Effect Of Surface Heterogeneity Research Articles

The effects of surface heterogeneity on erosion and sedimentation and their implications for of soil properties at postmining sites

Erosion is often mentioned as a serious problem namely in vegetation free areas such as post mining soils. Much less attention has been paid to the role of erosion and deposition on habitat formation. Study describes the effect of erosion and deposition on soil chemical and physical properties in sites with various topography using an array of artificial postmining catchments located near Sokolov (Czech Republic). All the study sites are formed by the deposition of postmining overburden consisting of clays impregnated with carbonates. Falcon was established in 2019 and allows a detailed assessment of the first stages of ecosystem development. It consists of four parallel catchments (0.25 ha each); two are rehabilitated, and two are not. The reclaimed areas are leveled and planted with alders, whereas the unreclaimed sites created longitudinal terrain waves to mimic the situation after heaping. Detailed surface change studies by means of erosion pins and 3D terrain models created with the help of drones revealed that the surface elevation rises in the flat catchments and decreased in the wave-like catchments. In contrast, sediment loss through surface runoff shows no difference between the flat and wave-like areas. Considerable heterogeneity in the erosion process is observed in wave-like areas; the upper part of the terrain waves is heavily eroded, while eroded material accumulates in the depression. The depressions contain more silt and clay material and have higher water retention rates and lower infiltration rates, whereas the opposite is true for elevated wave tops. Study show that erosion and deposition play key role in microhabitat formation, which can be crucial in future ecosystem development.

Nanoscale Patterning of Surface Nanobubbles by Focused Ion Beam.

Surface nanobubbles forming on hydrophobic surfaces in water present an exciting opportunity as potential agents of top-down and bottom-up nanopatterning. The formation and characteristics of surface nanobubbles are strongly influenced by the physical and chemical properties of the substrate. In this study, focused ion beam (FIB) milling is used for the first time to spatially control the nucleation of surface nanobubbles with 75 nm precision. The spontaneous formation of nanobubbles on alternating lines of a self-assembled monolayer (octadecyltrichlorosilane) patterned by FIB is detected by atomic force microscopy. The effect of chemical vs topographical surface heterogeneity on the formation of nanobubbles is investigated by comparing samples with OTS coating applied pre- vs post-FIB patterning. The results confirm that nanoscale FIB-based patterning can effectively control surface nanobubble position by means of chemical heterogeneity. The effect of FIB milling on nanobubble morphology and properties, including contact angle and gas oversaturation, is also reported. Molecular dynamics simulations provide further insight into the effects of FIB amorphization on surface nanobubble formation. Combined experimental and simulation investigations offer insights to guide future nanobubble-based patterning using FIB milling.

Representing effects of surface heterogeneity in a multi-plume eddy diffusivity mass flux boundary layer parameterization

Representing effects of surface heterogeneity in a multi-plume eddy diffusivity mass flux boundary layer parameterization

Challenges and perspective on the modelling of high-Re, incompressible, non-equilibrium, rough-wall boundary layers

The present paper gives an overview of the recent modelling activities under NATO-STO AVT-349, focussed on the understanding and modelling of boundary layers for incompressible, high-Reynolds-number flows subject to non-equilibrium conditions such as strong pressure gradients, three-dimensionality, and surface roughness and heterogeneity. For this, we consider simpler cases where the above flow conditions are present separately or in a reduced number of combinations. First, we focus on the effect of roughness on the outer flow and the problems associated to its characterisation and prediction, with a particular emphasis on the conditions necessary for outer-layer similarity to hold. We then focus on how the presence of adverse and favourable pressure gradients affects the effect of roughness, and to what extent the figures used to quantify it are still useful under such conditions. We also consider the effect of surface heterogeneity, the shortcomings when modelling it and how these can be addressed. We then focus on the effect on the outer layer of pressure gradients and non-equilibrium conditions, to what extent similarity holds in those conditions, and how RANS models perform for such flows, identifying routes for their improvement to handle pressure gradients and non-equilibrium. We also discuss the use of data-driven and machine-aided methods in closure models.

