Mass Transport Model Research Articles

Numerical investigation of impact of crystal diameter fluctuations on intrinsic point defects distribution in Si crystal grown by Czochralski method

Intrinsic point defects distribution is primarily controlled by the crystal pulling rate and temperature gradient directly at growth interface in silicon crystals grown using the Czochralski (Cz) method. The fluctuation in crystal diameter during the Cz process is one of the primary features associated with the temporal variation in growth process parameters, such as the pulling rate and heater power in the growth system, and which is expected to affect the thermal stress, defects, and dopant incorporation in a growing crystal. In this study, we numerically investigated the effect of temporal variation in crystal diameter on the intrinsic point defects distribution in a silicon crystal grown using the Cz method. The point defect dynamics in the crystal were numerically evaluated within a two-dimensional axisymmetric unsteady global heat and mass transport model for dynamically pulled silicon crystals, considering the shape of the crystal and diameter variation. Unsteady numerical simulations showed that the distribution of intrinsic point defects near crystal side surface in a growing silicon crystal significantly depends on the temporal variation in the crystal diameter.

Multi-physical modeling and fabrication of high-performance IPMC actuators with serrated interface

Ionic Polymer–Metal Composite (IPMC) has been widely recognized as a promising and representative candidate of soft intelligent materials actuated under low voltage. In the last few years, the importance of the electrode/substrate interface has received growing attention for research on both the modeling of ion-based mass transport and practical performance of the manipulation of ionic electro-active actuators. In this paper, based on a macroscopic serrated interface morphology, the influences of the interface were revealed comprehensively by distinguishing the bending direction as well as the variation of interfacial area, excisional volume and moment of inertia. The offsetting interaction from different aspects were analyzed in detail. On this basis, an interesting result showed that, contrary to current understanding, an enlarged interface area did not necessarily lead to better deformation, which was primarily ascribed to the trade-off of influences from the increasing excisional volume and decreasing bending inertia moment. In addition, a corresponding fabrication process was established, which verified experimentally that IPMC with a super simple macroscopic serrated interface can present a high electro-active performance, providing a minimalist design strategy for ionic electroactive polymer structures.

Pore-Scale Modeling of Mass Transport in Partially Saturated Cathode Gas Diffusion Layers of Proton Exchange Membrane Fuel Cell

Proton exchange membrane fuel cells (PEMFCs) have the advantages of high specific power, good stability, and zero emissions, making them clean and efficient energy conversion devices. Water management is one of the technical challenges limiting the development of PEMFC, with liquid water blocking the pores and increasing the resistance to mass transport. In this paper, a two-dimensional (2D) multiphase lattice Boltzmann (LB) model is developed to obtain the liquid water morphology within the gas diffusion layer (GDL). A 2D multicomponent flow Lattice Boltzmann model considering electrochemical reactions is established to investigate the effects of water saturation, activation overpotential, and pressure difference between the inlet and outlet gas channels on mass transport. At high water saturation, the liquid water forms water films within the GDL preventing reactive gas transport and water vapor are blocked near the catalyst layer making it difficult to remove. The PEMFC can achieve higher current densities at high activation overpotentials, but oxygen starvation will be exacerbated. Increasing the pressure difference between the inlet and outlet gas passages effectively increases the oxygen concentration and reduces the water vapor concentration in the GDL. The present study improves the understanding of the effect of GDL microstructure on mass transport and performance of PEMFC from the mesoscopic scale.

The influence of feedwater pH on membrane charge ionization and ion rejection by reverse osmosis: An experimental and theoretical study

Modeling mass transport of ions across the polyamide active layer of a reverse osmosis (RO) membrane requires a comprehensive understanding of membrane structure and chemistry. For instance, membrane charge ionization and thus salt transport greatly depend on feedwater pH and composition, but these relations are not yet well understood. To address this gap in understanding, a one dimensional model is developed that couples transport of all ions using the extended Donnan steric partitioning pore model. The model includes membrane charge ionization as well as interaction with H+ and OH−-ions. The dependence of ion rejection and permeate pH is described as function of feedwater pH. Finally, model predictions are quantitatively compared with experimental data by adjusting a few fitting parameters using the Nelder-Mead algorithm. Contrary to other RO studies, we show that the polyamide is only weakly charged, but this small charge still plays a key role to determine membrane performance. These findings reveal the key role of local pH in the ionization of membrane functional groups, and how local charge affects overall membrane rejection of ions as well as permeate pH.

