Free Diffusion Coefficient Research Articles

Diffusion Studies of Glucose and Sucrose in Chitosan Membranes and Beads for Enzymatic Production Processes

AbstractThe diffusion of glucose and sucrose was investigated in membrane and bead experiments. Concentration‐dependent diffusion coefficients of pure glucose and sucrose were determined in precipitated chitosan membranes of varying thickness using diffusion cell experiments. Contrary to fructose, the resulting diffusion coefficients of glucose and sucrose did not reach their free diffusion coefficients at infinite dilution suggesting additional interactions between chitosan and these two sugars. Counter‐diffusion in bead experiments showed a good agreement between predicted and measured data allowing the inclusion of the diffusion data in the simulation of the proposed production process for laminaribiose. In conclusion, the encapsulation in chitosan presented a good trade‐off between increased mass transfer resistance as evaluated by the Thiele modulus and improved thermal stability and antibacterial activity.

Multi-scale modeling of isobutane alkylation with 2-butene using composite ionic liquids as catalyst

The alkylation kinetics of isobutane with 2-butene catalyzed by composite ionic liquid (CIL) was investigated with batch experiments. The optimized reaction time of CIL-catalyzed alkylation was found to be less than 30 s, much shorter than the traditional H2SO4-catalyzed one. Based on the carbonium ion mechanism, the kinetic model was further established, in which the concentration profiles of three groups of key components in alkylates with time can be well predicted, i.e. trimethylpentane (TMPs), dimethylhexanes (DMHs) and heavy ends (HEs). The rate constant related to the formation of TMPs in the CIL alkylation is more than two orders of magnitude larger than that in the H2SO4 alkylation. The enhancement of the rate constants for the CIL alkylation at the macroscopic scale can be ascribed into the higher solvation and diffusion of isobutane in the CIL at the microscopic scale, which is confirmed by the solvation free energy and diffusion coefficient calculation using molecular dynamics simulation. Hopefully, the multi-scale information in this work can bring novel insights into the understanding of CIL-catalyzed alkylation and further the design and optimization of this process.

Diffusion of cytokines in live lymph node tissue using microfluidic integrated optical imaging

Communication and drug efficacy in the immune system rely heavily on diffusion of proteins such as cytokines through the tissue matrix. Available methods to analyze diffusion in tissue require microinjection or saturating the tissue in protein, which may alter local transport properties due to damage or rapid cellular responses. Here, we developed a novel, user-friendly method – Microfluidic Integrated Optical Imaging (micro-IOI) – to quantify the effective diffusion coefficient of bioactive proteins in live tissue samples ex vivo. A microfluidic platform was used to deliver picograms of fluorescently labelled cytokines to microscale regions within slices of murine lymph node, and diffusion was monitored by widefield fluorescence microscopy. Micro-IOI was validated against theory and existing methods. Free diffusion coefficients were within 8% and 24% of Stokes-Einstein predictions for dextrans and cytokines, respectively. Furthermore, diffusion coefficients for dextrans and proteins in a model matrix were within 1.5-fold of reported results from fluorescence recovery after photobleaching (FRAP). We used micro-IOI to quantify the effective diffusion of three cytokines from different structural classes and two different expression systems – tumor necrosis factor alpha (TNF-α), interferon gamma (IFN-γ), and interleukin-2 (IL-2), from human and mouse – through live lymph node tissue. This is the first method to directly measure cytokine transport in live tissue slices, and in the future, it should promote a deeper understanding of the dynamics of cell-cell communication and enable targeted immunotherapy design.

Methane diffusion in shales with multiple pore sizes at supercritical conditions

Methane diffusion is a very important gas-transport mechanism in shales. Meanwhile, one of the biggest differences between shale gas reservoirs and conventional gas reservoirs is a multiscale pore structure in the former. Two kinds of methane diffusion experiments are conducted in this work to measure methane diffusion coefficients in shale cores at supercritical conditions. Experimental results show that (1) a free molecular diffusion coefficient is averaged to be 1.214 × 10−10 m2/s at reservoir conditions from the isobaric diffusion experiments; (2) however, the Knudsen diffusion, surface diffusion and configurational diffusion coefficients in the pressure decay experiments are more significant for shale gas development. It is presented that Knudsen diffusion and surface diffusion appear simultaneously as gas transports in matrix nanopores, the mean diffusion coefficients of which are 4.99 × 10−14 m2/s for pores of a diameter smaller than 4 nm and 9.03 × 10−9 m2/s for pores of a diameter bigger than 4 nm. The mean configurational diffusion coefficient for dissolved gas is calculated as 2.06 × 10−22 m2/s. In addition, the four types of diffusion coefficients mentioned above are also theoretically calculated through their corresponding models to compare with the experimental results. Due to the measured methane diffusion coefficients corresponding to a wide range of pore sizes, a relationship between gas diffusion and pore size is obtained by the combination of theoretical and experimental results, and this can guide to further analyze the comprehensive diffusion behavior in shale gas development, as well as the relative contribution of each diffusion during different production stages. This work sheds light on the gas diffusion behavior over multiple pore sizes, which is beneficial for further quantitatively understanding shale gas transport in matrix during production.