Unraveling the influence of surface functionalities on gas Physisorption: A comprehensive study on SBA-15 nanoporous material from Monte Carlo simulation for improved Textural-Energetic characterization

In this study, we conducted experimental and Monte Carlo simulation studies in the grand canonical ensemble (GCMC) to investigate the role of molecular orientation and surface heterogeneity on the adsorption of N2 at 77 K. Our research focused on a series of ordered nanoporous materials (SBA-15) with varying degrees of oxygen functionalities. Specifically, we examined the effects of surface heterogeneity on the calculation of pore size distribution (PSD) and the Brunauer-Emmett-Teller (BET) area of porous materials. To provide a comprehensive perspective, we compared our results with three levels of surface oxidation, including a pristine case without any surface oxidation.The results from both our experimental and simulation data reveal the importance of chemical heterogeneity in determining equilibrium properties such as molecular packing within the pores, differential enthalpies of adsorption, and N2 orientation distribution. Our findings suggest that accurate characterization of surface heterogeneity is crucial for understanding gas adsorption in nanoporous materials and for developing better models for predicting their performance in various applications. Moreover, our simulations revealed substantial changes in the molecular orientation of adsorbate particles with increasing surface heterogeneity. This insight provides valuable information about the behavior of molecules within the nanoporous materials, further enhancing our understanding of the complex adsorption processes in these systems.

Water thin films on kaolinite gibbsite and edge surfaces and their effects on surface wettability in relation to geological carbon sequestration

Geological carbon sequestration (GCS) is a promising method to alleviate CO2 emission, while CO2 structural trapping is one of main GCS mechanisms, in which the storage capacity is strongly dependent on CO2-water–rock contact angle. Although CO2-water-kaolite contact angle on basal surfaces has been studied, the knowledge about kaolinite edge surface wettability remains unknown. In this work, we use molecular dynamics (MD) simulations to study CO2-water-kaolinite contact angle on kaolinite gibbsite and edge surfaces under a typical GCS condition (330 K and 200 bar). The common belief is that surface wettability in presence of water is determined by surface hydroxyl (–OH) group density. While the surface –OH group density of kaolinite edge surface is much lower than that of gibbsite surface, both gibbsite and edge surfaces are strongly water-wet. Edge surface is better hydrated than gibbsite surface as both silanol and aluminol groups can form hydrogen bonding with water molecules thanks to large effective water accessible volume around them, while pocket water can further anchor water film. Therefore, the atomic-level surface characteristics dictate interfacial water structures which determine CO2-water-kaolinite contact angle. Our study provides important insights into the effect of surface heterogeneity on interfacial water structures, and kaolinite gibbsite and edge surface wettability which is crucial to the optimization of GCS processes.

Pore-scale simulation of low-salinity waterflooding in mixed-wet systems: effect of corner flow, surface heterogeneity and kinetics of wettability alteration

The initial wettability state of the candidate oil reservoirs for low-salinity waterflooding (LSWF) is commonly characterized as mixed-wet. In mixed-wet systems, both the two-phase flow dynamics and the salt transport are significantly influenced by the corner flow of the wetting phase. Thus this study aims at comprehensive evaluation of LSWF efficiency by capturing the effect of corner flow and non-uniform wettability distribution. In this regard, direct numerical simulations under capillary-dominated flow regime were performed using the OpenFOAM Computational Fluid Dynamics toolbox. The results indicate that corner flow results in the transport of low-salinity water ahead of the primary fluid front and triggers a transition in the flow regime from a piston-like to multi-directional displacement. This then makes a substantial difference of 22% in the ultimate oil recovery factors between the 2D and quasi-3D models. Furthermore, the interplay of solute transport through corners and wettability alteration kinetics can lead to a new oil trapping mechanism, not reported in the literature, that diminishes LSWF efficiency. While the findings of this study elucidate that LSWF does exhibit improved oil recovery compared to high-salinity waterflooding, the complicating phenomena in mixed-wet systems can significantly affect the efficiency of this method and make it less successful.

Adsorption Kinetics of Tartrazine Dye on Activated Carbon Derived from Guava (Psidium guajava) Seeds

Azo dyes are widely used in various industries. However, many of these dyes are carcinogenic and reduce light penetration into aqueous systems, posing a threat to human health and hampering photosynthesis in aquatic environments. In this study, guava seeds were used to produce activated carbon by chemical activation with ZnCl2. The carbon was characterized and used as an adsorbent to remove tartrazine dye in aqueous medium. X-ray diffraction showed the formation of a material with disordered graphitic planes, typical of activated carbons. The equilibrium time for the dyeactivated carbon system was found to be 80 min by the Southwell plot method. The adsorbent removed 97.6% of the dye, representing an adsorbed concentration of 1.62 mg g−1 for an adsorbent dosage of 12 g L−1. The pseudo-second-order and Elovich kinetic models provided the best fit to experimental data, suggesting that chemisorption is the predominant mechanism, combined with the effect of surface heterogeneity. From an environmental point of view, the results suggest that the activated carbon produced is an efficient material for the treatment of industrial wastewater containing azo dyes.

