Microscale Transport Processes Research Articles

Bingham plastic fluids flow analysis in multimembranes fitted porous medium

A mathematical analysis is presented for the flow of a Bingham plastic fluid propelled by the multi-membranes pumping mechanism through porous media. Two successive membranes with different amplitude, diameter, and phase lag, are fitted at the upper wall of the channel, and the lower wall is stationary. Due to the simultaneous propagation of both membranes, the pressure is generated at the membrane's position, which helps in propelling the fluids in forward and backward directions depending upon the compression and expansion cycles of the membranes. The low Reynolds number assumption and lubrication theory are utilized to linearize the governing equations, which are further analytically derived, and then employing MATLAB codes to compute the illustrations for the interpretation of the results. The effects of key parameters like plug flow region, pore size and diameter of membranes on the velocity field, wall shear stress, pressure gradient, fanning friction factor, head loss and particle trajectories, are analysed in the microchannel. Results of the present model conclude that the geometrical properties of membranes, rheological properties of fluids and porosity of the medium significantly alter the flow and pumping characteristics which give valuable insights for the design of micro-valve less pumping actuators to be aimed at controlling microscale transport processes in various medical diagnoses and treatments.

Spreadsheet analysis of the field-driven start-up flow in a microfluidic channel.

We discuss, in this article, the solution method of the unsteady electroosmotic flow of Newtonian fluid in a square microfluidic channel cross-section in the framework of spreadsheet analysis. We demonstrate the implementation of the finite difference scheme, which is used for the discretization of the transport equations governing the flow dynamics of the present problem, in the spreadsheet tool. Also, we have shown the implementation details of different boundary conditions, which are typically used for the underlying electrohydrodynamics in a microfluidic channel, in the spreadsheet analysis tool. We show that the results obtained from the spreadsheet analysis match accurately with the numerical solutions for both the electrostatic potential distribution and the flow velocity. Our results of this analysis justify the credibility of the spreadsheet tool for capturing the intricate details of the electrically actuated microflows during the initial transiences, that is, for the start-up flows and the phenomenon due to the electrical double layer effect, quite effectively. The inferences of this analysis will open up a new research paradigm of microfluidics and microscale transport processes by providing the potential applicability of the spreadsheet tools to obtain the flow physics of our interest in a very intuitive and less expensive manner.

Coupled lattice Boltzmann simulation method for bidomain type models in cardiac electrophysiology with multiple time-delays

In this work, we propose a mathematical model of the cardiac electrophysiology which take into account time delays in signal transmission, in order to capture the whole activities of macro- to micro-scale transport processes, and use this model to analyze the propagation of electrophysiological waves in the heart by using a developed coupling Lattice Boltzmann Method (LBM). The propagation of electrical activity in the heart is mathematically modeled by a modified bidomain system. As transmembrane potential evolves, the domain has anisotropical properties which are transposed into intracellular and extracellular conductivity. The new bidomain system is a multi-scale, stiff and strongly nonlinear coupled reaction-diffusion model in the shape of a set of ordinary differential equations coupled with a set of partial differential equations with multiple time delays. Due to delays, dynamic and geometry complexity, numerical simulation and implementation of this type of coupled systems are very ambitious mathematical and computational problems but are crucial in several biomedical applications. We introduce a modified LBM scheme, reliable, efficient, stable and easy to implement in the context of such bidomain systems with multiple time delays. Numerical tests to confirm effectiveness and accuracy of our approach are provided and, the influence and impact of delays to restore normal heart rhythm are analyzed.

Mathematical modeling and analysis of dynamic effects of multiple time-varying delays on electrophysiological wave propagation in the heart

In this work, we propose a mathematical model of the cardiac electrophysiology which takes into account time delays in signal transmission, in order to capture the whole activities of macro- to micro-scale transport processes, and use this model to analyze the propagation of electrophysiological waves in the heart. The propagation of electrical activity in the heart is mathematically modeled by a modified bidomain system. As transmembrane potential evolves, the domain has anisotropical properties which are transposed into intracellular and extracellular conductivity. The new bidomain system is a multi-scale, stiff and strongly nonlinear coupled reaction–diffusion model in the shape of a set of ordinary differential equations coupled with a set of partial differential equations with multiple time delays. First, the mathematical models are introduced. Afterward the existence and uniqueness of solution of the state equation are proved as well as stability result. A numerical calculation is performed by using a coupling Lattice Boltzmann Method.

