Diffusive Transport Properties Research Articles

Diffusive and convective transport properties and pore-network characteristics of recycled, compacted concrete aggregates for use as road pavement materials

Gas transport parameters, such as gas diffusivity (Dp/D0) and air permeability (ka) of materials, and pore-network properties play important roles in the movement of gases and water vapor in road pavement layers and contribute to assessment of the urban heat island effect in urban areas. This study carried out a series of laboratory tests to measure the Dp/D0 and ka of recycled concrete aggregates (RCA) used for road base and subbase materials at variable fines contents and moisture conditions. The results revealed bimodal patterns in both water retention and the derived pore-size distribution curves for tested RCA samples. Both fines and initial moisture contents under compaction affected the characteristics of pore networks and structures, such as the effective pore space and water blockage effects that control the gas transport parameters of porous media in RCA samples. Especially, the increase of fines significantly reduced the pore-network parameters. The structure-dependent water-induced linear reduction (SWLR) model functioned well to predict the Dp/D0 of RCA samples when the air-filled porosity was less than 0.175 cm3 cm−3. The most likely windows for ka of RCA samples were predicted by equations developed from the SWLR model.

Diffusion coefficients and MSD measurements on curved membranes and porous media.

We study some geometric aspects that influence the transport properties of particles that diffuse on curved surfaces. We compare different approaches to surface diffusion based on the Laplace-Beltrami operator adapted to predict concentration along entire membranes, confined subdomains along surfaces, or within porous media. Our goal is to summarize, firstly, how diffusion in these systems results in different types of diffusion coefficients and mean square displacement measurements, and secondly, how these two factors are affected by the concavity of the surface, the shape of the possible barriers or obstacles that form the available domains, the sinuosity, tortuosity, and constrictions of the trajectories and even how the observation plane affects the measurements of the diffusion. In addition to presenting a critical and organized comparison between different notions of MSD, in this review, we test the correspondence between theoretical predictions and numerical simulations by performing finite element simulations and illustrate some situations where diffusion theory can be applied. We briefly reviewed computational schemes for understanding surface diffusion and finally, discussed how this work contributes to understanding the role of surface diffusion transport properties in porous media and their relationship to other transport processes.

Systematic Workflow for Efficient Identification of Local Representative Elementary Volumes Demonstrated with Lithium-Ion Battery Cathode Microstructures

The concept of a representative elementary volume (REV) is key for connecting results of pore-scale simulations with continuum properties of microstructures. Current approaches define REVs only based on their size as the smallest volume in a heterogeneous material independent of its location and under certain aspects representing the same material at the continuum scale. However, the determination of such REVs is computationally expensive and time-consuming, as many costly simulations are often needed. Therefore, presented here is an efficient, systematic, and predictive workflow for the identification of REVs. The main differences from former studies are: (1) An REV is reinterpreted as one specificsub-volume of minimal size at a certain location that reproduces the relevant continuum properties of the full microstructure. It is therefore called a local REV (lREV) here. (2) Besides comparably cheap geometrical and statistical analyses, no further simulations are needed. The minimum size of the sub-volume is estimated using the simple statistical properties of the full microstructure. Then, the location of the REV is identified solely by evaluating the structural properties of all possible candidates in a very fast, efficient, and systematic manner using a penalty function. The feasibility and correct functioning of the workflow were successfully tested and validated by simulating diffusive transport, advection, and electrochemical properties for an lREV. It is shown that the lREVs identified using this workflow can be significantly smaller than typical REVs. This can lead to significant speed-ups for any pore-scale simulations. The workflow can be applied to any type of heterogeneous material, even though it is showcased here using a lithium-ion battery cathode.