A Novel Method for Diagnosing Land–Atmosphere Coupling Sensitivity in a Single-Column Model

Abstract The response of boundary layer properties and cloudiness to changes in surface evaporative fraction (EF) is investigated in a single-column model to quantify the locally coupled impact of subgrid surface variations on the atmosphere during summer. Sensitive coupling days are defined when the model atmosphere exhibits large variations across a range of EFs centered on the analyzed value. Coupling sensitivity exists as both positive feedback (cloudiness increases with EF) and negative feedback (clouds increase with decreasing EF) regimes. The positive regime manifests in shallow convection situations, which are capped by a strengthened inversion and subsidence, restricting the vertical extent of convection to just above the boundary layer. Surfaces with larger EF (greater surface latent heat flux) can inject more moisture into the vertically confined system, lowering the cloud base and an increasing cloud liquid water path (LWP). Negative feedback regimes tend to manifest when large-scale deep convection, such as from mesoscale convective systems and fronts, is advected through the domain, where convection strengthens over surfaces with a lower EF (greater surface sensible heat flux). The invigoration of these systems by the land surface leads to an increase in LWP through strengthened updrafts and stronger coupling between the boundary layer and the free atmosphere. These results apply in the absence of heterogeneity-induced mesoscale circulations, providing a one-dimensional dynamical perspective on the effect of surface heterogeneity. This study provides a framework of intermediate complexity, lying between parcel theory and high-resolution coupled land–atmosphere modeling, and therefore isolates the relevant first-order processes in land–atmosphere interactions. Significance Statement Cloud formation, distribution, and other properties may be sensitive to heterogeneous surfaces depending on the strength and location of such heterogeneities and the background atmospheric state. This may drive differences in the cloud population depending on which part of the domain one is located. This may also lead to mesoscale circulations, which may strengthen or weaken this effect. Currently, climate models act on scales (∼100 km) that are too large to explicitly represent these processes, which are strongest at smaller scales (around 5–40 km). Therefore, subgrid-scale heterogeneity is neglected, and any predictability and model fidelity it may provide is lost. We use a simple model to diagnose sensitivity of the local atmosphere to surface variations meant to represent possible subgrid heterogeneity, providing a first-order estimate of its effect. We conclude that preferentially sensitive atmospheric states exist that lead to positive and/or negative feedback between land and atmosphere. This information is valuable to future climate model parameterizations aimed at improving the representation of these feedbacks.

High-Resolution Image Products Acquired from Mid-Sized Uncrewed Aerial Systems for Land–Atmosphere Studies

We assess the viability of deploying commercially available multispectral and thermal imagers designed for integration on small uncrewed aerial systems (sUASs, <25 kg) on a mid-size Group-3-classification UAS (weight: 25–600 kg, maximum altitude: 5486 m MSL, maximum speed: 128 m/s) for the purpose of collecting a higher spatial resolution dataset that can be used for evaluating the surface energy budget and effects of surface heterogeneity on atmospheric processes than those datasets traditionally collected by instrumentation deployed on satellites and eddy covariance towers. A MicaSense Altum multispectral imager was deployed on two very similar mid-sized UASs operated by the Atmospheric Radiation Measurement (ARM) Aviation Facility. This paper evaluates the effects of flight on imaging systems mounted on UASs flying at higher altitudes and faster speeds for extended durations. We assess optimal calibration methods, acquisition rates, and flight plans for maximizing land surface area measurements. We developed, in-house, an automated workflow to correct the raw image frames and produce final data products, which we assess against known spectral ground targets and independent sources. We intend this manuscript to be used as a reference for collecting similar datasets in the future and for the datasets described within this manuscript to be used as launching points for future research.

