dynamic systems

The aim of this study was to understand why two closed dynamic systems with a very similar design gave large differences in soil CO₂ efflux measurements (PP systems and LI-COR). Both in the field (forest beech stand) and in the laboratory, the PPsystems gave higher estimations of soil CO₂ efflux than the LI-COR system (ranging from 30% to 50%). The difference in wind speed occurring within the soil respiration chambers (0.9 m s⁻¹ within the SRC-1 and 0.4 m s⁻¹ within the LI-6000-09 chambers) may account for the discrepancy between the two systems. An excessive air movement inside the respiration chamber is thought to disrupt the high laminar boundary layer over the forest floor. This would promote an exhaust of the CO₂ accumulated into the upper soil layers into the chamber and a lateral diffusion of CO₂ in the soil towards the respiration chamber. The discrepancy between the two systems was reduced (i) by decreasing fan speed within the SRC-1, (ii) by increasing wind speed over the soil surface outside the respiration chamber, or (iii) by using an artificial soil design without high CO₂ concentration in soil pores. We show that wind speed is an important component of soil CO₂ diffusion which must be taken into account when measuring soil CO₂ efflux, even on very fine textured soil like silt-loam soil. Proper measurement can be achieved by maintaining wind speed inside the chamber below 0.4 m s⁻¹ since low wind speed conditions predominate under forest canopies. However, more accurate measurements will be obtained by regulating wind speeds within the chamber at a velocity representative of the wind speed recorded simultaneously at the floor surface. This revised version was published online in June 2006 with corrections to the Cover Date.     

Reduction of molecular gas diffusion through gaskets in leaf gas exchange cuvettes by leaf‐mediated pores

There is an ongoing debate on how to correct leaf gas exchange measurements for the unavoidable diffusion leakage that occurs when measurements are done in non‐ambient CO₂ concentrations. In this study, we present a theory on how the CO₂ diffusion gradient over the gasket is affected by leaf‐mediated pores (LMP) and how LMP reduce diffusive exchange across the gaskets. Recent discussions have so far neglected the processes in the quasi‐laminar boundary layer around the gasket. Counter intuitively, LMP reduce the leakage through gaskets, which can be explained by assuming that the boundary layer at the exterior of the cuvette is enriched with air from the inside of the cuvette. The effect can thus be reduced by reducing the boundary layer thickness. The theory clarifies conflicting results from earlier studies. We developed leaf adaptor frames that eliminate LMP during measurements on delicate plant material such as grass leaves with circular cross section, and the effectiveness is shown with respiration measurements on a harp of Deschampsia flexuosa leaves. We conclude that the best solution for measurements with portable photosynthesis systems is to avoid LMP rather than trying to correct for the effects.     

Effects of Boundary Layer Conductance on Leaf Gas Exchange

Using an improved gas-exchange technique for leaf chamber the authors' conclusions derived from electrical analogy analysis and simulation have been tested. In most devices for gas-exchange measurements, a fixed ventilation speed is used, which results in a fixed boundary layer conductance of leaf, but the results of experiments are often used to predict canopy transpiration or photosynthesis where the boundary layer conductance changes with the position of the leaf in the canopy and the wind speed above the canopy. To change the boundary layer conductance of a leaf, a barrier of variable size was inserted into the leaf chamber to decrease the wind speed over the leaf. The responses of stomatal conductance, net photosynthetic rate, and transpiration rate to light were then measured. The relationships amongst them have been tested. The experimental results matched well with the results predicted by electrical analogy analysis and simulation in most cases.     

Optimum leaf size predicted by a novel leaf energy balance model incorporating dependencies of photosynthesis on light and temperature

To clarify relationships between leaf size and the environment variables, we constructed an energy balance model for a single leaf incorporating Leuning’s stomatal conductance model and Farquhar’s leaf photosynthesis model. We ran this model for various environmental conditions paying particular attention to the leaf boundary layer. The leaf size maximizing the rate of photosynthesis per unit leaf area (A) at a high irradiance differed depending on the air temperature. In warm environments, A increased with decrease in leaf size, whereas in cool environments, there was the leaf size maximizing A. With the increase in leaf size, the CO₂ concentration inside the leaf (C _i) decreased and the leaf temperature increased, both due to lower boundary layer conductance. At low air temperatures, the negative effect of low C _i on A in large leaves was compensated by the increase in leaf temperature towards the optimum temperature for A. This balance determined the optimum leaf size for A at low air temperatures. With respect to water use efficiency, large leaves tended to be advantageous, especially in cool environments at low-to-medium irradiances. Some temperature-dependent trends in leaf size observed in nature are discussed based on the present results.     

