Increase In Length Scale Research Articles

Turbulence with associated kinetic energy budget in the region of wave-blocking formed over an obstacle

Turbulence characteristics in the region of wave-blocking over a submerged forward-facing obstacle is explored, and the results are compared with those of base-flow over the obstacle. Wave-blocking over obstacle is setup, adjusting the strong incoming flow with counter-propagating waves, and confirmed by linear dispersion relation. A variation in the flow is detected in three distinct segments: flow from the upstream, wave-blocking over the obstacle and the waves propagating from the downstream. The instantaneous velocity is recorded using a three-dimensional micro-acoustic Doppler velocimeter along the flow. Turbulence properties such as the mean velocity, Reynolds stress, turbulent kinetic energy, and associated coherent structures around the wave-blocking are discussed. Moreover, power spectral density, kinetic energy budget, and turbulence length- and time-scales are examined. The stress fractions to the total shear stress contribute higher for only flow than those of wave-blocking over obstacle. The power-spectral peaks at a fixed frequency for wave-blocking along lee side are greater than those of base-flow over obstacle. Kinetic energy budget for only flow over the obstacle is much higher than that of wave-blocking, indicating loss of energy due to wave-blocking. In the near-bed region, length-scale increases indicating the higher momentum and energy transfer. Increase in anisotropy plays significant role in the production. Results are valuable to ship sailing, design of coastal structures, and sediment transport.

Bioengineering approaches for patient-specific analysis of placenta structure and function

The leading cause of perinatal mortality is fetal growth restriction (FGR), defined as in utero fetal growth below the 10th percentile. Insufficient exchange of oxygen and nutrients at the maternal-fetal interface is associated with FGR. This transport occurs through the vasculature of the placenta, particularly in the terminal villi, where the vascular membranes have a large surface area and are the thinnest. Altered structure of the placenta villi is thought to contribute to decreased oxygen exchange efficiency, however, understanding how the three-dimensional microstructure and properties decrease this efficiency remains a challenge. Here, a novel, multiscale workflow is presented to quantify patient-specific biophysical properties, 3D structural features, and blood flow of the villous tissue. Namely, nanoindentation, optical coherence tomography, and ultrasound imaging were employed to measure the time-dependent material properties of placenta tissue, the 3D structure of villous tissue, and blood flow through the villi to characterize the microvasculature of the placenta at increasing length scales. Quantifying the biophysical properties, the 3D architecture, and blood flow in the villous tissue can be used to infer changes in maternal-fetal oxygen transport at the villous membrane. Overall, this multiscale understanding will advance knowledge of how microvascular changes in the placenta ultimately lead to FGR, opening opportunities for diagnosis and intervention.

Inextensional vibrations of thin spherical shells using strain gradient elasticity theory

We study inextensional vibrations of the spherical shell using strain gradient elasticity theory under Kirchhoff-Love hypotheses. For admissibility of the inextensional deformations the shell is punctured by making a tiny hole. The shell is assumed to be made of linearly elastic, homogeneous, and isotropic material. The closed form expression for the frequencies of inextensional modes of vibration of spherical caps of various polar angles and that of nearly complete spherical shell are derived using Rayleigh's method. Towards this, the displacement and velocity fields are obtained by setting the membrane strains to zero. Further, to facilitate the existence of inextensional vibrations, boundaries are assumed to be traction free. The frequencies are computed for the positive and negative signs in the strain gradient term of the constitutive law. The computed frequencies, employing negative sign are found to be higher than those computed using classical elasticity theory. The opposite effect is seen when the frequencies are computed with the positive sign. Further, the frequencies are found to saturate when the positive sign is used in the constitutive law. Parametric studies viz. variation in frequencies with the circumferential wavenumbers for different values of length scale parameter, variation in frequencies with circumferential wavenumbers for different values of polar angles and a given length scale parameter, variation of frequency with increasing polar angle for a given circumferential wavenumber, variation of saturation wavenumber with increasing polar angle, and increasing length scale parameter are carried out. The frequencies of nearly a spherical shell with increasing circumferential wavenumber are also computed.

