Smoluchowski Model Research Articles

Numerical assessments of geometry, proximity and multi-electrode effects on electroporation in mitochondria and the endoplasmic reticulum to nanosecond electric pulses

Most simulations of electric field driven bioeffects have considered spherical cellular geometries or probed symmetrical structures for simplicity. This work assesses cellular transmembrane potential build-up and electroporation in a Jurkat cell that includes the endoplasmic reticulum (ER) and mitochondria, both of which have complex shapes, in response to external nanosecond electric pulses. The simulations are based on a time-domain nodal analysis that incorporates membrane poration utilizing the Smoluchowski model with angular-dependent changes in membrane conductivity. Consistent with prior experimental reports, the simulations show that the ER requires the largest electric field for electroporation, while the inner mitochondrial membrane (IMM) is the easiest membrane to porate. Our results suggest that the experimentally observed increase in intracellular calcium could be due to a calcium induced calcium release (CICR) process that is initiated by outer cell membrane breakdown. Repeated pulsing and/or using multiple electrodes are shown to create a stronger poration. The role of mutual coupling, screening, and proximity effects in bringing about electric field modifications is also probed. Finally, while including greater geometric details might refine predictions, the qualitative trends are expected to remain.

Multi-stage electroporation dynamics induced by ionization wave–substrate interaction in cold plasma jet

The reactive species-independent nature of cold plasma's electric field is pivotal in biomedical applications. This work proposes to connect the plasma fluid model and the asymptotic Smoluchowski model for electroporation, providing a unified framework to investigate the evolution of the electric field in the biological substrate and the multi-stage electroporation response of the human cell. Two common substrates with distinct dielectric properties, namely, the cultivation medium and epidermis, are selected to report three stages of ionization wave (IW)–substrate interaction. The three-stage streamer discharge dynamics (restrike, axial-radial transition, and radial expansion of IW) induce three-stage cell electroporation dynamics (slow charging, fast charging, and electroporation), though the two processes are asynchronous. Specifically, the inner membrane covered the cell nucleus with ultra-short charging time that undergoes only the first two discharge stages in both substrates. Whether the cell membrane is exposed to the third stage of discharge depends on the permittivity of the substrate. The asynchrony can be attributed to the difference in the charging time of the cell membranes and substrates affected by the substrate permittivity. The presented model can provide quantitative insights into the cell electroporation induced by the IW–substrate interaction and theoretical guidance for plasma biomedical applications.

Design of Modular, 3D‐Printed Millifluidic Mixers to Enable Sequential NanoPrecipitation (SNaP) for the Tunable Synthesis of Drug‐Loaded Nanoparticles and Microparticles

AbstractSequential NanoPrecipitation (SNaP) is a nascent controlled precipitation process for the tunable formation of polymeric particles for drug delivery and bioimaging. While SNaP utilizes the same self‐assembly principles as one‐step Flash NanoPrecipitation, SNaP is a two‐step assembly process in which the particle core formation is initiated during a first mixing step followed by particle stabilization in a second mixing step. Current SNaP experimental set‐ups use commercial millifluidic mixers connected in series, which have several limitations, including the inability to access short inter‐mixer delay times (Td). A robust, 3D‐printed, modular mixer design that enables access to short Td's (〈 25 ms) not previously accessible is reported. For the first time, it is demonstrated that decoupling the assembly steps improves control over particle size, expanding the attainable size range to include both nanoparticles and microparticles. It is empirically proven that inter‐mixer Td is a key parameter for particle size control and that particle size scales with Td in agreement with Smoluchowski's model of diffusion‐limited growth. The formation of particles ranging in size from 160 nm to 1.2 µm is shown. Finally, the applicability of the new mixers is established by encapsulating fluorophores and therapeutics into particles for the first time via SNaP.