Leaf and environmental parameters influencing transpiration: Theory and field measurements

Summary The influence of variations in the boundary air layer thickness on transpirtion due to changes in leaf dimension or wind speed was evaluated at a given stomatal resistance (r _s) for various combinations of air temperature (T _a) and total absorbed solar energy expressed as a fraction of full sunlight (S _ffs). Predicted transpiration was found to either increase or decrease for increases in leaf size depending on specific combinations of T _a, S _ffs, and r _s. Major reductions in simulated transpiration with increasing leaf size occurred for shaded, highly reflective, or specially oriented leaves (S _ffs=0.1) at relatively high T _a when r _s was below a critical value of near 500 s m^-1. Increases in S _ffs and decreases in T _a lowered this critical resistance to below 50 s m^-1 for S _ffs=0.7 and T _a=20°C. In contrast, when r _s was above this critical value, an increase in leaf dimension (or less wind) resulted in increases in transpiration, especially at high T _a and S _ffs. For several combinations of T _a, S _ffs, and r _s, transpiration was minimal for a specific leaf size. These theoretical results were compared to field measurements on common desert, alpine, and subalpine plants to evaluate the possible interactions of leaf and environmental parameters that may serve to reduce transpiration in xeric habitats.     

Boundary layer resistance and temperature distribution on still and flapping leaves: I. Theory and laboratory experiments

If the evaporation is uniform on a flat exposed leaf, forced convection will also be nearly uniform, and the leaf temperature will vary with the square root of the distance from the leading edge. Then the resistance expressed in terms of the proper, i.e., average, temperature has the same value as the resistance of a leaf at uniform temperature. Compared to a steady laminar flow, the turbulence of a realistic wind decreases the resistance by a constant factor of about 2.5. The same constant factor was observed whether the leaf was flapping or not, when the wind velocity was not too low.     

Leaf diffusion resistance, illuminance, and transpiration

Stepwise increases in fluorescent illuminance, imposed as a single variable in a controlled environment, induced progressive stomatal opening in 8 plant species, as evidenced by a consistent decrease in leaf diffusion resistance (R_L), ranging from 15 to 70 sec cm⁻¹ in darkness to about 1 sec cm⁻¹ at approximately 40 kilolux. The minimum R_L values were the same for the upper and the lower epidermis, provided that stomatal density was adequate. Saturation illuminance was not achieved in any species; extrapolation indicates that 50 kilolux would bring about full stomatal opening (R_L ≤ 0.1 sec cm⁻¹).

In 4 species, reasonable agreement was obtained in a controlled environment between transpiration as measured by weight loss and that calculated from determination of (a) the difference in water vapor density from leaf to air, (b) the boundary layer resistance, and (c) the leaf diffusion resistance. This result confirms the physical validity of the resistance measurement procedure.

     

Diffusion from a Circular Stoma through a Boundary Layer: A FIELD-THEORETICAL ANALYSIS

The case of diffusion of a gas from a single circular stoma through an unstirred boundary layer of finite thickness into a perfectly stirred atmosphere free of convective effects is examined theoretically, with the gas assumed to be at constant concentration across the stoma. The analysis employs a mathematical solution to an analogous problem in electrostatic physics previously obtained by Kuz'min (1972 Sov Phys Tech Phys 17: 473-476). The diffusion flux is shown to be no more than 1% greater than that into a perfectly unstirred atmosphere if the boundary layer is thicker than 40 times the stomatal radius. Under the conditions assumed, for realistic boundary-layer and stomatal dimensions, taking the diffusion flux through the boundary layer to be linear with the stomatal radius would usually involve no significant error. This result may indicate that the principal effect of wind velocity on mass exchange between leaf and atmosphere may be exerted through influencing convection outside the boundary layer rather than through determining the thickness of that layer.     