Coupled lattice Boltzmann method for numerical simulations of fully coupled heart and torso bidomain system in electrocardiology

In this work, a modified coupling Lattice Boltzmann Model (LBM) in simulation of cardiac electrophysiology is developed in order to capture the detailed activities of macro- to micro-scale transport processes. The propagation of electrical activity in the human heart through torso is mathematically modeled by bidomain type systems. As transmembrane potential evolves, we take into account domain anisotropical properties using intracellular and extracellular conductivity, such as in a pacemaker or an electrocardiogram, in both parallel and perpendicular directions to the fibers. The bidomain system represents multi-scale, stiff and strongly nonlinear coupled reaction-diffusion models that consist of a set of ordinary differential equations coupled with a set of partial differential equations. Due to dynamic and geometry complexity, numerical simulation and implementation of bidomain type systems are extremely challenging conceptual and computational problems but are very important in many real-life and biomedical applications. This paper suggests a modified LBM scheme, reliable, efficient, stable and easy to implement in the context of such bidomain systems. Numerical tests to confirm effectiveness and accuracy of our approach are provided and the propagation of electrophysiological waves in the heart is analyzed.

Microphysics in Astrophysical Plasmas

Although macroscale features dominate astrophysical images and energetics, the physics is controlled through microscale transport processes (conduction, diffusion) that mediate the flow of mass, momentum, energy, and charge. These microphysical processes manifest themselves in key (all) boundary layers and also operate within the body of the plasma. Crucially, most plasmas of interest are rarefied to the extent that classical particle collision length- and time-scales are long. Collective plasma kinetic phenomena then serve to scatter or otherwise modify the particle distribution functions and in so-doing govern the transport at the microscale level. Thus collisionless plasmas are capable of supporting thin shocks, current sheets which may be prone to magnetic reconnection, and the dissipation of turbulence cascades at kinetic scales. This paper lays the foundation for the accompanying collection that explores the current state of knowledge in this subject. The richness of plasma kinetic phenomena brings with it a rich diversity of microphysics that does not always, if ever, simply mimic classical collision-dominated transport. This can couple the macro- and microscale physics in profound ways, and in ways which thus depend on the astrophysical context.

Electrowetting of evaporating extended meniscus

The natural tendency of the contact line of an extended curved meniscus to retract on application of heat is countered using electrowetting. The effect of electrowetting during evaporation is experimentally evaluated by measuring the thickness profile of a meniscus near the microscopic contact line region using image analyzing interferometry. The system consists of a meniscus of surfactant (SDS) laden water film over a silicon substrate (with native oxide) subjected to heating followed by incremental imposition of electric fields. Results show that the resultant electrostatic pressure enhances suction towards the hot spot and the subsequent spreading can offset meniscus retraction. Additional insights into the related microscale transport processes including in situ evaluation of the Hamaker constant are obtained through a comprehensive model using the augmented Young–Laplace equation, interfacial phase transfer and lubrication theory. A comparison of average heat flux for conditions with and without electric field (∼8 V) demonstrates substantial (more than 100%) enhancement, highlighting the potential of electrowetting in micro-cooling applications.