Concentration‐Dependent Diffusion Coefficients for Fructose in Highly Permeable Chitosan Polymers

AbstractThe concentration‐dependent diffusion coefficient of fructose in precipitated chitosan membranes was determined using diffusion cells. Experiments showed that boundary layers on both sides of the membrane could not be neglected when the diffusion coefficient in chitosan is close to the free diffusion coefficient. Hence, the influence of the boundary layers was covered by measuring membranes with different thickness. The diffusion coefficient in chitosan at infinite dilution was found to be around the free diffusion coefficient. With increasing concentration, the diffusion coefficient in chitosan decreases faster than the free diffusion coefficient. Thus, the product of diffusion coefficient and concentration difference shows a maximum implying an optimum concentration for mass transfer.

Lattice Boltzmann simulations of diffusion through native and steam-exploded softwood bordered pits

Bordered pits connect adjacent tracheid cells in softwoods and enable water transport between them. Knowledge of how large molecules, such as polysaccharides and enzymes, are transported through pits is important to understand the extraction process of valuable biopolymers from wood. The main mass transport mechanism for large dissolved molecules in wood is diffusion, and this is investigated through mathematical modeling in the lattice Boltzmann framework utilizing SEM images and 3D reconstruction of an actual bordered pit to compute an effective diffusion coefficient. Confocal laser scanning microscopy is used to find the unobstructed diffusion coefficients in a free aqueous solution using fluorescent diffusion probes of dextran. The effect of steam explosion on pit structure is explored through the use of a simplified model. The importance of different components of a bordered pit is investigated using simulation data, and results show that the most important structural features are the borders. Expressions for the effective diffusion coefficient as a function of the free diffusion coefficient are presented for a native and for a steam-exploded pit, respectively.

Fluorescence correlation spectroscopy experiments to quantify free diffusion coefficients in reaction-diffusion systems: The case of Ca^{2+} and its dyes.

Many cell signaling pathways involve the diffusion of messengers that bind and unbind to and from intracellular components. Quantifying their net transport rate under different conditions then requires having separate estimates of their free diffusion coefficient and binding or unbinding rates. In this paper, we show how performing sets of fluorescence correlation spectroscopy (FCS) experiments under different conditions, it is possible to quantify free diffusion coefficients and on and off rates of reaction-diffusion systems. We develop the theory and present a practical implementation for the case of the universal second messenger, calcium (Ca^{2+}) and single-wavelength dyes that increase their fluorescence upon Ca^{2+} binding. We validate the approach with experiments performed in aqueous solutions containing Ca^{2+} and Fluo4 dextran (both in its high and low affinity versions). Performing FCS experiments with tetramethylrhodamine-dextran in Xenopus laevis oocytes, we infer the corresponding free diffusion coefficients in the cytosol of these cells. Our approach can be extended to other physiologically relevant reaction-diffusion systems to quantify biophysical parameters that determine the dynamics of various variables of interest.

Investigation of hydrogen isotopes interaction with lithium CPS under reactor irradiation

This work describes the experimental results of a study of tritium generation and release from the lithium capillary porous system (CPS) under neutron irradiation. The experiments were performed at the IVG1.M research reactor (Kurchatov, Kazakhstan) at a power level of 6MW and temperatures from 325 to 840°С. The studies were performed using two modes: with constant pumping out of the experimental ampoule device (differential mode) and with tritium accumulation in ampoule device (AD) with absence of the pumping out (integrated mode). The diffusion coefficients of free tritium atoms in liquid lithium under neutron irradiation were obtained. The Arrhenius dependence of free tritium atoms diffusion coefficient in lithium was derived as D=0.17·exp(−145/RT).

Validation of surface-to-volume ratio measurements derived from oscillating gradient spin echo on a clinical scanner using anisotropic fiber phantoms.