The effect of gravity on surface temperatures of plant leaves

A fundamental study was conducted to develop a facility having an adequate air circulation system for growing healthy plants over a long-term under microgravity conditions in space. To clarify the effects of gravity on heat exchange between plant leaves and the ambient air, surface temperatures of sweet potato and barley leaves and replica leaves made of wet paper and copper were evaluated at gravity levels of 0.01, 1.0, 1.5 and 2.0 g for 20 s each during parabolic aeroplane flights. Thermal images were captured using infrared thermography at an air temperature of 26 degrees C, a relative humidity of 18% and an irradiance of 260 W m-2. Mean leaf temperatures increased by 0.9-1.0 degrees C with decreasing gravity levels from 1.0 to 0.01 g and decreased by 0.5 degrees C with increasing gravity levels from 1.0 to 2.0 g. The increase in leaf temperatures was at most 1.9 degrees C for sweet potato leaves over 20 s as gravity decreased from 1.0 to 0.01 g. The boundary layer conductance to sensible heat exchange decreased by 5% when the gravity decreased from 1.0 to 0.01 g at the air velocity of 0.2 m s-1. The decrease in the boundary layer conductance with decrease in the gravity levels was more significant in a lower air velocity. Heat exchange between leaves and the ambient air was more retarded at lower gravity levels because of less sensible and latent heat transfers with less heat convection.     

Estimates of the diffusion resistance of some large sunflower leaves in the field

Studies were made of resistance to gaseous exchange between large sunflower leaves and the bulk air in a crop canopy. Two components of the diffusive pathway for mass and sensible heat were evaluated; A) the resistance from the interior of the leaf to the leaf surface, and B) the resistance from the surface of the leaf through the leaf boundary air layer to the bulk air.     

Stomatal control of transpiration from a developing sugarcane canopy

Abstract. Stomatal conductance of single leaves and transpiration from an entire sugarcane (Saccharum spp. hybrid) canopy were measured simultaneously using independent techniques. Stomatal and environmental controls of transpiration were assessed at three stages of canopy development, corresponding to leaf area indices (L) of 2.2, 3.6 and 5.6. Leaf and canopy boundary layers impeded transport of transpired water vapour away from the canopy, causing humidity around the leaves to find its own value through local equilibration rather than a value determined by the humidity of the bulk air mass above the canopy. This tended to uncouple transpiration from direct stomatal control, so that transpiration predicted from measurement of stomatal conductance and leaf-to-air vapour pressure differences was increasingly overestimated as the reference point for ambient vapour pressure measurement was moved farther from the leaf and into the bulk air. The partitioning of control between net radiation and stomata was expressed as a dimensionless decoupling coefficent ranging from zero to 1.0. When the stomatal aperture was near its maximum this coefficient was approximately 0.9, indicating that small reductions in stomatal aperture would have had little effect on canopy transpiration. Maximum rates of transpiration were, however, limited by large adjustments in maximum stomatal conductance during canopy development. The product of maximum stomatal conductance and L. a potential total canopy conductance in the absence of boundary layer effects, remained constant as L increased. Similarly, maximum canopy conductance, derived from independent micrometeorological measurements, also remained constant over this period. Calculations indicated that combined leaf and canopy boundary layer conductance decreased with increasing L such that the ratio of boundary layer conductance to maximum stomatal conductance remained nearly constant at approximately 0.5. These observations indicated that stomata adjusted to maintain both transpiration and the degree of stomatal control of transpiration constant as canopy development proceeded.     

Influence of the flow regime on the efficiency of a gas-liquid two-phase medium filtration

An easy technique, consisting in injecting air into the liquid stream, is proposed to enhance the permeate flux in crossflow filtration of a model fluid (i.e a bentonite suspension). The injected air promotes turbulence and increases the superficial crossflow velocity that leads to a regular disturbance of the boundary layer. A systematic study of different two-phase configurations points up that the slug flow seems the most appropriate regime. The resulting permeate rate is increased up to 140%, in comparison with the usual filtration processes.