Dehydration‐driven mass loss from packs of sintering hydrous silicate glass particles

AbstractGlass sintering involves the densification of packs of particles and the expulsion of the interparticle pore gas. The pore space begins as a convolute interconnected interparticle network, and ends as distributed isolated bubbles; two configurations that are separated by the percolation threshold. Here, we perform experiments in which (i) the particles are initially saturated in H2O at 871 K, and (ii) they are then heated non‐isothermally at different rates to temperatures in excess of 871 K. In step (ii), H2O becomes supersaturated and the particles diffusively lose mass as they sinter together. We use thermogravimetry to track the loss of mass with time. We find that the mass loss is initially well predicted by solutions to Fick's second law in spherical coordinates with the appropriate material and boundary conditions. However, as the sintering pack crosses the percolation threshold at a time predicted by sintering theory, we find that the mass loss deviates from simple diffusional solutions. We interpret this to be the result of an increase in the diffusion distance from the particle‐scale to the scale of the sintering pack itself. Therefore, we conclude that the open‐ to closed‐system transition that occurs at the percolation threshold is a continuous, but rapid jump for diffusive and other transport properties. We use a capillary Peclet number Pc to parameterize for this transition, such that at low Pc diffusive equilibrium is achieved before the sintering‐induced transition to closed system, whereas at high Pcthere is a “diffusion crisis” and disequilibrium may be maintained for longer relative timescales that depend on the system size.

A kidney proximal tubule model to evaluate effects of basement membrane stiffening on renal tubular epithelial cells.

The kidney tubule consists of a single layer of epithelial cells supported by the tubular basement membrane (TBM), a thin layer of specialized extracellular matrix (ECM). The mechanical properties of the ECM are important for regulating a wide range of cell functions including proliferation, differentiation and cell survival. Increased ECM stiffness plays a role in promoting multiple pathological conditions including cancer, fibrosis and heart disease. How changes in TBM mechanics regulate tubular epithelial cell behavior is not fully understood. Here we introduce a cell culture system that utilizes in vivo-derived TBM to investigate cell-matrix interactions in kidney proximal tubule cells. Basement membrane mechanics was controlled using genipin, a biocompatibility crosslinker. Genipin modification resulted in a dose-dependent increase in matrix stiffness. Crosslinking had a marginal but statistically significant impact on the diffusive molecular transport properties of the TBM, likely due to a reduction in pore size. Both native and genipin-modified TBM substrates supported tubular epithelial cell growth. Cells were able to attach and proliferate to form confluent monolayers. Tubular epithelial cells polarized and assembled organized cell-cell junctions. Genipin modification had minimal impact on cell viability and proliferation. Genipin stiffened TBM increased gene expression of pro-fibrotic cytokines and altered gene expression for N-cadherin, a proximal tubular epithelial specific cell-cell junction marker. This work introduces a new cell culture model for cell-basement membrane mechanobiology studies that utilizes in vivo-derived basement membrane. We also demonstrate that TBM stiffening affects tubular epithelial cell function through altered gene expression of cell-specific differentiation markers and induced increased expression of pro-fibrotic growth factors.

Flame Anchoring of an H2/O2 Non-Premixed Flamewith O2 Transcritical Injection

The article is devoted to the analysis of the flame anchoring mechanism in the test case MASCOTTE C-60 RCM2 on supercritical hydrogen/oxygen combustion at 60 bar, with transcritical (liquid) injection of oxygen. The case is simulated by means of the in-house parallel code HeaRT in the three-dimensional LES framework. The cubic Peng–Robinson equation of state in its improved translated volume formulation is assumed. Diffusive mechanisms and transport properties are accurately modeled. A finite-rate detailed scheme involving the main radicals, already validated for high-pressure H2/O2 combustion, is adopted. The flow is analysed in terms of temperature, hydrogen and oxygen instantaneous spatial distributions, evidencing the effects of the vortex shedding from the edges of the hydrogen injector and of the separation of the oxygen stream in the divergent section of its tapered injector on the flame anchoring and topology. Combustion conditions are characterised by looking at the equivalence ratio and compressibility factor distributions.