Two-phase mass transport model for microfluidic fuel cell with narrow electrolyte flow channel

Microfluidic fuel cells employ liquid electrolyte stream instead of conventional polymer electrolyte membrane to compartmentalize the anode and cathode, leading to the improvement of flexibility in practical applications. To boost the electrochemical performance and simplify operating conditions, a two-dimensional two-phase model is developed for a microfluidic fuel cell with a single narrow electrolyte channel, where a transport barrier layer is set close to the cathode to inhibit fuel crossover and remove the blank electrolyte stream. The shortened width of electrolyte channel decreases the distance between the anode and cathode, enhancing the fuel and proton transport and elevating the power density effectively. The generated gaseous CO2 via electrochemical reaction increases mass transfer resistance of liquid fuel through the anode catalyst layer, resulting in dramatic decrease in the fuel concentration and effective active area in the anode catalyst layer. Consequently, the transport of proton and fuel in the anode limits the output power density at high current densities. The numerical results provide a deep understanding of two-phase mass-transport in microfluidic fuel cell with a single narrow electrolyte channel and help better design and operation of this type microfluidic fuel cell.

Transport and surface reaction model of a photocatalytic membrane during the radical filtration of methylene blue

• A photocatalytic membrane was fabricated for water purification and it was tested and described. • Synergy between photocatalytic degradation and membrane filtration is explored. • Simple 1D mass transport model describes the dead-end photocatalytic membrane process. • A methylene blue discoloration of 68–23% was reached with the lowest to the highest filtration rate. This study explores the synergy between photocatalytic oxidation and membrane filtration using a photocatalytic membrane. Titanium dioxide coated alumina membranes were fabricated and tested in a customized Photocatalytic Membrane Reactor (PMR) module. The discoloration of methylene blue (MB), 3.2 mg·L −1 in an aqueous solution, was evaluated in dead-end filtration mode. A simple 1D analytic transport and surface reaction model was used based on advection and diffusion, containing intrinsic retention by the membrane and reaction kinetics to predict the permeate concentration. The discoloration of MB by the photocatalytic membrane could be well described by a single retention and reaction rate constant (second Damköhler number) for fluxes from 1.6 to 16.2 L·m −2 ·h −1 . The model furthermore indicates the potential synergy between membrane retention, which leads to increased concentration, and accompanying photocatalytic conversion, at the membrane surface.

Mass Transport Model of Radiation Response: Calibration and Application to Chemoradiation for Pancreatic Cancer

The benefit of radiation therapy for pancreatic ductal adenocarcinoma (PDAC) remains unclear. We hypothesized that a new mechanistic mathematical model of chemotherapy and radiation response could predict clinical outcomes a priori, using a previously described baseline measurement of perfusion from computed tomography scans, normalized area under the enhancement curve (nAUC). We simplified an existing mass transport model that predicted cancer cell death by replacing previously unknown variables with averaged direct measurements from randomly selected pathologic sections of untreated PDAC. This allowed using nAUC as the sole model input to approximate tumor perfusion. We then compared the predicted cancer cell death to the actual cell death measured from corresponding resected tumors treated with neoadjuvant chemoradiation in a calibration cohort (n = 80) and prospective cohort (n = 25). After calibration, we applied the model to 2 separate cohorts for pathologic and clinical associations: targeted therapy cohort (n = 101), cetuximab/bevacizumab + radiosensitizing chemotherapy, and standard chemoradiation cohort (n = 81), radiosensitizing chemotherapy to 50.4 Gy in 28 fractions. We established the relationship between pretreatment computed v nAUC to pathologically verified blood volume fraction of the tumor (r = 0.65; P = .009) and fractional tumor cell death (r = 0.97-0.99; P < .0001) in the calibration and prospective cohorts. On multivariate analyses, accounting for traditional covariates, nAUC independently associated with overall survival in all cohorts (mean hazard ratios, 0.14-0.31). Receiver operator characteristic analyses revealed discrimination of good and bad prognostic groups in the cohorts with area under the curve values of 0.64 to 0.71. This work presents a new mathematical modeling approach to predict clinical response from chemotherapy and radiation for PDAC. Our findings indicate that oxygen/drug diffusion strongly influences clinical responses and that nAUC is a potential tool to select patients with PDAC for radiation therapy.