A Review of Microscale Transport in the Thermal Processing of New and Emerging Advanced Materials

This paper reviews the microscale transport processes that arise in the fabrication of advanced materials. In many cases, the dimensions of the device being fabricated are in the micrometer length scale and, in others, underlying transformations that determine product quality and characteristics are at micro- or nanoscale levels. The basic considerations in these transport phenomena are outlined. A few important materials processing circumstances are considered in detail. These include the fabrication of multilayer and hollow optical fibers, as well as those where micro- and nanoscale dopants are added to achieve desired optical characteristics, thin film fabrication by chemical vapor deposition, and microscale coating of fibers and devices. It is shown that major challenges are posed by the simulation and experimentation, as compared with those for engineering or macroscale dimensions. These include accurate simulation to capture large gradients and variations over relatively small dimensions, simulating high pressures and viscous dissipation effects in microchannels, modeling effects such as surface tension that become dominant at microscale dimensions, and coupling micro- and nanoscale mechanisms with boundary conditions imposed at the macroscale. Similarly, measurements over microscale dimensions are much more involved than those over macro- or industrial scales because of difficult access to the regions of interest, relatively small effects such as tension, buoyancy effects, viscous rupture, bubble entrapment, and other mechanisms that are difficult to measure and that can make the process infeasible. It thus becomes difficult to achieve desired accuracy for validating the mathematical and numerical models. This paper reviews some of the approaches that have been adopted to overcome these difficulties. Comparisons between experimental and numerical results are included to show fairly good agreement, indicating the validity of the modeling of transport.

Role of solid surface structure on evaporative phase change from a completely wetting corner meniscus

The transport processes that occur at small length scales are greatly influenced by interfacial and intermolecular forces. Surface roughness at the nanoscale generates additional intermolecular interactions that arise due to the increased surface area. In this work, we have experimentally studied how the magnitude as well as the shape of surface roughness influences the microscale transport processes that occur in the contact line region of a liquid corner meniscus. The surface roughness contribution to the interaction potential was calculated and a direct relationship between the wetting properties of the liquid and the underlying surface properties was obtained. Since the underlying roughness alters the surface potential, the shape of the meniscus and in turn, the resulting capillary and disjoining pressure forces also changed. Atomic force microscopy was utilized to obtain a detailed characterization of the shape of the prepared surfaces. Surface morphology features were obtained from a height-height correlation function. These features were related to the wetting and transport properties of the meniscus at the contact line. Finally, the modified capillary and disjoining pressure forces on the structured surfaces were observed to influence the evaporative heat transfer from the corner meniscus.

An X-Ray Tomography Based Lattice Boltzmann Simulation Study on Gas Diffusion Layers of Polymer Electrolyte Fuel Cells

This work reports a feasibility study into the combined full morphological reconstruction of fuel cell structures using X-ray computed micro- and nanotomography and lattice Boltzmann modeling to simulate fluid flow at pore scale in porous materials. This work provides a description of how the two techniques have been adapted to simulate gas movement through a carbon paper gas diffusion layer (GDL). The validation work demonstrates that the difference between the simulated and measured absolute permeability of air is 3%. The current study elucidates the potential to enable improvements in GDL design, material composition, and cell design to be realized through a greater understanding of the nano- and microscale transport processes occurring within the polymer electrolyte fuel cell.

Mixing-controlled biodegradation in a toluene plume — Results from two-dimensional laboratory experiments

Various abiotic and biotic processes such as sorption, dilution, and degradation are known to affect the fate of organic contaminants, such as petroleum hydrocarbons in saturated porous media. Reactive transport modeling of such plumes indicates that the biodegradation of organic pollutants is, in many cases, controlled by mixing and therefore occurs locally at the plume's fringes, where electron donors and electron-acceptors mix. Herein, we aim to test whether this hypothesis can be verified by experimental results obtained from aerobic and anaerobic degradation experiments in two-dimensional sediment microcosms. Toluene was selected as a model compound for oxidizable contaminants. The two-dimensional microcosm was filled with quartz sand and operated under controlled flow conditions simulating a contaminant plume in otherwise uncontaminated groundwater. Aerobic degradation of toluene by Pseudomonas putida mt-2 reduced a continuous 8.7 mg L − 1 toluene concentration by 35% over a transport distance of 78 cm in 15.5 h. In comparison, under similar conditions Aromatoleum aromaticum strain EbN1 degraded 98% of the toluene infiltrated using nitrate (68.5 ± 6.2 mg L − 1 ) as electron acceptor. A major part of the biodegradation activity was located at the plume fringes and the slope of the electron-acceptor gradient was steeper during periods of active biodegradation. The distribution of toluene and the significant overlap of nitrate at the plume's fringe indicate that biokinetic and/or microscale transport processes may constitute additional limiting factors. Experimental data is corroborated with results from a reactive transport model using double Monod kinetics. The outcome of the study shows that in order to simulate degradation in contaminant plumes, detailed data sets are required to test the applicability of models. These will have to deal with the incorporation of existing parameters coding for substrate conversion kinetics and microbial growth.