Water hyacinths retain river plastics

Rivers represent one of the main conduits for the delivery of plastics to the sea, while also functioning as reservoirs for plastic retention. In tropical regions, rivers are exposed to both high levels of plastic pollution and invasion of water hyacinths. This aquatic plant forms dense patches at the river surface that drift due to winds and currents. Recent work suggests that water hyacinths play a crucial role in influencing plastic transport, by efficiently trapping the majority of surface plastic within their patches. However, a comprehensive understanding of the interaction between water hyacinths and plastics is still lacking. We hypothesize that the properties relevant to plastic transport change due to their trapping in water hyacinth patches. In particular, the length scale, defined as the characteristic size of the transported material, is a key property in understanding how materials move within rivers. Here, we show that water hyacinth patches trap on average 54%–77% of all observed surface plastics at the measurement site (Saigon river, Vietnam). Both temporally and spatially, we found that plastic and water hyacinth presence co-occur. The formation of plastic-plant aggregates carries significant implications for both clean-up and monitoring purposes, as these aggregates can be detected from space and need to be jointly removed. In addition, the length scale of trapped plastics (∼4.0 m) was found to be forty times larger than that of open water plastics (∼0.1 m). The implications of this increased length scale for plastic transport dynamics are yet to be fully understood, calling for further investigation into travel distances and trajectories. The effects of plastic trapping likely extend to other key properties of plastic-plant aggregates, such as effective buoyancy and mass. Given the prevalence of plant invasion and plastic pollution in rivers worldwide, this research offers valuable insights into the complex environmental challenges faced by numerous rivers.

Orientation Dependency of 3D printed SHCC at increasing length scale

In the first part of this study, the inclination-dependent effects on a single fibre embedded in 3D printable strain hardening cementitious composite are studied. Two distinct failure modes (i.e., slipping rupture and complete pull-out) were found in the experimental results. Based on these failure modes two separate slip-hardening factors have been determined and analysed with an analytical fibre pull-out model. The second part of the study focused on the influence of multiple fibres with varying inclination angles on single- and multiple-cracking specimens. These tests have been performed for specimens that were casted and printed, to analyse the effect on ductility due to the extrusion process. Three orthogonal directions were examined within the printed specimens during testing. The amount of energy dissipated during the crack opening is strongly orientation-dependent for 3DP-SHCC and does not significantly increase in the main printing direction compared to casted SHCC. Furthermore, the orientation-dependent ductility is evaluated in bending with the use of a 4PB test. Allowing multiple layers of fibre-reinforced material to become active at the same time. The strain hardening effect found in a single crack is amplified by the material’s capability to develop multiple cracks, ultimately leading to a significant increase in its impact on engineering applications related to bending.

Effects of Stress‐Driven Melt Segregation on Melt Orientation, Melt Connectivity and Anisotropic Permeability

AbstractStress‐driven melt segregation may have important geochemical and geophysical effects but remains a poorly understood process. Few constraints exist on the permeability and distribution of melt in deformed partially molten rocks. Here, we characterize the 3D melt network and resulting permeability of an experimentally deformed partially molten rock containing several melt‐rich bands based on an X‐ray microtomography data set. Melt fractions range from 0.08 to 0.28 in the ∼20‐μm‐thick melt‐rich bands, and from 0.02 to 0.07 in the intervening ∼30‐μm‐thick regions. We simulated melt flow through subvolumes extracted from the reconstructed rock at five length scales ranging from the grain scale (3 μm) to the minimum length required to fully encompass two melt‐rich bands (64 μm). At grain scale, few subvolumes contain interconnected melt, and permeability is isotropic. As the length scale increases, more subvolumes contain melt that is interconnected parallel to the melt bands, but connectivity diminishes in the direction perpendicular to them. Even if melt is connected in all directions, permeability is lower perpendicular to the bands, in agreement with the elongation of melt pockets. Permeability parallel to the bands is proportional to melt fraction to the power of an exponent that increases from ∼2 to 5 with increasing length scale. The permeability in directions parallel to the bands is comparable to that for an isotropic partially molten rock. However, no flow is possible perpendicular to the bands over distances similar to the band spacing. Melt connectivity limits sample scale melt flow to the plane of the melt‐rich bands.