A phase field model for mass transport with semi-permeable interfaces

In this paper, a thermaldynamical consistent model for mass transfer across permeable moving interfaces is proposed by using the energy variation method. We consider a restricted diffusion problem where the flux across the interface depends on its conductance and the difference of the concentration on each side. The diffusive interface phase-field framework used here has several advantages over the sharp interface method. First of all, explicit tracking of the interface is no longer necessary. Secondly, interfacial conditions can be incorporated with a variable diffusion coefficient. Finally, topological changes of interfaces can be handed easily. A detailed asymptotic analysis confirms the diffusive interface model converges to the existing sharp interface model as the interface thickness goes to zero. An energy stable numerical scheme is developed to solve this highly nonlinear coupled system.Numerical simulations first illustrate the consistency of theoretical results on the sharp interface limit. Then a convergence study and energy decay test are conducted to ensure the efficiency and stability of the numerical scheme. To illustrate the effectiveness of our phase-field approach, several examples are provided, including a study of a two-phase mass transfer problem where droplets with deformable interfaces are suspended in a moving fluid.

Multiphase Fluid Dynamics and Mass Transport Modeling in a Porous Electrode toward Hydrogen Evolution Reaction

The intrinsic activity of hydrogen evolution reaction (HER) catalysts has been significantly improved in the past decades, and current efforts are devoted to implement these catalysts for HER applications through electrode design and fabrication. However, HER in an electrode usually involves complex processes including electrochemical reaction, ion transport, bubble behavior, and gas–liquid flow near the electrode surface. The coupling of different processes makes it difficult to accurately analyze the effect of each process on the HER performance of the electrode. In this paper, a multiphase fluid dynamics and mass transport model is proposed to decouple the HER processes and provide a deep understanding on the interactions among those processes. The results reveal a strong interaction between ion transport inside the electrode and bubble detachment/ascending outside the electrode. The surface design can effectively improve the velocity profile of the liquid and hence dominate the ion transport near the electrode, whereas the design of pore structure can remarkably enhance the ions diffusion inside the electrode. In addition, external forced electrolyte flow can further enhance the fluid convection and ion transport when the speed of forced flow is higher than that induced by bubble ascending. These results conclude that the proposed model contributes to the understanding of interactions among electrochemical reaction, ion transport, bubble behavior, and gas–liquid flow near the electrode surface, providing a guideline for HER electrode design.

Numerical solution and mathematical modelling of mass transport from medicated stent

Restenosis in arteries is a major problem which can be controlled by using medicated stents. The controlled drug transport from medicated stents has a great effect in decreasing restenosis in arteries. Drug is coated on stents to keep away from the re-narrowing of the artery wall. This device has an advantage of a flexible time delivery of a curative drug to the adjoining blood vessel tissues. The aim of this study is to formulate a mathematical model which describe the process of drug transport from arterial wall and medicated stent. For this purpose, a 3D model is investigated to measure the impact of mass transport from drug eluting stent. The blood flow is modelled by dimensionless Navier stokes equations and the concentration of drug is driven by dimensionless’ convection diffusion equation. The effect of diffusive and advective forces are discovered and these forces can be used to control the drug mass transport. Moreover, the effect of dimensionless parameters such as Peclet number porosity k and on mass transport from medicated stent and tissue layers is investigated. Characteristic Based Split Galerkin (CBSG) technique is applied to solve the dimensionless equations. In the application of stent-based drug delivery, the governing equations in this exploration give the premise of a plan for examining and computing mass transport in medicated stent and artery wall. The numerical results support to offer a good insight into the possible impacts of various parameters.