Experimental Investigation of Evaporation and Condensation in the Contact Line Region of a Thin Liquid Film Experiencing Small Thermal Perturbations

Image-analyzing interferometry technique is successfully used to study microscale transport processes related to a curved microfilm on a solid substrate. Digital image processing is used to analyze the images of interference fringes, leading to the evaluation of liquid (heptane) film thickness and curvature profiles at different inclinations on a high refractive index glass surface. The curvature profiles obtained at different inclinations clearly demonstrate that there is a maximum in curvature near the junction of the adsorbed film (of uniform thickness) and the curved film, and then it becomes constant in the thicker portions of the film. The adsorbed film thickness is measured for horizontal as well as inclined positions. Experimentally obtained values of the dispersion constants are compared to those predicted from the Dzyaloshinskii-Lifshitz-Pitaevskii (DLP) theory, and reasonable agreements were obtained. A parameter alpha is defined and experimentally evaluated to quantify the closeness of the system to equilibrium. The nonequilibrium behavior of this parameter alpha is also observed with certain heat input at a particular inclination. A small thermal perturbation is used to force the liquid meniscus to undergo a cycle of alternating condensation and evaporation. High-speed video-microscopy and subsequent image analysis are used for data analysis. The numerical solution of a model that takes into account the balance between the suction and the capillary force is compared with the data to elicit new insights into the evaporation/condensation phenomena and to estimate the interfacial temperature differences for near-equilibrium situations.

Electrokinetic transport through rough microchannels.

Surface roughness is present in most microfluidic devices as a result of the microfabrication techniques or particle adhesion. It is highly desirable to understand the roughness effect on microscale transport processes. In this study, we developed a 3-D, finite-volume-based numerical model to simulate electroosmotic transport in microchannels with rectangular prism rough elements on the surfaces. Various configurations of roughness were investigated, and the results show different degrees of an even-out effect on liquid transport due to the roughness-induced local pressure field and the variation of the electroosmotic slip boundary velocities. 3D-sample transport through rough microchannels was analyzed. The results demonstrate that the sample's transport under the electrical field is much faster in the pathway between the rough elements; the concentration field in the height and width direction is not uniform. The influence of the electrokinetic properties on liquid flow and sample transport was studied. It was found that the increase of the electroosmotic mobility or the decrease of the electrophoretic mobility can dramatically enhance the uniformity of the concentration field.

Microscale Transport Processes in the Evaporator of a Constrained Vapor Bubble

Microgravity experiments on a constrained vapor bubble heat exchanger (CVB) are being developed for the space station. Results are presented of precursory experiments and modeling on microscale transport processes in the evaporator of the vertical constrained vapor bubble in the Earth's environment. A nonisothermal experimental setup was designed and built to study heat transfer and fluid flow in an ethanol/quartz vertical CVB system. Temperature profiles were measured using an in situ Labview® data acquisition system via thermocouples. Film thickness profiles were measured using image analyzing interferometry. A mathematical model was developed to yield the liquid film curvature profile in the evaporator. Experimentally measured curvature profiles were in good agreement with modeling results. A theoretical relation between the curvature and temperature profiles in the Earth's environment was developed. Under microgravity conditions, an analytical expression that reveals an inherent relation between temperature and liquid film curvature profiles was derived for the first time.