A diffusion measurement in the short-time surface-to-volume ratio (S/V) limit (Mitra et al., Phys Rev Lett. 1992;68:3555) can disentangle the free diffusion coefficient from geometric restrictions to diffusion. Biophysical parameters, such as the S/V of tissue membranes, can be used to estimate microscopic length scales non-invasively. However, due to gradient strength limitations on clinical MRI scanners, pulsed gradient spin echo (PGSE) measurements are impractical for probing the S/V limit. To achieve this limit on clinical systems, an oscillating gradient spin echo (OGSE) sequence was developed. Two phantoms containing 10 fiber bundles, each consisting of impermeable aligned fibers with different packing densities, were constructed to achieve a range of S/V values. The frequency-dependent diffusion coefficient, D(ω), was measured in each fiber bundle using OGSE with different gradient waveforms (cosine, stretched cosine, and trapezoidal), while D(t) was measured from PGSE and stimulated-echo measurements. The S/V values derived from the universal high-frequency behavior of D(ω) were compared against those derived from quantitative proton density measurements using single spin echo (SE) with varying echo times, and from magnetic resonance fingerprinting (MRF). S/V estimates derived from different OGSE waveforms were similar and demonstrated excellent correlation with both SE- and MRF-derived S/V measures (ρ ≥ 0.99). Furthermore, there was a smoother transition between OGSE frequency f and PGSE diffusion time when using teffS/V=9/64f, rather than the commonly used teff = 1/(4f), validating the specific frequency/diffusion time conversion for this regime. Our well-characterized fiber phantom can be used for the calibration of OGSE and diffusion modeling techniques, as the S/V ratio can be measured independently using other MR modalities. Moreover, our calibration experiment offers an exciting perspective of mapping tissue S/V on clinical systems.

FCS experiments to quantify Ca2+ diffusion and its interaction with buffers.

Ca2+ signals are ubiquitous. One of the key factors for their versatility is the variety of spatio-temporal distributions that the cytosolic Ca2+ can display. In most cell types Ca2+ signals not only depend on Ca2+ entry from the extracellular medium but also on Ca2+ release from internal stores, a process which is in turn regulated by cytosolic Ca2+ itself. The rate at which Ca2+ is transported, the fraction that is trapped by intracellular buffers, and with what kinetics are thus key features that affect the time and spatial range of action of Ca2+ signals. The quantification of Ca2+ diffusion in intact cells is quite challenging because the transport rates that can be inferred using optical techniques are intricately related to the interaction of Ca2+ with the dye that is used for its observation and with the cellular buffers. In this paper, we introduce an approach that uses Fluorescence Correlation Spectroscopy (FCS) experiments performed at different conditions that in principle allows the quantification of Ca2+ diffusion and of its reaction rates with unobservable (non-fluorescent) Ca2+ buffers. To this end, we develop the necessary theory to interpret the experimental results and then apply it to FCS experiments performed in a set of solutions containing Ca2+, a single wavelength Ca2+ dye, and a non-fluorescent Ca2+ buffer. We show that a judicious choice of the experimental conditions and an adequate interpretation of the fitting parameters can be combined to extract information on the free diffusion coefficient of Ca2+ and of some of the properties of the unobservable buffer. We think that this approach can be applied to other situations, particularly to experiments performed in intact cells.

Thermodynamic properties and drying kinetics of Bauhinia forficata Link leaves

ABSTRACT The aim of this study was to determine the effective diffusion coefficient and the thermodynamic properties of Bauhinia forficata Link leaves, considering two forms of thickness measurements and to describe the process by fitting mathematical models. The leaves were collected, taken to the laboratory and prepared to start the drying process in which four temperatures (40, 50, 60 and 70 °C) were applied. After the drying process, the effective diffusion coefficient was determined through the theory of diffusion in liquid, allowing to obtain the values of the activation energy, enthalpy, entropy and Gibbs free energy. The description of the drying process was performed by setting the thirteen mathematical models used to represent constant drying of agricultural products. The Valcam model was selected to represent the drying kinetics B. forficata Link. Increased temperature promotes: decreasing enthalpy and entropy; increasing Gibbs free energy and effective diffusion coefficient. The effective diffusion coefficient is higher when the rib thickness is considered; thus, it is recommended to standardize and/or specify the points of measurement of leaf thickness.

Quantum statistics of classical particles derived from the condition of a free diffusion coefficient.

We derive an equation for the current of particles in energy space; particles are subject to a mean-field effective potential that may represent quantum effects. From the assumption that noninteracting particles imply a free diffusion coefficient in energy space, we derive Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein statistics. Other new statistics are associated to a free diffusion coefficient; their thermodynamic properties are analyzed using the grand partition function. A negative relation between pressure and energy density for low temperatures can be derived, suggesting a possible connection with cosmological dark energy models.