Modeling the Flow Response to Surface Heterogeneity during a Semi-Idealized Diurnal Cycle

Abstract To characterize the effects of subgrid surface heterogeneity, the blending-height concept has been developed as a coupling strategy for surface parameterization schemes used in numerical weather prediction models. Previous modeling studies have tested this concept using stationary conditions with one-dimensional strips of surface roughness. Here, large-eddy simulations are used to examine the response of the blending height and effective surface roughness to tiled land-cover heterogeneity, or a two-dimensional chessboard pattern of alternating high and low vegetation given a diurnal cycle of solar irradiance in subarctic conditions. In each experiment, the length scale of the roughness elements is increased while the total domain fraction of each vegetation type is kept constant. The effective surface roughness was found to decrease with increasing length scale of surface cover heterogeneity, which is shown to have a significant impact on estimated wind turbine power calculated from logarithmic wind profiles. In stable conditions, the blending height in cases with large heterogeneity length scales was found to exist well above the surface layer. Because the behavior of the blending height has implications for coupled models, a simple model for the blending height as a function of heterogeneity length scale is introduced.

Investigating simultaneous effects of temperature, surface heterogeneity and geometry on fluid mixing in electroosmotic flow considering temperature dependent properties by Nernst–Planck Poisson method

Numerical study of the effect of temperature and heat transfer as well as surface heterogeneity effects on mixing and electroosmotic flow in microchannels with convergent/divergent and straight mixing chamber is carried out. The fluid properties and surface zeta potentials are assumed to be temperature dependent. Based on the Nernst–Planck Poisson model, the governing equations of this problem include the Laplace equation, Poisson equation, Navier–Stokes and the propagation equation as well as the energy equation, respectively for the distribution of external electric field, distribution of internal electric field due to the charge of ions, fluid motion, concentration field and temperature distribution, which are solved by the finite element method. Flow rate, the mixing efficiency and a new parameter called mixing capacity, which is achieved by multiplying flow rate by mixing efficiency, are obtained for convergent/divergent and straight microchannels in a constant external electric field distributed under different wall temperatures, and performance of the geometries in flow transfer and mixing development is investigated. For electroosmotic flow, heterogeneous microchannels create vortices which improve mixing. Different arrangements of heterogeneous pieces of the surface create different patterns of vortices, each of which has different effects in the various geometries on fluid flow and mixing. Also, the dependence of the molecular diffusion on temperature causes increasing the mixing of species with the temperature increment. The results show that divergent microchannels have the maximum flow rate and the minimum mixing efficiency, but this efficiency can be increased by increasing the wall temperature. Convergent microchannels also have high mixing efficiency due to low flow rates and sufficient time for mixing even at low and near ambient temperatures, although their mixing capacity is less than the divergent microchannels.

Effect of Macroscopic Surface Heterogeneities on an Advancing Contact Line.

The shape of a liquid-air interface advancing on a heterogeneous surface was studied experimentally, together with the force induced by the pinning of the contact line to surface defects. Different surfaces were considered with circular defects introduced as arrays of cocoa butter patches or small circular holes. These heterogeneous surfaces were submerged in aqueous ethanol solutions while measuring the additional force arising from the deformation of the advancing contact line and characterizing the interface shape and its pinning on the defects. Initially, the submersion force is linear with submerged depth, suggesting a constant defect-induced stiffness. This regime ends when the contact line depins from the defects. A simple scaling is proposed to describe the depinning force and the depinning energy. As the defect separation increases, the interface stiffness is found to increase too, with a weak dependency on the defect radius. This interaction between defects cannot be captured by simple scaling but can be well predicted by a theory considering the interface deformation in the presence of a periodic arrays of holes. Creating a four-phase contact line by including solid defects (cocoa butter) reduced pinning forces. The radius of the defect had a nonlinear effect on the depinning depth. The four-phase contact line resulted in depinning before the defects were fully submerged. These experimental results and the associated theory help to understand quantitatively the extent to which surface heterogeneities can slow down wetting. This in turn paves the way to tailoring the design of heterogeneous surfaces toward desired wetting performances.