An Alternative Methodology to Compute the Geometric Tortuosity in 2D Porous Media Using the A-Star Pathfinding Algorithm

Geometric tortuosity is an essential characteristic to consider when studying a porous medium’s morphology. Knowing the material’s tortuosity allows us to understand and estimate the different diffusion transport properties of the analyzed material. Geometric tortuosity is useful to compute parameters, such as the effective diffusion coefficient, inertial factor, and diffusibility, which are commonly found in porous media materials. This study proposes an alternative method to estimate the geometric tortuosity of digitally created two-dimensional porous media. The porous microstructure is generated by using the PoreSpy library of Python and converted to a binary matrix for the computation of the parameters involved in this work. As a first step, porous media are digitally generated with porosity values from 0.5 to 0.9; then, the geometric tortuosity is determined using the A-star algorithm. This approach, commonly used in pathfinding problems, improves the use of computational resources and complies with the theory found in the literature. Based on the obtained results, the best geometric tortuosity–porosity correlations are proposed. The selection of the best correlation considers the coefficient of determination value (99.7%) with a confidence interval of 95%.

Anomalous diffusion in single and coupled standard maps with extensive chaotic phase spaces

We investigate the long-term diffusion transport and chaos properties of single and coupled standard maps. We consider model parameters that are known to induce anomalous diffusion in the maps’ phase spaces, as opposed to normal diffusion which is associated with Gaussian distribution properties of the kinematic variables. This type of transport originates in the presence of the so-called accelerator modes, i.e. non-chaotic initial conditions which exhibit ballistic transport, which also affect the dynamics in their vicinity. We first systematically study the dynamics of single standard maps, investigating the impact of different ensembles of initial conditions on their behavior and asymptotic diffusion rates, as well as on the respective time-scales needed to acquire these rates. We consider sets of initial conditions in chaotic regions enclosing accelerator modes, which are not bounded by invariant tori. These types of chaotic initial conditions typically lead to normal diffusion transport. We then setup different arrangements of coupled standard maps and investigate their global diffusion properties and chaotic dynamics. Although individual maps bear accelerator modes causing anomalous transport, the global diffusion behavior of the coupled system turns out to depend on the specific configuration of the imposed coupling. Estimating the average diffusion properties for ensembles of initial conditions, as well as measuring the strength of chaos through computations of appropriate indicators, we find conditions and systems’ arrangements which systematically favor the suppression of anomalous transport and long-term convergence to normal diffusion rates.

Determining Local Transport Properties in Gas Diffusion Layers Using Pore Network Modelling

Understanding the relationship between local liquid water distribution in gas diffusion layers (GDLs) and transport properties in polymer electrolyte fuel cells can lead to improved GDL and flow-field channel configurations for improved performance. Modelling studies have shown that transport properties can spatially vary in the through-plane direction and under different regions of the flow-field [1], [2]. Further modelling studies may unveil unique insights on spatially varying properties of the GDL at different operating conditions.In this study, x-ray synchrotron imaging was used in conjunction with pore network modelling to reveal transport properties local to the GDL in the land and channel regions. First, liquid water distribution within the GDL was obtained using in operando x-ray synchrotron imaging. Micro computed tomography images of the GDL were obtained and used to generate representative pore network models of the materials. Pore network models were partially invaded from stochastically selected inlet pores using invasion percolation to match the average experimental saturation of land, channel, and overall regions. Next, we performed transport simulations on the partially saturated pore networks to determine the diffusivity, permeability, and oxygen transport resistance of each GDL region. Oxygen transport resistance values determined from the simulations were compared to experimental values obtained via limiting current experiments to isolate the contribution of the GDL to transport resistance at limiting current.The methodology presented in this work can be used to evaluate transport properties of various GDL designs. The local transport properties obtained in this work will be incorporated into computational fluids dynamics modelling to improve simulation accuracy.[1] P. A. García-Salaberri, J. T. Gostick, G. Hwang, A. Z. Weber, and M. Vera, “Effective diffusivity in partially-saturated carbon-fiber gas diffusion layers: Effect of local saturation and application to macroscopic continuum models,” Journal of Power Sources, vol. 296, pp. 440–453, 2015, doi: 10.1016/j.jpowsour.2015.07.034.[2] N. Ge et al., “Resolving the gas diffusion layer substrate land and channel region contributions to the oxygen transport resistance of a partially-saturated substrate,” Electrochimica Acta, p. 135001, 2019, doi: 10.1016/j.electacta.2019.135001.