Generalizing electroosmotic-flow predictions over charge-modulated periodic topographies: tuneable far-field effects

The classical Helmholtz–Smoluchowski (HS) model of electroosmosis holds for homogeneously charged interfaces in contact with a fluid layer bearing an equal and opposite net charge. However, inhomogeneities in the surface charge and topography are inevitable, either as practical materials and fabrication artefacts, or at times as deliberately introduced modulations for flow control. In an effort to arrive at an analytically tractable theoretical framework for addressing the underlying electro-mechanical coupling, here, we generalize the traditional HS theory to an extent where both the surface charge and topographies may bear arbitrary and independent periodic forms. Using a spectral-asymptotic approach, we further arrive at closed-form expressions for describing the resulting electroosmotic pumping for topographic features with small characteristic amplitude to pattern period ratio, as relevant for most practical scenarios. We subsequently execute full-scale numerical simulations without any restrictions on the surface charge and topography variations to assess the efficacy of the theoretical framework. The corresponding test beds include distinctive signature patterns – for example, a square-wave surface charge distribution on trapezoidal pit topographies. Our results reveal that the charge–topography interplay induces an anisotropic flow drift, deviating from the classical HS paradigm. This, in turn, provides new quantitative insights into highly selective electroosmotic flow control via judicious design of the charge and topographical patterns, resulting in controllable accentuation, attenuation, nullification, deflection and even complete reversal of the flow. Our analysis further establishes a provision of estimating the zeta potentials of naturally ‘contaminated’ surfaces, as well as explaining the electrophoresis of large inhomogeneous particles; a paradigm that remained to be explored thus far.

Diffusion-Limited Kinetics in Reactive Systems.

A proper representation of chemical kinetics is vital to understanding, modeling, and optimizing many important chemical processes. In liquid and surface phases, where diffusion is slow, the rate at which the reactants diffuse together limits the overall rate of many elementary reactions. Commonly, the textbook Smoluchowski theory is utilized to estimate effective rate coefficients in the liquid phase. On surfaces, modelers commonly resort to much more complex and expensive Kinetic Monte Carlo (KMC) simulations. Here, we extend the Smoluchowski model to allow the diffusing species to undergo chemical reactions and derive analytical formulas for the diffusion-limited rate coefficients for 3D, 2D, and 2D/3D interface cases. With these equations, we are able to demonstrate that when species react faster than they diffuse they can react orders of magnitude faster than predicted by Smoluchowski theory, through what we term "the reactive transport effect". We validate the derived steady-state equations against particle Monte Carlo (PMC) simulations, KMC simulations, and non-steady-state solutions. Furthermore, using PMC and KMC simulations, we propose corrections that agree with all limits and the computed data for the 2D and 2D/3D interface steady-state equations, accounting for unique limitations in the associated derived equations. Additionally, we derive equations to handle couplings between diffusion-limited rate coefficients in reaction networks. We believe these equations should make it possible to run much more accurate mean-field simulations of liquids, surfaces, and liquid-surface interfaces accounting for diffusion limitations and the reactive transport effect.

A generalized Knudsen theory for gas transport with specular and diffuse reflections

Gas permeation through nanopores is a long-standing research interest because of its importance in fundamental science and many technologies. The free molecular flow is conventionally described by Knudsen theory, under the diffuse reflection assumption. Recent experiments reported ballistic molecular transport of gases, which urges for the development of theoretical tools to address the predominant specular reflections on atomically smooth surfaces. Here we develop a generalized Knudsen theory, which is applicable to various boundary conditions covering from the extreme specular reflection to the complete diffuse reflection. Our model overcomes the limitation of Smoluchowski model, which predicts the gas flow rate diverging to infinity for specular reflection. It emphasizes that the specular reflection can reduce the dissipation flow rate. Our model is validated using molecular dynamics simulations in various scenarios. The proposed model provides insights into the gas transport under confinement and extends Knudsen theory to free molecular flow with specular reflections.

Coagulative Nucleation in the Copolymerization of Methyl Methacrylate-Butyl Acrylate under Monomer-Starved Conditions.