Water‐ and air‐filled pore networks and transport parameters under drying and wetting processes

AbstractThe connectivity and tortuosity of fluid‐filled pore networks in the water and air phases strongly influence the mass transport in porous media. Moisture conditions (water content and distribution) alter water‐ or air‐filled pore networks. In this study, using a sand column with variable saturated conditions, water‐ and air‐filled pore networks were analyzed using X‐ray computed tomography (CT). Water and air transport parameters, including hydraulic conductivity, gas diffusion coefficient, and air permeability, were measured. The objectives were (a) to identify the effects of entrapped air on the water‐filled pore network and hydraulic conductivity and (b) to understand the water‐ and air‐filled pore networks and relevant transport parameters in the sand column during the drying and wetting processes. Measurements of hydraulic conductivity using quasisaturated samples showed that hydraulic conductivity was drastically reduced when smaller in situ air bubbles were present inside the sand column. At the same air‐filled porosity, higher gas diffusivity and air permeability were obtained under wetting than those during drying. X‐ray CT image analysis revealed that the air‐filled pore network connectivity during wetting was higher than that during drying, resulting in enhanced gas transport parameters during the wetting process. The observed differences in water‐ and air‐filled pore networks during drying and wetting processes are highly promising for future multiphase mass transport models in soils.

H2 permeation and its influence on gases through a SAPO-34 zeolite membrane

This work analysed the permeation of binary and ternary H2-containing mixtures through a SAPO-34 membrane, aiming at investigating how hydrogen influences and its permeation is influenced by the presence of the other gaseous species, such as CO2 and CH4. We considered the behaviour of various gas mixtures in terms of permeability and selectivity at various temperatures (25–300 °C), feed pressures (400–1000 kPa) and compositions by means of an already validated mass transport model, which is based on surface and gas translation diffusion. We found that the presence of CO2 and CH4 in the H2-containing mixtures influences in a similar way the H2 permeation, reducing its permeability of about 80% compared to the single-gas value because of their stronger adsorption. On the other hand, H2 promotes the permeation of CO2 and CH4, causing an increment of their permeability with respect to those as single gases. These combined effects reflected in interesting selectivity values in binary mixture (e.g., CO2/H2 about 11 at 25 °C, H2/CH4 about 9 at 180 °C), which showed the potential of SAPO-34 membranes in treating of H2-containing mixtures.

Comparative investigation of a lattice Boltzmann boundary treatment of multiphase mass transport with heterogeneous chemical reactions.

Multiphase reactive transport in porous media is an important component of many natural and engineering processes. In the present study, boundary schemes for the continuum species transport-lattice Boltzmann (CST-LB) mass transport model and the multicomponent pseudopotential model are proposed to simulate heterogeneous chemical reactions in a multiphase system. For the CST-LB model, a lattice-interface-tracking scheme for the heterogeneous chemical reaction boundary is provided. Meanwhile, a local-average virtual density boundary scheme for the multicomponent pseudopotential model is formulated based on the work of Li etal. [Li, Yu, and Luo, Phys. Rev. E 100, 053313 (2019)10.1103/PhysRevE.100.053313]. With these boundary treatments, a numerical implementation is put forward that couples the multiphase fluid flow, interfacial species transport, heterogeneous chemical reactions, and porous matrix structural evolution. A series of comparison benchmark cases are investigated to evaluate the numerical performance for different pseudopotential wetting boundary treatments, and an application case of multiphase dissolution in porous media is conducted to validate the present models' ability to solve complex problems. By applying the present LB models with reasonable boundary treatments, multiphase reactive transport in various natural or engineering scenarios can be simulated accurately.