Understanding degeneracy of two-point correlation functions via Debye random media.

It is well known that the degeneracy of two-phase microstructures with the same volume fraction and two-point correlation function S_{2}(r) is generally infinite. To elucidate the degeneracy problem explicitly, we examine Debye random media, which are entirely defined by a purely exponentially decaying two-point correlation function S_{2}(r). In this work, we consider three different classes of Debye random media. First, we generate the "most probable" class using the Yeong-Torquato construction algorithm [Yeong and Torquato, Phys. Rev. E 57, 495 (1998)1063-651X10.1103/PhysRevE.57.495]. A second class of Debye random media is obtained by demonstrating that the corresponding two-point correlation functions are effectively realized in the first three space dimensions by certain models of overlapping, polydisperse spheres. A third class is obtained by using the Yeong-Torquato algorithm to construct Debye random media that are constrained to have an unusual prescribed pore-size probability density function. We structurally discriminate these three classes of Debye random media from one another by ascertaining their other statistical descriptors, including the pore-size, surface correlation, chord-length probability density, and lineal-path functions. We also compare and contrast the percolation thresholds as well as the diffusion and fluid transport properties of these degenerate Debye random media. We find that these three classes of Debye random media are generally distinguished by the aforementioned descriptors, and their microstructures are also visually distinct from one another. Our work further confirms the well-known fact that scattering information is insufficient to determine the effective physical properties of two-phase media. Additionally, our findings demonstrate the importance of the other two-point descriptors considered here in the design of materials with a spectrum of physical properties.

Mobility of selenium oxyanions in clay-rich media: A combined batch and diffusion experiments and synchrotron-based spectroscopic investigation

Selenium-79 is considered as a critical radionuclide in safety assessment of high-level radioactive waste deep geological repository in clay-rich formations, owing to its long half-life and its anionic form in three relevant oxidation states (VI, IV,-II). An in-depth understanding of the diffusive transport properties of Se is therefore essential, especially due to its high sensitivity to oxido-reduction conditions. Here, the mobility of selenite and selenate in claystone samples (Callovo-Oxfordian, East of Paris Basin, France) under anoxic conditions is assessed by combining batch and diffusion experiments, and synchrotron-based spectroscopic mapping of diffusion fronts.Results showed that selenite and selenate behaved distinctly. Selenate diffused similarly to the reference anionic tracer, 36Cl−, without significant sorption or reduction. Selenite showed a sorption behaviour that increased with the decrease of the initial concentration from 10−3 to 10−6 mol L−1, values of distribution ratio (Rd) from batch experiments ranging from 10 to about 250 mL g−1. Selenite in-diffusion experiments showed that a pure diffusion model with reversible sorption was able to roughly reproduce the evolution of dissolved selenite in solution over time. However, additional reactions were required to properly describe the irregular shape of the selenite diffusion profiles in the solid. Mapping of Se oxidation state in diffusion fronts within the claystone coupons showed the presence of reduced Se (Se (0), Se(-I) and/or Se(-II)) along a fringe located at about 2 mm beneath the surface, possibly explaining the irregular shape of diffusion profiles. In the superficial zone (0–2 mm), oxidizing perturbations are assumed to account for the preservation of selenite under this oxidation state. These perturbations would also bias batch results in the same manner. Deeper in the claystone sample, diffusing selenite was observed, with a content steadily decreasing up to 7 mm from the inlet. The results suggest that, even after more than 500 days of diffusion, Se reduction would occur progressively along the diffusion pathways.