Coagulative nucleation in the copolymerization of methyl methacrylate-butyl acrylate (MMA-BA) via semicontinuous emulsion heterophase polymerization (SEHP) under monomer-starved conditions in latexes with high solid content (50.0 wt %) and low concentrations of surfactant is reported. The SEHP technique allows the obtention of latex with high colloidal stability and has potential industrial application in polymer synthesis. High instantaneous conversions (>90%) and a high-ratio polymerization rate/addition rate (Rp/Ra) ≥ 0.9 were obtained at low times until the final copolymerization, which confirmed the starved conditions in the systems at the highest surfactant concentrations. The particle size exhibited a linear size increment at conversions between 0 and 40% induced by homogeneous nucleation, a transition region between 40 and 50%, and non-linear behavior at higher conversions by coagulative nucleation. These three behaviors were also observed in the particle surfactant coverage area (Sc), Z-potential, particle coagulation rate (dNp/dt) by the Smoluchowski model, final particle size (Dpz), and number particle (Np) through the reaction. By means of transmission electron microscopy (TEM) images, the onset of coagulation was observed from 50% of conversion until the end of the reaction. In addition, in both processes of copolymerization, tacticity was displayed (mainly syndiotacticity).

Studying first passage problems using neural networks: A case study in the slit-well microfluidic device.

This study presents deep neural network solutions to a time-integrated Smoluchowski equationmodeling the mean first passage time of nanoparticles traversing the slit-well microfluidic device. This physical scenario is representative of a broader class of parametrized first passage problems in which key output metrics are dictated by a complicated interplay of problem parameters and system geometry. Specifically, whereas these types of problems are commonly studied using particle simulations of stochastic differential equationmodels, here the corresponding partial differential equationmodel is solved using a method based on deep neural networks. The results illustrate that the neural network method is synergistic with the time-integrated Smoluchowski model: together, these are used to construct continuous mappings from key physical inputs (applied voltage and particle diameter) to key output metrics (mean first passage time and effective mobility). In particular, this capability is a unique advantage of the time-integrated Smoluchowski model over the corresponding stochastic differential equationmodels. Furthermore, the neural network method is demonstrated to easily and reliably handle geometry-modifying parameters, which is generally difficult to accomplish using other methods.

Modeling and simulation of current-clamp electroporation

Current-Clamp electroporation refers to the application of a constant current across a membrane which results in voltage fluctuations due to the creation of electropores. This method allows for the measurement of electroporation across a long timescale (minutes) and facilitates the comparison between experimental and theoretical studies. Of particular interest is the claim in the literature that current-clamp electroporation results in the creation of a single pore. We simulated current-clamp electroporation using the Smoluchowski and Langevin equations and identified two possible mechanisms to explain the observed voltage fluctuations. The voltage fluctuations may be due to a single pore or a few pores growing and shrinking via a negative feedback mechanism or the opening and closing of pores in a larger population of pores. Our results suggest that current-clamp conditions do not necessarily result in the creation of a single pore. Additionally, we showed that the Langevin model is more accurate than the Smoluchowski model under conditions where there are only a few pores.

Impact of electroosmosis and joule heating effects on peristaltic transport with thermal radiation of hyperbolic tangent fluid through a porous media in an endoscope

The current study explores the impact of electro-osmotic flow, radiation, Joule heating through porous medium on the peristaltic motion of tangent hyperbolic fluid in an endoscope with the assumptions of low Reynolds number and long wavelength. Between two coaxial tubes, a non-Newtonian hyperbolic tangent fluid is considered in cylindrical form. The Helmholtz–Smoluchowski model is used to describe the electroosmosis processes. The Homotopy Perturbation technique (HPM) is imposed to deal the equations of nonlinear partial differential equations. The impact of various physical parameters on velocity, temperature, heat generation coefficient, and coefficient of skin friction were graphically depicted. The significant outcome of the present study is that the impact of the electro-osmotic parameter in the first half diminishes and then enhances the velocity profile for the positive value of electroosmosis parameter. Joule heating enhances the temperature profile whereas Hartmann number and thermal radiation diminish the rate of heat transfer. And also, Darcy number enhances the skin friction coefficient. The present study can be applicable in the bio microfluidics to regulate fluid flow through microchannels and also examining the cancer tumour elimination and artery blockage treatment in biomedical.