The Effect of Surface Heating Heterogeneity on Boundary Layer Height and Its Dependence on Background Wind Speed

AbstractThe planetary boundary layer height (PBLH) is a fundamental variable of the planetary boundary layer (PBL). The effect of surface heterogeneity is challenging in the PBL parameterization for numerical weather and climate models. Here we use large eddy simulation data to investigate the impact of surface heating heterogeneity on the PBLH spatial variations and mean values over a domain of typical mesoscale model grid size. It is found that this impact depends on background wind condition. Variance decomposition and Fourier spectra both reveal that for the fully developed sheared convective PBL, surface heterogeneity contributes little to the spatial variation of PBLH, except for the case with heterogeneity scale of 14.4 km. This suggests that surface heterogeneity with length scales less than ∼10 km, which is typical for mesoscale modeling, does not induce significant subgrid spatial variation of PBLH. The domain‐averaged PBLH is found to generally increase as surface heterogeneity scale decreases, until reaching the scale on the order of PBLH. The findings can be used to inform the parameterization development of PBL processes over heterogeneous surface.

Effect of Surface Heterogeneities on Interactions between Air Bubbles and Heterogeneous Surfaces.

The effects of surface heterogeneities on bubble-particle interactions have received little attention although heterogeneities are common for varieties of substance surfaces. In this work, heterogeneous surfaces consisting of discrete hydrophilic dots on a hydrophobic background were fabricated. The interactions between air bubbles and heterogeneous surfaces with different hydrophilic area fractions were investigated using a high-sensitivity microbalance coupled with a high-speed video camera. It was found that the snap-in, maximum adhesion, and pull-off forces increased as the hydrophilic area fraction decreased. These experimental results were compared with the calculated interaction forces. The comparison between experimental results and the calculated interaction forces showed that the normalized contact line length (δ) should be considered in the calculation of the snap-in force, and its value was between 1 and the δ value corresponding to the maximum pinning strength. In contrast, δ = 1 is more appropriate for the calculation of maximum adhesion force, indicating that the corrugations in the three-phase contact line could be neglected. These findings demonstrate that discrete hydrophilic defects make bubble-surface attachment difficult but have nearly no effect on bubble-surface detachment. Better understanding of the interactions between air bubbles and heterogeneous surfaces potential offers a new thought to control the bubble-particle interactions using appropriately design of particle surfaces.

Coronilla juncea, a native candidate for phytostabilization of potentially toxic elements and restoration of Mediterranean soils

Soil contamination pattern due to industrial activities often leads to high concentrations of potentially toxic elements (PTE) decreasing with depth. This spatial heterogeneity of the soil contamination may have significant consequences on the soil properties and soil living communities. We evaluated the effects of both surface and solum soil contamination heterogeneity on Coronilla juncea L. (Fabaceae) functional traits in field conditions and the phytostabilization potential of this species. Plant and soil samples were collected on 3 sites along a PTE contamination gradient. The correlations between PTE concentration in plant and soil samples at 2 depths, physico-chemical properties of soil, plant biomass and soil microbial activity were tested. Field measurements highlight a decreasing PTE concentration with soil depth in addition to an important surface heterogeneity of As, Cu, Pb, Sb and Zn soil concentrations. Root PTE concentrations in C. juncea did not follow soil PTE concentrations. Concentrations of PTE in the root parts were higher than those of the aerial parts. Low PTE translocation and root symbioses with microorganisms suggest that this native plant species may play a role as engineer species with positive implications for the phytostabilization of Mediterranean PTE contaminated soils and their ecological restoration.

Wetting behavior of sessile droplet affected by chemical heterogeneity size: A theoretical and simulative analysis with consideration of contact line width

The effect of surface heterogeneity of solid substrate on the wetting behavior of sessile droplets is systematically investigated. A theory is proposed to predict the contact angle by considering the droplet to be a spherical cap and the contact line to have a width. Comprehensive molecular dynamics (MD) simulations are implemented to validate this theory, which shows good agreement. Based on this theory, the relationship between the wetting behavior of sessile droplets and the heterogeneity pattern of chemically heterogeneous surfaces is established, which manifests that the contact angle can be precisely controlled. Further, the influence of the heterogeneity size on wetting is quantified, which indicates that the contact angle behavior is quite distinct with the contact line width as the critical value of the heterogeneity size. The reason is analyzed theoretically through the location of the contact line with a width, giving an intuitive comprehension of the underlying mechanism.