The modulation of coherent structures by the near-wall motions of particles

Particle–wall interaction generates strong particle near-wall motion, including collision bounce and impact splashing. To distinguish the effect of particles and particle near-wall motions on the turbulent coherent structure, this study carried out three different cases of sand-laden two-phase flow measurements: a uniform sand release at the top, local-laying sand bed and global-laying sand bed (Liu et al., J. Fluid Mech., vol. 943, 2022, A8). Based on large field of view particle image velocimetry/particle tracking velocimetry measurements, we obtained the velocity field of a two-dimensional gas–solid two-phase dilute faction flow $(\varPhi _{v} \sim O(10^{-4}))$ with a friction Reynolds number $R e_{\tau }$ of 3950. Results indicate that particles weaken the high- and low-velocity iso-momentum zones and hairpin vortices, resulting in the increased length scale of the coherent structure. However, the collision bounce and impact splashing break up the inner iso-momentum zone and hairpin vortices while enhancing them in the outer region, thus reducing the structure scale. In addition, the upward-moving particles increase the large-scale structure inclination angle, while the downward-moving particles decrease it. The linear coherence spectrum analysis suggests that the particles themselves do not change the structural self-similarity, but their saltation motions disrupt the similarity of the near-wall structure, making the inclination angle decrease with the scale, and the generated ascending particles reduce the aspect ratio of the streamwise to wall-normal direction in the outer region.

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.

Design optimization of integrated cooling inserts in modular Fischer-Tropsch reactors

Sustainable production of liquid fuels and feedstocks from atmospheric CO2 through carbon recycling technologies is necessary to broaden decarbonization efforts and further reduce global emissions. Fischer–Tropsch (FT) reactors can address this challenge by providing storable, high-value liquid hydrocarbon fuels and feedstocks from syngas generated through reductive CO2 utilization. FT technology, however, is most cost effective at large-scale, fixed-site plants and does not effectively address the smaller, globally distributed CO2 point sources. Alternatively, smaller, modular reactors can be composed together to the specific scale of the emission source, yielding a flexible solution that enables more widespread deployment. In these modular reactors, thermal management using a finned cooling insert embedded within the catalyst matrix is critical to maintaining the performance and viability. Thus, in this work, topology optimization is used to determine the cooling insert geometry that maximizes reactor productivity while preventing auto-thermal runaway. Optimal designs are generated for varying number of constituent fins and over a range of maximum operating temperatures. Constraints including minimum feature length-scales and prescribed cooling insert material are imposed on the designs to enhance manufacturability. The impact of design features such as insert tapering and increased length scale hierarchy is automatically revealed by the systematic design framework employed. This approach thus generates novel optimal geometries while automating, accelerating, and enhancing the design process compared to traditional heuristic approaches for cooling insert design in modular FT reactors.

Nonmonotonic Dynamical Correlations beneath the Surface of Glass-Forming Liquids.

Collective motion over increasing length scales is a signature of the vitrification process of liquids. We demonstrate how distinct static and dynamic length scales govern the dynamics of vitrifying films. In contrast to a monotonically growing static correlation length, the dynamical correlation length that measures the extent of surface-dynamics acceleration into the bulk displays a striking nonmonotonic temperature evolution that is robust also against changes in detailed interatomic interaction. This nonmonotonic change defines a crossover temperature T_{*} that is distinct from the critical temperature T_{c} of mode-coupling theory. We connect this nonmonotonic change to a morphological change of cooperative rearrangement regions of fast particles, and to the point where the decoupling of fast-particle motion from the bulk relaxation is most sensitive to fluctuations. We propose a rigorous definition of this new crossover temperature T_{*} within a recent extension of mode-coupling theory, the stochastic β-relaxation theory.

Increased SERCA2a sub-cellular heterogeneity in right-ventricular heart failure inhibits excitation-contraction coupling and modulates arrhythmogenic dynamics.

The intracellular calcium handling system of cardiomyocytes is responsible for controlling excitation-contraction coupling (ECC) and has been linked to pro-arrhythmogenic cellular phenomena in conditions such as heart failure (HF). SERCA2a, responsible for intracellular uptake, is a primary regulator of calcium homeostasis, and remodelling of its function has been proposed as a causal factor underlying cellular and tissue dysfunction in disease. Whereas adaptations to the global (i.e. whole-cell) expression of SERCA2a have been previously investigated in the context of multiple diseases, the role of its spatial profile in the sub-cellular volume has yet to be elucidated. We present an approach to characterize the sub-cellular heterogeneity of SERCA2a and apply this approach to quantify adaptations to the length-scale of heterogeneity (the distance over which expression is correlated) associated with right-ventricular (RV)-HF. These characterizations informed simulations to predict the functional implications of this heterogeneity, and its remodelling in disease, on ECC, the dynamics of calcium-transient alternans and the emergence of spontaneous triggered activity. Image analysis reveals that RV-HF is associated with an increase in length-scale and its inter-cellular variability; simulations predict that this increase in length-scale can reduce ECC and critically modulate the vulnerability to both alternans and triggered activity.This article is part of the theme issue ‘The cardiomyocyte: new revelations on the interplay between architecture and function in growth, health, and disease’.