Theoretical estimate of the effect of thermal agitation on ribosome motion generated by stochastic microswimming

The effect of thermal agitation on ribosome motion is evaluated through the Péclet number, assuming that the ribosome is self-propelled along the mRNA during protein synthesis by a swimming stroke consisting of a cycle of stochastically-generated ribosome configurations involving its two subunits. The ribosome velocity probability distribution function is obtained, giving an approximately normal distribution. Its mean and variance together with an estimate of the in vivo free diffusion coefficient of the ribosome and using only configuration changes of small size, give a Péclet number similar to motor proteins and microorganisms. These results suggest the feasibility of the stochastic microswimming hypothesis to explain ribosome motion.

Unified model of brain tissue microstructure dynamically binds diffusion and osmosis with extracellular space geometry.

We present a universal model of brain tissue microstructure that dynamically links osmosis and diffusion with geometrical parameters of brain extracellular space (ECS). Our model robustly describes and predicts the nonlinear time dependency of tortuosity (λ=sqrt[D/D^{*}]) changes with very high precision in various media with uniform and nonuniform osmolarity distribution, as demonstrated by previously published experimental data (D = free diffusion coefficient, D^{*} = effective diffusion coefficient). To construct this model, we first developed a multiscale technique for computationally effective modeling of osmolarity in the brain tissue. Osmolarity differences across cell membranes lead to changes in the ECS dynamics. The evolution of the underlying dynamics is then captured by a level set method. Subsequently, using a homogenization technique, we derived a coarse-grained model with parameters that are explicitly related to the geometry of cells and their associated ECS. Our modeling results in very accurate analytical approximation of tortuosity based on time, space, osmolarity differences across cell membranes, and water permeability of cell membranes. Our model provides a unique platform for studying ECS dynamics not only in physiologic conditions such as sleep-wake cycles and aging but also in pathologic conditions such as stroke, seizure, and neoplasia, as well as in predictive pharmacokinetic modeling such as predicting medication biodistribution and efficacy and novel biomolecule development and testing.

Molecular Dynamics Simulation Study of Permeation of Molecules through Skin Lipid Bilayer.

Stratum Corneum (SC), the outermost layer of skin, is mainly responsible for skin's barrier function. The complex lipid matrix of SC determines these barrier properties. In this study, the lipid matrix is modeled as an equimolar mixture of ceramide (CER), cholesterol (CHOL), and free fatty acid (FFA). The permeation of water, oxygen, ethanol, acetic acid, urea, butanol, benzene, dimethyl sulfoxide (DMSO), toluene, phenol, styrene, and ethylbenzene across this layer is studied using a constrained MD simulations technique. Several long constrained simulations are performed at a skin temperature of 310 K under NPT conditions. The free energy profiles and diffusion coefficients along the bilayer normal have been calculated for each molecule. Permeability coefficients are also calculated and compared with experimental data. The main resistance for the permeation of hydrophilic and hydrophobic permeants has been found to be in the interior of the lipid bilayer and near the lipid-water interface, respectively. The obtained permeability is found to be a few orders of magnitude higher than experimental values for hydrophilic molecules while for hydrophobic molecules more discrepancy was observed. Overall, the qualitative ranking is consistent with the experiments.

Permeability across lipid membranes

Molecular permeation through lipid membranes is a fundamental biological process that is important for small neutral molecules and drug molecules. Precise characterization of free energy surface and diffusion coefficients along the permeation pathway is required in order to predict molecular permeability and elucidate the molecular mechanisms of permeation. Several recent technical developments, including improved molecular models and efficient sampling schemes, are illustrated in this review. For larger penetrants, explicit consideration of multiple collective variables, including orientational, conformational degrees of freedom, are required to be considered in addition to the distance from the membrane center along the membrane normal. Although computationally demanding, this method can provide significant insights into the molecular mechanisms of permeation for molecules of medical and pharmaceutical importance. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

Membrane Cholesterol Substantially Alters the Free Energy Topology of Oxygen Transport

Molecular oxygen delivery to mitochondria is essential for aerobic metabolism. Oxygen must diffuse across multiple membranes on the cellular and tissue levels. A steady supply of oxygen is essential for normal cellular bioenergetics, so even modest membrane resistance could generate intracellular hypoxia and promote pathological shifts in energy metabolism. The extent to which the membranes resist oxygen diffusion depends on their composition and physical properties. In particular, the presence of cholesterol is known to slow oxygen diffusion, but the physical details of the phenomenon remain to be clarified. We have undertaken a systematic study of oxygen transport thermodynamics, using GPU-accelerated, all-atom molecular dynamics simulations. From microsecond-timescale, unrestrained simulations, we have calculated free energy and diffusion coefficient profiles tracking oxygen permeation in model bilayer systems consisting of POPC and/or 0 to 100 mol% cholesterol. With increasing cholesterol content, we observe a steady and dramatic increase in the activation energy associated with membrane crossing. Ongoing study addresses the kinetic impact and biological significance of this diffusional barrier.