Kinetics of photoinduced phase retardation in azo dye layer

ABSTRACT Photoalignment of liquid crystals with azo dyes has a high potential for display and non-display applications. In this study, we report the existence of abnormal relaxation of photoinduced retardation in azo dye layers. Our results were obtained on the experimental setup, where the phase retardation of azo dye was measured by a photoelastic modulator. This phenomenon indicates that the role of the rotational diffusion coefficient must be carefully studied. Uniaxial Boltzmann–Smoluchowski model was used for theoretical analysis of the experimental results. With the model that includes the relative order parameter, we examined its kinetics during pumping and different relaxation processes. The proportionality between the photoinduced retardation and the relative order parameter has enabled us to study the kinetics of latter one under the hypothesis of temporal dependence of the rotational diffusion coefficient. A qualitative agreement between experimental measurements and model calculations adequately describes the photoinduced relaxation kinetics. The proposed methodology of computation of the relative order parameter is unbiased for all values of the material parameters.

Numerical Analysis of the Heterogeneity Effect on Electroosmotic Micromixers Based on the Standard Deviation of Concentration and Mixing Entropy Index

One approach to achieve a homogeneous mixture in microfluidic systems in the quickest time and shortest possible length is to employ electroosmotic flow characteristics with heterogeneous surface properties. Mixing using electroosmotic flow inside microchannels with homogeneous walls is done primarily under the influence of molecular diffusion, which is not strong enough to mix the fluids thoroughly. However, surface chemistry technology can help create desired patterns on microchannel walls to generate significant rotational currents and improve mixing efficiency remarkably. This study analyzes the function of a heterogeneous zeta-potential patch located on a microchannel wall in creating mixing inside a microchannel affected by electroosmotic flow and determines the optimal length to achieve the desired mixing rate. The approximate Helmholtz–Smoluchowski model is suggested to reduce computational costs and simplify the solving process. The results show that the heterogeneity length and location of the zeta-potential patch affect the final mixing proficiency. It was also observed that the slip coefficient on the wall has a more significant effect than the Reynolds number change on improving the mixing efficiency of electroosmotic micromixers, benefiting the heterogeneous distribution of zeta-potential. In addition, using a channel with a heterogeneous zeta-potential patch covered by a slip surface did not lead to an adequate mixing in low Reynolds numbers. Therefore, a homogeneous channel without any heterogeneity would be a priority in such a range of Reynolds numbers. However, increasing the Reynolds number and the presence of a slip coefficient on the heterogeneous channel wall enhances the mixing efficiency relative to the homogeneous one. It should be noted, though, that increasing the slip coefficient will make the mixing efficiency decrease sharply in any situation, especially in high Reynolds numbers.

Sampling efficiency of the counting method for permeability calculations estimated with the inhomogeneous solubility-diffusion model.

Permeability is a key property in various fields such as membrane technology for chemical separation and transport of substances through cell membranes. At the molecular scale, the counting method uses the number of membrane crossings in a conventional unbiased molecular dynamics simulation to predict the permeability. This contribution investigates under which conditions the counting method has insufficient statistics. An equation is derived for a compartmental model based on the inhomogeneous solubility-diffusion (Smoluchowski) model, giving insight into how the flux correlates with the solubility of permeants. This equation shows that a membrane crossing is a rare event not only when the membrane forms a large free energy barrier but also when the membrane forms a deep free energy well that traps permeants. Such a permeant trap has a high permeability; yet, the counting method suffers from poor statistics. To illustrate this, coarse-grained MD was run for 16 systems of dipalmitoylphosphatidylcholine bilayer membranes with different permeant types. The composition rule for permeability is shown to also hold for fluxes, and it is highlighted that the considered thickness of the membrane causes uncertainty in the permeability calculation of highly permeable membranes. In conclusion, a high permeability in itself is not an effective indicator of the sampling efficiency of the counting method, and caution should be taken for permeants whose solubility varies greatly over the simulation box. A practical consequence relevant in, e.g., drug design is that a drug with high membrane permeability might get trapped by membranes thus reducing its efficacy.