Numerical Analysis Nucleation and Growth Conditions of Single-Crystallinity Control during Laser Surface Modification of Ni-Based Single-Crystal Superalloy Part I: Thermal and Chemical Determinants

Nucleation and growth conditions of single-crystallinity control are convincingly elaborated by multi-scale mathematical modeling of heat and mass transport to totally abate undesirable weld defects, e.g. disoriented crystal and hot cracking inside molten pool of nonequilibrium crystallization, in order to illustrate the usefulness of predictive capability through theory and experiment procedures. Crystal growth is complicated by crystallinity-dependent thermal and chemical driving forces in front of dendrite tip during viable laser surface modification of Ni-based single-crystal superalloy. These two thermal metallurgical determinants play crucial role in crack-insusceptible columnar crystal growth, which is favorably oriented throughout weld depth. There is particular challenge in complete elimination of disoriented crystal, i.e. stray grain formation, for acceptable surface quality. Conservative (001)/[100] crystalline orientation is desired to diminish Al concentration and supersaturation, and morphologically satisfy epitaxial growth kinetics to successfully lessen central cracking with satisfactory variability of laser power and welding speed. Comparatively, (001)/[110] crystalline orientation is disadvantageous to asymmetrically augment Al concentration and supersaturation and aggressively increase interface instability, microstructure heterogeneity and hot cracking vulnerability along disoriented crystal boundaries. Disoriented crystal is increasingly withstood if the Al concentration and supersaturation in front of dendrite tip are low enough and crack-unsusceptible part is relatively large enough in case of attractive (001)/[100] crystalline orientation with optimal range of heat input to ameliorate microstructure homogeneity. Crystalline orientation region varies with diverse welding configurations, and epitaxy across solid/liquid interface is also sensitive to heat input of laser processing, which necessitate high efficient welding conditions optimization. Considerable effort is made to distinguish diffusion-driven crystal growth between a series of combinations of multiple welding conditions, such as critical welding configuration and heat input. Metallographically, the morphologies of crystal growth and hot cracking are experimentally observed to consistently support kinetics calculation result and well explain correlation between solidification behavior and crystal growth.

Modeling the Local Environment within Porous Electrode during Electrochemical Reduction of Bicarbonate

The electrochemical reduction of bicarbonate to renewable chemicals without external gaseous CO2 supply has been motivated as a means of integrating conversion with upstream CO2 capture. The way that CO2 is formed and transported during CO2-mediated bicarbonate reduction in flow cells is profoundly different from conventional CO2 saturated and gas-fed systems and a thorough understanding of the process would allow further advancements. Here, we report a comprehensive two-phase mass transport model to estimate the local concentration of species in the porous electrode resultant from homogeneous and electrochemical reactions of (bi)carbonate and CO2. The model indicates that significant CO2 is generated in the porous electrode during electrochemical reduction, even though the starting bicarbonate solution contains negligible CO2. However, the in situ formation of CO2 and subsequent reduction to CO exhibits a plateau at high potentials due to neutralization of the protons by the alkaline reaction products, acting as the limiting step toward higher CO current densities. Nevertheless, the pH in the catalyst layer exhibits a relatively smaller rise, compared to conventional electrochemical CO2 reduction cells, because of the reaction between protons and CO32– and OH– that is confined to a relatively small volume. A large fraction of the CL exhibits a mildly alkaline environment at high current densities, while an appreciable amount of carbonic acid (0.1–1 mM) and a lower pH exist adjacent to the membrane, which locally favor hydrogen evolution, especially at low electrolyte concentrations. The results presented here provide insights into local cathodic conditions for both bicarbonate cells and direct-CO2 reduction membrane electrode assembly cells utilizing cation exchange membranes facing the cathode.

Coupled Heat-Mass Transport Modelling of Radionuclide Migration from a Nuclear Waste Disposal Borehole

Disposal of radioactive waste originating from reprocessing of spent research reactor fuel typically includes stainless steel canisters with waste immobilised in a glass matrix. In a deep borehole disposal concept, waste packages could be stacked in a disposal zone at a depth of one to potentially several kilometres. This waste will generate heat for several hundreds of years. The influence of combining a natural geothermal gradient with heat from decaying nuclear waste on radionuclide transport from deep disposal boreholes is studied by implementing a coupled heat-solute mass transport modelling framework, subjected to depth-dependent temperature, pressure, and viscosity profiles. Several scenarios of waste-driven heat loads were investigated to test to what degree, if any, the additional heat affects radionuclide migration by generating convection-driven transport. Results show that the heat output and the calculated radioactivity at a hypothetical near-surface observation point are directly correlated; however, the overall impact of convection-driven transport is small due to the short duration (a few hundred years) of the heat load. Results further showed that the calculated radiation dose at the observation point was very sensitive to the magnitude of the effective diffusion parameter of the host rock. Coupled heat-solute mass transport models are necessary tools to identify influential processes regarding deep borehole disposal of heat-generating long-lived radioactive waste.