Fracture network optimization for simulating 2D variable-density flow and transport

Numerical simulations in porous media with complex geometries such as fracture networks require irregular meshes with a large number of nodes. Discrete fracture models solve the flow and transport equations with the common node approach. These equations are usually solved simultaneously using common nodes, which increases the computational time as the number of nodes increases. Moreover, the mesh element size at fracture-matrix interfaces need to be further refined, increasing the total number of nodes and computational cost. The main objective of this paper is to efficiently model fracture networks. Therefore we: (i) modify a mesh generator algorithm to generate high-quality meshes for fracture networks where mesh refinement close to the fractures is allowed and (ii) investigate the possibility of reducing the required simulation time by reducing the number of total nodes by removing some fractures from a fracture network. Using a two-dimensional simulation domain of a fractured porous medium under saturated conditions with variable-density flow, we consider 3 statistically equivalent fracture networks embedded in a porous medium containing 50 fractures each with constant aperture. A simplified fracture network is obtained by finding the shortest path in each cluster between the 1st type boundary condition for transport and minimum points in each cluster, where a cluster is defined as all interconnected fractures with at least one fracture intersecting the contaminant source boundary condition. We compare results in terms of penetration depth of the 0.50 isochlore and the contaminant mass. This simplification strategy reduces computational times by up to 36%, while keeping the generated error below 20% both for the penetration depth of the 0.50 isochlore and for the contaminant mass. A sensitivity analysis is performed whereby the free diffusion coefficient, the matrix freshwater permeability, the porosity and the maximum density are modified. Based on these results, the proposed simplification strategy can estimate the penetration depth and the solute mass inside the domain for a wide range of parameter values, saving up to 58% of the CPU time.

Effects of shear and walls on the diffusion of colloids in microchannels

Colloidal suspensions flowing through microchannels were studied for the effects of both the shear flow and the proximity of walls on the particles' self-diffusion. Use of hydrostatic pressure to pump micron-sized silica spheres dispersed in water-glycerol mixture through poly(dimethylsiloxane) channels with a cross section of 30×24μm(2), allowed variation in the local Peclet number (Pe) from 0.01 to 50. To obtain the diffusion coefficients, image-time series from a confocal scanning laser microscope were analyzed with a method that, after finding particle trajectories, subtracts the instantaneous advective displacements and subsequently measures the slopes of the mean squared displacement in the flow (x) and shear (y) directions. For dilute suspensions, the thus obtained diffusion coefficients (D(x) and D(y)) are close to the free diffusion coefficient at all shear rates. In concentrated suspensions, a clear increase with the Peclet number (for Pe > 10) is found, that is stronger for D(x) than for D(y). This effect of shear-induced collisions is counteracted by the contribution of walls, which cause a strong local reduction in D(x) and D(y).

Ground Truth for Diffusion MRI in Cancer: A Model-Based Investigation of a Novel Tissue-Mimetic Material.

This work presents preliminary results on the development, characterisation, and use of a novel physical phantom designed as a simple mimic of tumour cellular structure, for diffusion-weighted magnetic resonance imaging (DW-MRI) applications. The phantom consists of a collection of roughly spherical, micron-sized core-shell polymer 'cells', providing a system whose ground truth microstructural properties can be determined and compared with those obtained from modelling the DW-MRI signal. A two-compartment analytic model combining restricted diffusion inside a sphere with hindered extracellular diffusion was initially investigated through Monte Carlo diffusion simulations, allowing a comparison between analytic and simulated signals. The model was then fitted to DW-MRI data acquired from the phantom over a range of gradient strengths and diffusion times, yielding estimates of 'cell' size, intracellular volume fraction and the free diffusion coefficient. An initial assessment of the accuracy and precision of these estimates is provided, using independent scanning electron microscope measurements and bootstrap-style simulations. Such phantoms may be useful for testing microstructural models relevant to the characterisation of tumour tissue.