Role of Ultrasonic Treatment on Microstructure, Multiscale Mechanical, and Tribological Behavior of 2D Tungsten Disulfide Reinforced Aluminum Composites

This article is the first report on the role of ultrasonic treatment (UST) on microstructural evolution, multiscale mechanical behavior, and tribological response in 2D tungsten disulfide (WS2) reinforced aluminum (Al6061) matrix composites. Delaunay triangulation calculations show that UST for 45 s enables a fourfold enhancement in the dispersion parameter of WS2 reinforcements in the Al6061 matrix from 0.08 to 0.32. Improved WS2 dispersion contributes to higher nucleation density with 52.7% grain refinement efficiency, achieving a fine‐grained Al6061–WS2 composite. The role of UST‐induced 2D reinforcement dispersion on the elastic deformation is established at progressively increasing length scales from individual grains to the bulk composite. It is accomplished by integrating the nanodynamic modulus mapping technique with a finite element modeling framework built on experimentally acquired microstructures and localized elastic moduli. It delineates a directly proportional relationship between UST‐induced dispersion and elastic modulus enhancement at all length scales from 10 to 700 μm. Excellent dispersion of the 2D layered WS2 homogenizes the tribological response of the composite material with a tenfold reduction in the volume of material lost during wear.

Gell-Mann-Low Criticality in Neural Networks.

Criticality is deeply related to optimal computational capacity. The lack of a renormalized theory of critical brain dynamics, however, so far limits insights into this form of biological information processing to mean-field results. These methods neglect a key feature of critical systems: the interaction between degrees of freedom across all length scales, required for complex nonlinear computation. We present a renormalized theory of a prototypical neural field theory, the stochastic Wilson-Cowan equation. We compute the flow of couplings, which parametrize interactions on increasing length scales. Despite similarities with the Kardar-Parisi-Zhang model, the theory is of a Gell-Mann-Low type, the archetypal form of a renormalizable quantum field theory. Here, nonlinear couplings vanish, flowing towards the Gaussian fixed point, but logarithmically slowly, thus remaining effective on most scales. We show this critical structure of interactions to implement a desirable trade-off between linearity, optimal for information storage, and nonlinearity, required for computation.

A workflow for rapid unbiased quantification of fibrillar feature alignment in biological images.

Measuring the organisation of the cellular cytoskeleton and the surrounding extracellular matrix (ECM) is currently of wide interest as changes in both local and global alignment can highlight alterations in cellular functions and material properties of the extracellular environment. Different approaches have been developed to quantify these structures, typically based on fibre segmentation or on matrix representation and transformation of the image, each with its own advantages and disadvantages. Here we present AFT-Alignment by Fourier Transform, a workflow to quantify the alignment of fibrillar features in microscopy images exploiting 2D Fast Fourier Transforms (FFT). Using pre-existing datasets of cell and ECM images, we demonstrate our approach and compare and contrast this workflow with two other well-known ImageJ algorithms to quantify image feature alignment. These comparisons reveal that AFT has a number of advantages due to its grid-based FFT approach. 1) Flexibility in defining the window and neighbourhood sizes allows for performing a parameter search to determine an optimal length scale to carry out alignment metrics. This approach can thus easily accommodate different image resolutions and biological systems. 2) The length scale of decay in alignment can be extracted by comparing neighbourhood sizes, revealing the overall distance that features remain anisotropic. 3) The approach is ambivalent to the signal source, thus making it applicable for a wide range of imaging modalities and is dependent on fewer input parameters than segmentation methods. 4) Finally, compared to segmentation methods, this algorithm is computationally inexpensive, as high-resolution images can be evaluated in less than a second on a standard desktop computer. This makes it feasible to screen numerous experimental perturbations or examine large images over long length scales. Implementation is made available in both MATLAB and Python for wider accessibility, with example datasets for single images and batch processing. Additionally, we include an approach to automatically search parameters for optimum window and neighbourhood sizes, as well as to measure the decay in alignment over progressively increasing length scales.