Precipitant Effects on Aggregates Structure of Asphaltene and Their Implications for Groundwater Remediation

Asphaltenes generally aggregate, then precipitate and deposit on the surfaces of environmental media (soil, sediment, aquifer, and aquitard). Previous studies have recognized the importance of asphaltene aggregates on the wettability of aquifer systems, which has long been regarded as a limiting factor that determines the feasibility and remediation efficiency of sites contaminated by heavy oils. However, the mechanisms/factors associated with precipitant effects on asphaltene aggregates structure, and how the precipitant effects influence the wettability of surfaces remain largely unknown. Here, we observe the particle-by-particle growth of asphaltene aggregates formed at different precipitant concentrations. Our results show that aggregates for all precipitant concentrations are highly polydisperse with self-similar structures. A higher precipitant concentration leads to a more compacted aggregates structure, while precipitant concentration near to onset point results in a less compact structure. The well-known Smoluchowski model is inadequate to describe the structural evolutions of asphaltene aggregates, even for aggregation scenarios induced by a precipitant concentration at the onset point where the Smoluchowski model is expected to explain the aggregate size distribution. It is suggested that aggregates with relative high fractal dimensions observed at high precipitant concentrations can be used to explain the relatively low Stokes settling velocities observed for large asphaltene aggregates. In addition, asphaltene aggregates with high fractal dimensions are likely to have high density of nanoscale roughness which could enhance the hydrophobicity of interfaces when they deposit on the sand surface. Findings obtained from this study advance our current understandings on the fate and transport of heavy oil contaminants in the subsurface environment, which will have important implications for designing and implementing more effective and efficient remediation technologies for contaminated sites.

Donnan-ion hydration model to estimate the electroosmotic permeability of clays

Electroosmotic permeability is a soil parameter that is fundamental for designing and implementing environmental remediation, dewatering, or soil stabilization processes. It presents a narrow range of variation compared to hydraulic permeability, so that in many occasions no experimental tests are carried out to determine it. Traditionally, the Helmholtz–Smoluchowski equation has been used to estimate electroosmotic permeability, despite having several drawbacks that make it difficult to apply, as it was deduced for large capillaries (unusual in clays) and its dependence on the zeta potential of the soil, difficult to measure and dependent on a wide variety of factors. The present work describes a semi-empirical formulation that allows the estimation of the electroosmotic permeability as a function of the specific surface area and the total void ratio and is based on the Donnan equilibrium and the ion hydration models. The parameters for modeling are calibrated and validated with experimental data, obtaining better results than those given by the Helmholtz–Smoluchowski model. In addition, the expected trends in the behavior of clays that can be found in the literature are obtained in a quantitative and consistent manner for different types of clays with variable water content and pore water salinity.

MULTIFLUID DESCRIPTION OF RAREFIED GAS MIXTURE FLOWS

In the present contribution attention is focused to extend the application of multifluid descriptions to rarefied conditions for the first time. To this aim, a multifluid Maxwell model and a multifluid Smoluchowski model are proposed for near wall behavior of the constituents of a rarefied gas mixture. Afterwards, multifluid balance equations in conjunction with these boundary conditions are solved for some slip flows of binary gas mixtures between parallel plates. The corresponding results are compared with those of a previously developed Navier–Stokes solver. Inspection of the results indicates that while the Navier–Stokes equations may lose their accuracy under high rarefaction, non–equilibrium features are properly captured by developed multifluid description. This successful method is thereafter utilized to discuss the consequences of velocity–slip, the tangential–momentum–accommodation coefficient, and mass disparity of the mixture constituents on the degree of non–equilibrium between the constituents of the gas mixtures between parallel plates.

Prion-like spreading of Alzheimer's disease within the brain's connectome.