Effects of Horizontal Resolution, Domain Size, Boundary Conditions, and Surface Heterogeneity on Coarse LES of a Convective Boundary Layer

Abstract Atmospheric properties in a convective boundary layer vary over a wide range of spatial scales and are commonly studied using large-eddy simulations (LES) in various configurations. We examine how the boundary layer depth and distribution of variability across scales are affected by LES grid spacing, domain size, inhomogeneity of surface properties, and external forcing. Two different setups of the Weather Research and Forecasting (WRF) model are analyzed. A semi-idealized configuration uses a periodic domain, flat surface, prescribed homogeneous surface heat fluxes, and horizontally uniform profiles of large-scale advective tendencies. A nested LES setup employs a larger domain and realistic initial and boundary conditions, including an interactive land surface model with representative topography and vegetation and soil types. Subdomains of identical size are analyzed for all simulations. Characteristic structure sizes are quantified using the variability scales L50 and L95, defined such that features smaller than that contain 50% and 95% of the total variance, respectively. Progressive increase in L50 from vertical velocity to temperature and moisture structures is systematically reproduced in all simulation configurations. This dependence of L50 on the considered variable complicates the development of scale-aware parameterizations for models with grid spacing in the “terra incognita”. In simulations using a larger domain with heterogeneous surface properties, the development of internal mesoscale patterns significantly affects variance distributions inside analyzed subdomains. Sizes of boundary layer structures also strongly depend on the LES grid spacing and, in case of heterogeneous surface and topography, on location of the subdomain inside a larger computational domain.

Interfacial studies on the effects of patterned anodes for guided lithium deposition in lithium metal batteries

The lifetime and health of lithium metal batteries are greatly hindered by nonuniform deposition and growth of lithium at the anode-electrolyte interface, which leads to dendrite formation, efficiency loss, and short circuiting. Lithium deposition is influenced by several factors including local current densities, overpotentials, surface heterogeneity, and lithium-ion concentrations. However, due to the embedded, dynamic nature of this interface, it is difficult to observe the complex physics operando. Here, we present a detailed model of the interface that implements Butler-Volmer kinetics to investigate the effects of overpotential and surface heterogeneities on dendrite growth. A high overpotential has been proposed as a contributing factor in increased nucleation and growth of dendrites. Using computational methods, we can isolate the aspects of the complex physics at the interface to gain better insight into how each component affects the overall system. In addition, studies have shown that mechanical modifications to the anode surface, such as micropatterning, are a potential way of controlling deposition and increasing Coulombic efficiency. Micropatterns on the anode surface are explored along with deformations in the solid-electrolyte interface layer to understand their effects on the dendritic growth rates and morphology. The study results show that at higher overpotentials, more dendritic growth and a more branched morphology are present in comparison to low overpotentials, where more uniform and denser growth is observed. In addition, the results suggest that there is a relationship between surface chemistries and anode geometries.

Grid resolution dependency of land surface heterogeneity effects on boundary‐layer structure

AbstractLand surface heterogeneity exerts a strong control on atmospheric boundary‐layer (ABL) evolution by spatially varying the distribution and partitioning of surface energy fluxes and triggering secondary circulations. The representation of this physical process in numerical weather prediction (NWP) models is especially affected in the terra incognita as the model grid resolution approaches the length‐scale of the largest eddies in the boundary layer. We explore these effects for a mesoscale strip‐like land surface inhomogeneity in land cover, soil moisture or a superposition of both embedded in an elsewhere homogeneous landscape. The study is conducted with the numerical weather prediction model ICON (ICOsahedral Nonhydrostatic), using the default operational level 2.5 Mellor–Yamada turbulence closure (MY) and a large‐eddy simulation (LES) configuration as a benchmark. While simulations with the default ABL scheme approach the LES reference when refining the spatial grid towards finer resolution, the model generates artificial circulations leading to ABL height oscillations when the horizontal grid resolution approaches the ABL height . The effect of these model‐induced circulations on the state of the boundary layer is even present with weak thermal heterogeneity under low background wind speed ( but diminishes with increasing background wind speed. The tuning of the asymptotic turbulent mixing length‐scale in the operational ABL scheme helps in reducing the amplitude of the oscillations, thereby reducing the artificially induced circulations due to thermal heterogeneity which might act as unintentional trigger for clouds and precipitation. Based on the tuned synthetic model data from sensitivity runs, we propose a new parametrization for a 2‐D as a function of , and , which is otherwise held as a constant in the ABL scheme.