Transport Properties and Physiological Activity of Arabinogalactan Complexes with Certain Nitrogen-Containing Compounds

The diffusion-transport properties of complexes based on arabinogalactan and its oxidized forms with nitrogen-containing compounds, 5-aminosalicylic acid, 4-aminosalicylic acid, and isonicotinic acid hydrazide, are studied under conditions simulating biological media. The complexation of polysaccharides and oligosaccharides with drugs leads to the creation of prolonged dosage forms. The dynamics of drug release from the complexes is influenced by the nature of the polysaccharide matrix and its molecular weight. The complexes based on the initial arabinogalactan have the greatest prolonging effect.

Transport of a Single Cold Ion Immersed in a Bose-Einstein Condensate.

We investigate transport dynamics of a single low-energy ionic impurity in a Bose-Einstein condensate. The impurity is implanted into the condensate starting from a single Rydberg excitation, which is ionized by a sequence of fast electric field pulses aiming to minimize the ion's initial kinetic energy. Using a small electric bias field, we study the subsequent collisional dynamics of the impurity subject to an external force. The fast ion-atom collision rate, stemming from the dense degenerate host gas and the large ion-atom scattering cross section, allow us to study a regime of frequent collisions of the impurity within only tens of microseconds. Comparison of our measurements with stochastic trajectory simulations based on sequential Langevin collisions indicate diffusive transport properties of the impurity and allows us to measure its mobility. Our results open a novel path to study dynamics of charged quantum impurities in ultracold matter.

A Fractional Drift Diffusion Model for Organic Semiconductor Devices

Because charge carriers of many organic semiconductors (OSCs) exhibit fractional drift diffusion (Fr-DD) transport properties, the need to develop a Fr-DD model solver becomes more apparent. However, the current research on solving the governing equations of the Fr-DD model is practically nonexistent. In this paper, an iterative solver with high precision is developed to solve both the transient and steady-state Fr-DD model for organic semiconductor devices. The Fr-DD model is composed of two fractional-order carriers (i.e., electrons and holes) continuity equations coupled with Poisson’s equation. By treating the current density as constants within each pair of consecutive grid nodes, a linear Caputo’s fractional-order ordinary differential equation (FrODE) can be produced, and its analytic solution gives an approximation to the carrier concentration. The convergence of the solver is guaranteed by implementing a successive over-relaxation (SOR) mechanism on each loop of Gummel’s iteration. Based on our derivations, it can be shown that the Scharfetter–Gummel discretization method is essentially a special case of our scheme. In addition, the consistency and convergence of the two core algorithms are proved, with three numerical examples designed to demonstrate the accuracy and computational performance of this solver. Finally, we validate the Fr-DD model for a steady-state organic field effect transistor (OFET) by fitting the simulated transconductance and output curves to the experimental data.

BN-codoped CNT based nanoporous brushes for all-solid-state flexible supercapacitors at elevated temperatures

Porous graphitic carbon based nanostructured electrodes offer several advantages for energy storage applications, such as, high specific surface area, high active charge storage sites, suitable ion diffusion and excellent charge transport properties. Vertically aligned carbon nanotubes (CNTs) have widely been exploited for electrochemical energy storage in different architectures using various electrolytes. However, a 3D carbon based electrode with high mechanical flexibility, reliability along with high charge storage capacity with solid-state electrolyte have yet to be realized. Here we develop a simple spray pyrolysis process for synthesizing nanoporous brush-like CNTs grown radially on individual carbon fibers of a carbon cloth (CC) substrate and simultaneously codoping with boron (B) and nitrogen (N) heteroatoms. The obtained BNCNT-CC electrodes were utilized to fabricate highly flexible all solid state symmetrical supercapacitor cells. The cells demonstrated high aerial capacitance of 106.8 mF/cm2 (~21.4 F/cm3), excellent flexibility without any performance degradation, attractive capacitance retention (86.4%) even after 5000 charge/discharge cycles, stability above room temperature, 741.8 mWh/cm3 specific energy at 25 W/cm3 specific power and conservation of 56% of its initial energy at specific power of 1 kW/cm3. The results are distinctly better than previous reports as a whole in terms of different performance parameters and are attributed to the unique nanoporous structure, low combined series resistance, BN-codoping and diffusion controlled modulation in electrochemical energy storage characteristics.