Rarefied particle motions on hillslopes – Part 4: Philosophy

Abstract. Theoretical and experimental work (Furbish et al., 2021a, b, c) indicates that the travel distances of rarefied particle motions on rough hillslope surfaces are described by a generalized Pareto distribution. The form of this distribution varies with the balance between gravitational heating due to conversion of potential to kinetic energy and frictional cooling by particle–surface collisions. The generalized Pareto distribution in this problem is a maximum entropy distribution constrained by a fixed energetic “cost” – the total cumulative energy extracted by collisional friction per unit kinetic energy available during particle motions. The analyses leading to these results provide an ideal case study for highlighting three key elements of a statistical mechanics framework for describing sediment particle motions and transport: the merits of probabilistic versus deterministic descriptions of sediment motions, the implications of rarefied versus continuum transport conditions, and the consequences of increasing uncertainty in descriptions of sediment motions and transport that accompany increasing length scales and timescales. We use the analyses of particle energy extraction, the spatial evolution of particle energy states, and the maximum entropy method applied to the generalized Pareto distribution as examples to illustrate the mechanistic yet probabilistic nature of the approach. These examples highlight the idea that the endeavor is not simply about adopting theory or methods of statistical mechanics “off the shelf” but rather involves appealing to the style of thinking of statistical mechanics while tailoring the analysis to the process and scale of interest. Under rarefied conditions, descriptions of the particle flux and its divergence pertain to ensemble conditions involving a distribution of possible outcomes, each realization being compatible with the controlling factors. When these factors change over time, individual outcomes reflect a legacy of earlier conditions that depends on the rate of change in the controlling factors relative to the intermittency of particle motions. The implication is that landform configurations and associated particle fluxes reflect an inherent variability (“weather”) that is just as important as the expected (“climate”) conditions in characterizing system behavior.

Tip-induced mobilization upon cooling of Ni monolayers on Re(0001)

Usually, cooling a metal sample down to cryogenic temperatures leads to immobilization of the surface atoms. In this study, we demonstrate a movement of Ni adatoms at $4.6\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ on Ni films grown on a Re(0001) single crystal, while the surface is rigid at room temperature. The mobility is observed from 2 to 20 atomic-layer-thick films. Measurements at intermediate temperatures reveal an increasing mobility with decreasing temperature. The observed velocity of advancing steps is consistent with a model considering a sudden release of material, eventually triggered by the tip, followed by free diffusion. According to the model, an increasing length scale for the mobilization event with decreasing temperature, tentatively explained by epitaxial strain, is responsible for the inverse mobilization behavior.

Electrogravimetry and Structural Properties of Thin Silicon Layers Deposited in Sulfolane and Ionic Liquid Electrolytes.

Potentiostatic deposition of silicon is performed in sulfolane (SL) and ionic liquid (IL) electrolytes. Electrochemical quartz crystal microbalance with damping monitoring (EQCM-D) is used as main analytical tool for the characterization of the reduction process. The apparent molar mass (Mapp) is applied for in situ estimation of the layer contamination. By means of this approach, appropriate electrolyte composition and substrate type are selected to optimize the structural properties of the layers. The application of SL electrolyte results in silicon deposition with higher efficiency compared to the IL 1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide, [BMP][TFSI]. This has been associated with the instability of the IL in the presence of silicon tetrachloride and the enhanced incorporation of IL decomposition products into the growing silicon deposit. X-ray photoelectron spectroscopy (XPS) analysis supports the results about the layer composition, as suggested from the microgravimetric experiments. Attention has been given to the impact of practically relevant substrates (i.e., Cu, Ni, and vitreous carbon) on the reduction process. An effective deposition can be carried out on the metal electrodes in both electrolytes due to accelerated reaction kinetics for these types of substrates. However, on vitreous carbon (VC), a successful reduction of SiCl4 can only be accomplished in the IL, while the electroreduction process in SL is dominated by the decomposition of the electrolyte. For short deposition times, the scanning electron microscopy (SEM) images display rough morphologies in the nanometer range, which evolve further to structures with increased length scale of the surface roughness. The development of a rough interface during deposition, resulting in QCM damping at advanced stages of the process, is interpreted by a model accounting for the resistive force caused by the interaction of the liquid with a nonuniform layer interface. By using this approach, the individual contributions of the surface roughness and viscoelastic effects to the measured damping values are estimated.