Optical Evaluation of the Effect of Curvature and Apparent Contact Angle in Droplet Condensate Removal

The microscale transport processes in droplet condensation and removal due to interfacial phenomena were studied. In particular, this paper concerns the movement of a condensed ethanol sessile drop into a concave liquid film in the corner. An improved image analyzing procedure was used to evaluate the curvatures and contact angles for both the drop and the concave corner meniscus at different condensation rates. The experimental results demonstrated that the condensate removal rate was a function of the curvature and contact angle, which self-adjust to give the necessary force field. The use of a dimensionless, shape dependent, force balance was demonstrated. For small drops, the intermolecular force was found to be much larger than the gravitational force and dominated droplet removal. Microscale pressure fields can be experimentally measured whereas interfacial temperature differences cannot.

Nucleation, growth and surface movement of a condensing sessile droplet

The near-equilibrium microscale transport processes in a system composed of a small condensing sessile drop subsequently removed by capillarity into a corner meniscus were studied. Experimental results on the following three stages for ethanol with a small contact angle on heat-treated fused quartz were analyzed: droplet nucleation, droplet growth and the transfer of the liquid from the drop to the corner meniscus. The dynamic character of the experiment allowed the heterogeneous condensation/removal cycle to be related to the chemical potential gradient, which is a function of the excess free energy (due to the liquid shape) and an excess temperature. The liquid thickness profile and contact angle were obtained using image analyzing interferometry in which the interference fringes were recorded using a video camera attached to a microscope. The capillary pressure, the polar and apolar components of the spreading coefficient, and the excess free energy were obtained from the equilibrium thickness profile data and the extended Young–Laplace equation. Using the derivative of the excess free energy per unit volume, flat film thicknesses in the film thickness range 0.6< δ <6.2 nm were found to be unstable. Transient profile data also gave the nucleation rate, the condensation heat flux and the liquid flow field on the substrate. The temperature field was related to the condensation flux and the pressure field using a Kelvin–Clapeyron (chemical potential) model for intefacial mass flux. Non-measurable interfacial temperature differences of the order of 10 −4 K can generate easily measurable changes in the excess free energy. Extremely small interfacial temperature differences have a large effect on transport processes. We find that there are sufficient interfacial models and experimental measurement techniques available to describe the nucleation, growth, and surface removal of a condensing partially wetting sessile droplet.

OPTICAL MEASUREMENT OF MICROSCALE TRANSPORT PROCESSES IN DROPWISE CONDENSATION

The optimum use of interfacial free-energy gradients to control fluid flow in small regions naturally leads to simpler passive heat transfer systems. In this context, "passive" refers to the natural pressure field for fluid flow due to changes in the intermolecular force field resulting from an imposed nonisothermal temperature field. Although the particular constrained vapor bubble (CVB) discussed can be viewed as a large version of a wickless heat pipe, it is a much more general heat transfer concept. Herein, it is an ideal system for the optical study of microscale transport processes in droplet condensation due to interfacial phenomena. This article concerns the movement of a single condensed ethanol sessile drop into a concave liquid film. The intermolecular force is found to be much larger than the gravitational force and dominates condensate removal. A dimensionless force balance for viscous shear stress demonstrates the effect of changes in the contact angle and curvature. A dimensionless difference in free energy is identified as the cause of spontaneous condensate removal.

3D imaging of porous media using laser scanning confocal microscopy with application to microscale transport processes

We present advances in the application of laser scanning confocal microscopy (LSCM) to image, reconstruct, and characterize statistically the microgeometry of porous geologic and engineering materials. We discuss technical and practical aspects of this imaging technique, including both its advantages and limitations. Confocal imaging can be used to optically section a material, with sub-micron resolution possible in the lateral and axial planes. The resultant volumetric image data, consisting of fluorescence intensities for typically ~50 million voxels in XYZ space, can be used to reconstruct the three-dimensional structure of the two-phase medium. We present several examples of this application, including studying pore geometry in sandstone, characterizing brittle failure processes in low-porosity rock deformed under triaxial loading conditions in the laboratory, and analyzing the microstructure of porous ceramic insulations. We then describe approaches to extract statistical microgeometric descriptions from volumetric image data, and present results derived from confocal volumetric data sets. Finally, we develop the use of confocal image data to automatically generate a three-dimensional mesh for numerical pore-scale flow simulations.