Is natural convection within an aquifer a critical phenomenon in deep borehole heat exchangers' efficiency?

Deep borehole heat exchangers (BHEs) can be utilised effectively for geothermal (heat) extraction from up to a few kilometres below the subsurface using the conventional closed U-loop or coaxial configurations. These systems take advantage of the high enthalpy energy in the deeper ground without relying on fracture flow extraction/injection, hence avoiding the complexity and uncertainty of hydraulic fracturing to enhance the permeability of deep aquifers. Despite the recent theoretical advancement in deep BHE systems, recent studies mainly assume conductive heat transfer in the ground, neglecting the effects of groundwater and heat convection (natural or forced) on the system’s thermal capacity. This simplified assumption could result in underestimating geothermal extraction efficiency given the extensive fluctuations in groundwater thermo-physical properties, particularly at high temperatures. Therefore, the ultimate goal of this study is to investigate the extent to which the thermal performance of deep coaxial borehole heat exchangers (CBHEs) is affected by natural convection in deep aquifers. This is achieved by developing a novel numerical approach for reliable quantification of thermal yield, accounting for conduction and the commonly overlooked thermo-induced convection in aquifers - using a tested 3D finite element heat and mass transport model. Considering groundwater parameters’ temperature dependency, the resultant buoyancy in groundwater and the effects of gravity, parametric studies are undertaken for various ranges of permeability, carrier fluid velocity and CBHEs depth. The overall validity of the model is tested against published experimental data. It is concluded that higher carrier fluid inflow rates for a given CBHE depth can lead to up to 43% higher CBHEs thermal efficiency when the aquifer’s permeability is high (k = 10−10 m2). Furthermore, the results indicate that a higher aquifer permeability, hence a substantial thermo-induced heat exchange in the aquifer, has a more pronounced effect on CBHEs thermal yield than carrier fluid inflow rate in shorter CBHEs (63% vs 17% increase), which contradicts the behaviour of longer CBHEs in which the thermo-induced convective heat transfer in aquifers with higher permeability, i.e., k = 10−10 m2 and carrier fluid inflow rate could have a similar effect on the system’s efficiency (45% vs 43% increase). In general, it is concluded that an accurate evaluation of how system parameters such as the inflow rate and CBHE’s depth could contribute to CBHE’s thermal yield requires a good understanding of the impacts of aquifer’s characteristics, i.e., temperatures, permeability and depth on thermo-induced heat exchange in the aquifer, which is facilitated using the proposed numerical model.

Effects of coupling of mass transport and blood viscosity models for microchannel flows

In this study, various aspects of a continuum transport model for blood, which is treated as a suspension of red blood cells, are thoroughly investigated. Earlier, treating blood as a suspension of rigid spherical particles in plasma was reasonably successful in mimicking flow dynamics in microchannels of size 40 μ m , comparable to 4 μ m , the dimension of a red blood cell (RBC). However, it is still not entirely clear whether such success owes to the coupling of mass and momentum transport, or to a sophisticated viscosity model for blood. To understand this in detail, we obtain semi-analytical solutions to the continuum model, in the presence and absence of the coupling of mass transport of RBCs, that connects the hematocrit concentration to the local viscosity, for fully developed blood flow in circular and rectangular microchannels. In this study, the transport of RBCs in flowing fluid is modeled by the diffusive flux model (DFM). Thus, overall, we have a hierarchy of continuum models using various viscosity models for blood, with progressive inclusion of physical complexities. Our results clearly highlight the importance of such a coupled approach, without which the results are quantitatively, and sometimes even qualitatively, different. In addition, our study serves as a thorough comparison of different viscosity models for blood, especially the steady state and transient models, recently proposed by Apostolidis and Beris (2014) and Apostolidis et al. (2015), respectively. We observe that, though the transient model reduces exactly to the description by the steady model over a range of low to moderate shear rates, the transient model shows some differences, especially for the RBC concentration in the low shear rate region. In the semi-analytical framework, the Darcy friction factor and cell free layer thickness have also been computed for circular cross-sections and a range of aspect ratios of a rectangular microchannel. Our results also indicate that the cell free layer attains a constant thickness when the aspect ratio of a rectangular microchannel reaches a critical maximum value for a specified average hematocrit. • Rectangular microchannel flow is investigated by coupling with the transport of RBC. • Even a finely tuned viscosity model without RBC transport is shown to be inadequate. • Frictional characteristics are derived in the form of a semi-analytical solution. • The model is found to predict the cell free layer thickness quite well. • The steady viscosity model overpredicts WSS when compared to the transient model.