Dynamic disorder phonon scattering mediated by Cu atomic hopping and diffusion in Cu3SbSe3

Cu3SbSe3 that exhibits distinct liquid-like sublattice due to the heterogeneous bonding environment has emerged as a promising low cost superionic semiconductor with intrinsic ultralow thermal conductivity. However, the relationship between atomic dynamics resulting in liquid-like diffusion and anomalous phonon transport properties remains poorly understood. Herein, combing ab initio molecular dynamics with temperature-dependent Raman measurements, we have performed a thorough investigation on the lattice dynamics of Cu3SbSe3. Superionic transition is unveiled for both structurally inequivalent Cu atoms at elevated temperatures, while the Se-formed tetrahedral framework can simultaneously maintain. An intermediate state of Cu3SbSe3 through the mixture of quasi-1D/2D Cu nearest-neighbor vacancy hopping is discovered below the superionic transition temperature. Our results also manifest that phonons predominately involved with Cu contributions along diffusion channels have been strongly scattered during the superionic transition, whereas the liquid-like diffusion of Cu is too slow to completely breakdown the propagation of all transverse phonon modes. The insight provided by this work into the atomic dynamics and phonon scattering relationship may pave the way for further phonon engineering of Cu3SbSe3 and related superionic materials.

Diffusion in heterogeneous discs and spheres: New closed-form expressions for exit times and homogenization formulas.

Mathematical models of diffusive transport underpin our understanding of chemical, biochemical, and biological transport phenomena. Analysis of such models often focuses on relatively simple geometries and deals with diffusion through highly idealized homogeneous media. In contrast, practical applications of diffusive transport theory inevitably involve dealing with more complicated geometries as well as dealing with heterogeneous media. One of the most fundamental properties of diffusive transport is the concept of mean particle lifetime or mean exit time, which are particular applications of the concept of first passage time and provide the mean time required for a diffusing particle to reach an absorbing boundary. Most formal analysis of mean particle lifetime applies to relatively simple geometries, often with homogeneous (spatially invariant) material properties. In this work, we present a general framework that provides exact mathematical insight into the mean particle lifetime, and higher moments of particle lifetime, for point particles diffusing in heterogeneous discs and spheres with radial symmetry. Our analysis applies to geometries with an arbitrary number and arrangement of distinct layers, where transport in each layer is characterized by a distinct diffusivity. We obtain exact closed-form expressions for the mean particle lifetime for a diffusing particle released at an arbitrary location, and we generalize these results to give exact, closed-form expressions for any higher-order moment of particle lifetime for a range of different boundary conditions. Finally, using these results, we construct new homogenization formulas that provide an accurate simplified description of diffusion through heterogeneous discs and spheres.

Transient diffusion and two-regime localization of discrete breatherlike excitations in nonlinear Schrödinger lattice with disorder.

We systematically simulate and analyze the motion of discrete breatherlike excitations (DBEs) in the nonlinear Schrödinger lattice with random potentials. A universal transient diffusion of the DBEs is observed for short timescales (t≲10^{3}). For longer timescales (t up to 10^{5}), the DBEs become localized. Such localization, depending on the DBE powers, has two different regimes: Regime I is the Anderson-like localization induced by the disorder, while Regime II is an enhanced localization attributed to both the disorder and discreteness. Our study is expected to shed light on understanding the interplay between disorder and strong nonlinearity, from the diffusive transport and localization properties of nonlinear localized excitations in random media.