The prion hypothesis states that misfolded proteins can act as infectious agents that template the misfolding and aggregation of healthy proteins to transmit a disease. Increasing evidence suggests that pathological proteins in neurodegenerative diseases adopt prion-like mechanisms and spread across the brain along anatomically connected networks. Local kinetic models of protein misfolding and global network models of protein spreading provide valuable insight into several aspects of prion-like diseases. Yet, to date, these models have not been combined to simulate how pathological proteins multiply and spread across the human brain. Here, we create an efficient and robust tool to simulate the spreading of misfolded protein using three classes of kinetic models, the Fisher–Kolmogorov model, the Heterodimer model and the Smoluchowski model. We discretize their governing equations using a human brain network model, which we represent as a weighted Laplacian graph generated from 418 brains from the Human Connectome Project. Its nodes represent the anatomic regions of interest and its edges are weighted by the mean fibre number divided by the mean fibre length between any two regions. We demonstrate that our brain network model can predict the histopathological patterns of Alzheimer’s disease and capture the key characteristic features of finite-element brain models at a fraction of their computational cost: simulating the spatio-temporal evolution of aggregate size distributions across the human brain throughout a period of 40 years takes less than 7 s on a standard laptop computer. Our model has the potential to predict biomarker curves, aggregate size distributions, infection times, and the effects of therapeutic strategies including reduced production and increased clearance of misfolded protein.

Experimental and analytical study on electro-osmosis in low-permeability soil considering the pore size effect

Existing electro-osmotic calculation models are mostly based on the assumption of a porous medium with uniform pores, whereas natural soil has pores of different sizes. This is especially significant in the case of low-permeability soil, whose pore size can vary over five or six orders of magnitude, from the nanometre to the millimetre scale. Experimental results have revealed significant differences in the electro-osmotic flow characteristics of soils with various pore sizes, indicating a strong dependence on pore size distribution (PSD). This dependence is termed the pore size effect (PSE) on electro-osmosis. In this paper, a series of one-dimensional electro-osmosis experiments on three types of low-permeability clay soil are conducted to quantify the PSE on electro-osmosis. Based on the experimental results and an analysis of electro-osmotic characteristics, a modified analytical approach considering the actual soil PSD and its effect on electro-osmosis is proposed and thereby two modified analytical models are established. Using the experimental results, the modified models are compared with the existing Helmholtz–Smoluchowski model and other models that assume uniform pores. The results show that the PSE increases with increasing thickness of the electric double layer and that the modified models can be used to reasonably calculate the electro-osmotic permeability of low-permeability soil.

US: Chroma Color – plastics masterbatch

In this study, the widely applied modified Smoluchowski model of flocculation kinetics based on the existence of two simultaneous processes, namely aggregation and breakup, is further developed by combining it with the fractal theory. The floc properties including the floc size and fractal dimension are extracted using online data acquisition through light scattering technique and combined into the model. The new method has been carefully examined by three flocculation systems using kaolin suspension as synthetic water and different typical flocculants. The theoretic flocculation kinetic curves are in good agreement with the experimental data with the determination coefficients larger than 0.9 by nonlinear regression. Moreover, the flocculation kinetic characteristics of different flocculation systems under various conditions are discussed based on the kinetic rates calculated from the modified model in detail. In summary, the new method for calculation of flocculation kinetics is more universal and simpler to operate, and is expected to be a useful tool in real water treatment operations.

Accurate modeling of Knudsen diffusion in nanopores using a physical-based boundary model

Gas transport in nanopores plays an important role in modern industry, such as shale gas exploitation, sea water desalination, fuel battery, etc. Owing to the small pore size, gas transport in nanopores is dominated by Knudsen diffusion, where the gas molecular motion is fully determined by the gas-surface interaction at the boundary. Classic theories of Knudsen diffusion, such as the “Smoluchowski model” and “extended Smoluchowski model”, were developed based on empirical gas-surface interaction models. These empirical boundary models may not be accurate to capture the key mechanism of Knudsen diffusion, particularly when the surface roughness is small, such as the case of carbon nanotubes. In this work, the influence of the empirical boundary models on Knudsen diffusion is studied in detail. Theoretical analysis indicates that the Knudsen diffusivity in one-dimensional pores critically depends on the correlation between gas molecular scattering angles on the pore surface. Benchmarked by molecular dynamics simulations, empirical boundary models show notable errors in the prediction of the scattering angle correlation, despite the fact that the accurate tangential momentum accommodation coefficient is used. In contrast, the physical-based boundary model, developed recently by our group, can accurately and efficiently reproduce the molecular dynamics simulation results. Its performance is further demonstrated in the modeling of the Knudsen diffusivity in a one-dimensional cylindrical pore, which predicts more accurate results than the Smoluchowski model and extended Smoluchowski model.