Multiscale elastic anisotropy of a shale characterized by cross-scale big data nanoindentation

An experimental study is presented of the elastic anisotropy of a shale at different length scales probed by a cross-scale, big data-based, statistical nanoindentation technique. A large number (~1000) of indentation measurements with depths of up to ~8 μm were conducted under continuous stiffness measurement mode on each of three differently oriented (i.e., 0°, 45°, and 90° relative to the bedding plane) samples, yielding massive depth-dependent Young’s modulus datasets for different orientations. Segmentation at different depths of these continuous modulus-depth curves resulted in multiple sub-datasets that were statistically deconvoluted, leading to the extraction of Young’s moduli of mechanically distinct phases at each segmentation depth, which were then re-assembled against depth. Such modulus-depth curves, each pertaining to a specific phase, were further fitted by the surround effect model to determine the elastic moduli of individual minerals at the microscale and the bulk rock at the macroscale. Results show that the shale possesses multiscale elastic anisotropy: at the macroscale, the bulk rock’s horizontal Young’s modulus is 1.24 times greater than the vertical counterpart; at the microscale, the clay matrix is highly anisotropic, with anisotropy ratios of 1.36 and 1.96 at the 45° and 90° orientations referenced to the bedding plane, while the anhedral, coarse-grained minerals (i.e., quartz and feldspar) are only slightly anisotropic owing to their random orientation and equidimensional geometry, suggesting that the macroscale elastic anisotropy is mainly attributed to the highly anisotropic clay matrix that acts as a major load-bearing medium, but disturbed by isolated, randomly distributed silt and sand particles embedded as solid inclusions in the clay matrix. As such, the degree of anisotropy decreases with increasing length scale. The origin, formation, and evolution of such multiscale anisotropy are discussed in terms of the shale’s composition, depositional history, and post-depositional geological processes.

Slow dynamics of supercooled hydration water in contact with lysozyme: examining the cage effect at different length scales

ABSTRACT We study by computer simulation the dynamics of hydration water in solution with lysozyme upon approaching the glassy state of water. We calculate the self-density correlation function at different wavelengths to test the Mode Coupling Theory (MCT) of glassy dynamics at different length scales. The results show a strict and clear relation of the behaviour of the structural relaxation with the cage effect. We find a good agreement with the predictions of the MCT in the short and medium scale range, while at increasing length scales the interaction of water molecules with the protein's substrate induces deviations from the MCT behaviour, as found in previous studies. Besides at low temperatures the slow dynamics deviates from MCT due to hopping processes, similar to the bulk, as witnessed by a crossover from a fragile behaviour to a strong behaviour. We show that this deviation is evident at all length scales. Interestingly, we find that in the fragile region the confining cage decreases in radius with temperature while in the strong region it appears stable.

Buoyancy-driven dispersion in confined drying of liquid binary mixtures

We investigate the impact of buoyancy on the solute mass transport in an evaporating liquid mixture (non-volatile solute $+$ solvent) confined in a slit perpendicular to the gravity. Solvent evaporation at one end of the slit induces a solute concentration gradient which in turn drives free convection due to the difference between the densities of the solutes and the solvent. From the complete model coupling mass transport and hydrodynamics, we first use a standard Taylor-like approach to derive a one dimensional non-linear advection-dispersion equation describing the solute concentration process for a dilute mixture. We then perform a complete analysis of the expected regimes using both scaling analysis and asymptotic solutions of this equation. The validity of this approach is confirmed using a thorough comparison with the numerical resolution of both the complete model and the 1D advection-dispersion equation. Our results show that buoyancy-driven free convection always impacts solute mass transport at long time scales, dispersing solutes in a steadily increasing length scale along the slit. Beyond this confined drying configuration, our work also provides an easy way for evaluating the relevance of buoyancy on mass transport in any other microfluidic configuration involving concentration gradients.