Continuous-time random-walk model for anomalous diffusion in expanding media

Expanding media are typical in many different fields, e.g., in biology and cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties such as the set of positional moments and the Green's function. Here, we focus on the characterization of such effects when the diffusion process is described by the continuous-time random-walk (CTRW) model. As is well known, when the medium is static this model yields anomalous diffusion for a proper choice of the probability density function (pdf) for the jump length and the waiting time, but the behavior may change drastically if a medium expansion is superimposed on the intrinsic random motion of the diffusing particle. For the case where the jump length and the waiting time pdfs are long-tailed, we derive a general bifractional diffusion equation which reduces to a normal diffusion equation in the appropriate limit. We then study some particular cases of interest, including Lévy flights and subdiffusive CTRWs. In the former case, we find an analytical exact solution for the Green's function (propagator). When the expansion is sufficiently fast, the contribution of the diffusive transport becomes irrelevant at long times and the propagator tends to a stationary profile in the comoving reference frame. In contrast, for a contracting medium a competition between the spreading effect of diffusion and the concentrating effect of contraction arises. In the specific case of a subdiffusive CTRW in an exponentially contracting medium, the latter effect prevails for sufficiently long times, and all the particles are eventually localized at a single point in physical space. This "big crunch" effect, totally absent in the case of normal diffusion, stems from inefficient particle spreading due to subdiffusion. We also derive a hierarchy of differential equations for the moments of the transport process described by the subdiffusive CTRW model in an expanding medium. From this hierarchy, the full time evolution of the second-order moment is obtained for some specific types of expansion. In the case of an exponential expansion, exact recurrence relations for the Laplace-transformed moments are obtained, whence the long-time behavior of moments of arbitrary order is subsequently inferred. Our analytical and numerical results for both Lévy flights and subdiffusive CTRWs confirm the intuitive expectation that the medium expansion hinders the mixing of diffusive particles occupying separate regions. In the case of Lévy flights, we quantify this effect by means of the so-called "Lévy horizon."

Spatially Different Tissue-Scale Diffusivity Shapes ANGUSTIFOLIA3 Gradient in Growing Leaves

The spatial gradient of signaling molecules is pivotal for establishing developmental patterns of multicellular organisms. It has long been proposed that these gradients could arise from the pure diffusion process of signaling molecules between cells, but whether this simplest mechanism establishes the formation of the tissue-scale gradient remains unclear. Plasmodesmata are unique channel structures in plants that connect neighboring cells for molecular transport. In this study, we measured cellular- and tissue-scale kinetics of molecular transport through plasmodesmata in Arabidopsis thaliana developing leaf primordia by fluorescence recovery assays. These trans-scale measurements revealed biophysical properties of diffusive molecular transport through plasmodesmata and revealed that the tissue-scale diffusivity, but not the cellular-scale diffusivity, is spatially different along the leaf proximal-to-distal axis. We found that the gradient in cell size along the developmental axis underlies this spatially different tissue-scale diffusivity. We then asked how this diffusion-based framework functions in establishing a signaling gradient of endogenous molecules. ANGUSTIFOLIA3 (AN3) is a transcriptional co-activator, and as we have shown here, it forms a long-range signaling gradient along the leaf proximal-to-distal axis to determine a cell-proliferation domain. By genetically engineering AN3 mobility, we assessed each contribution of cell-to-cell movement and tissue growth to the distribution of the AN3 gradient. We constructed a diffusion-based theoretical model using these quantitative data to analyze the AN3 gradient formation and demonstrated that it could be achieved solely by the diffusive molecular transport in a growing tissue. Our results indicate that the spatially different tissue-scale diffusivity is a core mechanism for AN3 gradient formation. This provides evidence that the pure diffusion process establishes the formation of the long-range signaling gradient in leaf development.