Continuum-Scale Gas Transport Modeling in Organic Nanoporous Media Based on Pore-Scale Density Distributions

SummaryWe present a continuum-scale mass transport model informed by pore-scale density distribution for gas diffusion through organic nanoporous media. A diffusion model and a sorption model are developed by considering multiple transport and storage mechanisms, including bulk diffusion and Knudsen diffusion for free phase, and surface diffusion and multilayer adsorption for sorbed phase. The continuum-scale diffusion equation is derived based on the free-phase concentration for the overall mass conservation of free and sorbed phases, carrying a newly defined effective diffusion coefficient and capacity factor to account for multilayer adsorption. Diffusion in free and sorbed phases is coupled with the sorption model, which provides pore-scale multilayer adsorption properties by utilizing a pore-scale simplified local density (SLD) method combined with the modified Peng-Robinson equation of state (PR-EOS) for confinement effect. The model was first implemented to analyze adsorption data from a krypton (Kr) adsorption experiment on graphite. Then, we applied the developed diffusion model to conduct the sensitivity analysis of the effects of pore size on gas transport for Kr-graphite and methane-coal systems. The model was finally used to study Kr diffusion profiles through a coal matrix obtained by using X-ray micro-computed tomography (microCT) imaging. The results show that the sorbed phase occupies most of the pore space in organic nanopores with less than 10 nm due to multilayer adsorption, and surface diffusion contributes significantly to the total mass flux. Therefore, neglecting the volume of sorbed phase and surface diffusion in organic nanoporous rocks may result in considerable errors in the prediction of hydrocarbon production. We also compared Brunauer-Emmett-Teller (BET) and Langmuir models by analyzing adsorption data for the wide pressure range up to the saturation pressure. The comparison between BET and Langmuir models shows that the Langmuir model can only match the adsorption isotherm at low pressure and yield lower effective surface diffusion coefficients. Therefore, implementing a Langmuir model may be erroneous for organic nanoporous media with strong adsorption capacity, particularly when pore pressure is high.

Modelling of mass transport and distribution of aptamer in blood-brain barrier for tumour therapy and cancer treatment

The blood-brain barrier (BBB) is a strong barrier against the entrance of drugs, which has made brain cancer treatment a major challenge. We have previously shown that targeting transferrin receptors using aptamers increased brain drug delivery. To get a better understanding of this phenomenon, in the present article, a mathematical model based on the finite element method was developed accounting for the fluid flow and mass transport of the aptamer molecule inside an 8 µm capillary vessel across a 14 µm blood-brain barrier domain. The fluid flow and mass transport equations were coupled to calculate the blood velocity and aptamer concentration profiles across the BBB. It was identified that the thickness of the astrocyte and endothelial cell layers are key parameters affecting the concentration of the aptamer delivered to the last neuron dendrites in the BBB. The predicted efficacy of the drug delivery (Capt/Cin) of 10.9% to 13.8% was calculated at a porosity of 0.5 to 0.9, respectively, at a blood velocity of 0.38 mm/s, which was independent of the inlet concentration of the aptamer. This low efficacy was attributed to the mass transfer resistance across endothelial cells, astrocyte and pericyte layers, which decreased the concentration by 6.7%. It was also identified that the main mechanism of drug delivery is switched from convective mass transport in the capillary layer (with Peclet number > 50) to mixed convection mass transport (1 < Peclet number < 5) in the porous layers and to diffusion only once aptamer reached the brain parenchyma (Peclet number < 1).