Field-driven dynamics of dilute gases, viscous liquids and polymer chains

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2007.Includes bibliographical references (p. [131]-136).This thesis is concerned with the exploration of field-induced dynamical phenomena arising in dilute gases, viscous liquids and polymer chains. The problems considered herein pertain to the slip-induced motion of a rigid, spherical or nonspherical particle in a fluid in the presence of an inhomogeneous temperature or concentration field or an electric field, and the dynamics of charged polymers animated by the application of an electric field. The problems studied in this thesis are unified by the existence of a separation of length scales between the macroscopic phenomena of interest and their microscopic underpinnings, and are treated by means of coarse-graining principles that exploit this scale separation. Specifically, the first part of this thesis investigates the dynamics caused by the existence of a slip velocity at a fluid-solid interface. The macroscopic slip boundary condition obtains from the asymptotic matching of the velocity within the microscale layer of fluid adjoining the solid surface, and the velocity in the bulk fluid. In the case of a gas, the microscopic length scale is constituted by the mean free path, and the layer of gas adjoining the solid boundary having a thickness of the order of the mean free path is referred to as the Knudsen layer. The parameter representing the ratio of the mean free path to the macroscopic length scale is the Knudsen number, denoted Kn. The widely-used Navier-Stokes and Fourier equations are valid away from the solid boundary at distances large compared to the mean free path in the limit Kn < 1, and necessitate the imposition of continuum boundary conditions on the gas velocity and temperature at the outer limit of the Knudsen layer. These macroscopic equations are typically solved subject to the no-slip of velocity and the equality of the gas and solid temperatures at the solid boundary.(cont) However, as first pointed out by Maxwell, the no-slip boundary condition fails to explain experimentally observed phenomena when imposed at the surface of a nonuniformly heated solid, and must be replaced by the thermal slip condition obtained via the asymptotic matching of the velocity within the Knudsen layer with that in the bulk gas. Slip has also been proposed to occur at liquid-solid boundaries under conditions of inhomogeneous temperature or concentration. In this thesis, we extend Faxen's laws for the force and torque acting on a spherical particle in a fluid with a prescribed undisturbed flow field to account for the existence of fluid slip at the particle surface. Additionally, we investigate the effect of particle asymmetry by studying the motion of a slightly deformed sphere in a fluid having a uniform unperturbed flow field, and demonstrate that the velocity of a force- and torque-free particle is independent of its size or shape. While the slip-induced motions studied in this thesis are presented in the context of thermally-induced slip arising from the existence of a temperature gradient, the results are equally applicable to more general phoretic transport, encompassing the electrokinetic slip condition employed in the treatment of charged particle dynamics in an electrolytic liquid. Analogous to the thermal slip condition imposed on a gas at the outer limit of the Knudsen layer, the electrokinetic slip condition is imposed at the outer limit of the layer of counterions surrounding a charged surface in an electrolytic liquid. The studies presented in this thesis have potential applications in aerosol and colloid technology, in the nonisothermal transport of particulates in porous media and MEMS devices, and in the electrophoresis of charged bodies. The behavior of a charged polymer molecule in an electric field constitutes the subject of the second part of this thesis.(cont) Motivated by the medical and technological necessity to effect the size-separation of DNA chains in applications ranging from the Human Genome Project to DNA-based criminology, we consider specifically the dynamics of electric-field driven DNA chains in size-based separation devices. The conventional technique of constant-field gel electrophoresis is ineffective in achieving the separation of long DNA chains whose sizes exceed a few tens of kilobase pairs, owing to the fact that the velocity becomes independent of chain size for long chains in a gel. This limitation of gel electrophoresis has spurred the development of alternative separation devices, such as obstacle courses confined to microchannels wherein the obstacles may be either microfabricated or formed from the self-assembly of paramagnetic beads into columns upon the imposition of a magnetic field transverse to the channel plane. Size separation in the latter devices arises from the fact that longer chains, when driven through the channel by an applied electric field, are more likely to collide with the obstacles and take longer to disentangle from the obstacle once a collision has occurred, relative to shorter chains. Consequently, a longer chain requires more time to traverse the array compared to a shorter chain. As a model for the transient chain stretching occurring subsequent to the collision of an electrophoresing DNA molecule with an obstacle, we study the unraveling of a single, tethered polymer molecule in a uniform solvent flow field. In the context of a polymer, the microscopic length scale is associated with the size of a monomer. We, however, employ a coarse-grained representation wherein the polymer is modeled by a chain of entropic springs connected by beads, with each bead representing several monomers, thereby enabling a continuum description of the solvent. We adopt the method of Brownian dynamics applied to the bead-spring model of the polymer chain.(cont) We consider both linear force-extension behavior, representative of chain stretching in a weak field, and the finitely-extensible wormlike chain model of DNA elasticity, which dominates chain stretching under strong fields. The results yield insight into the mechanism of tension propagation during chain unraveling, and are more generally applicable to situations involving transient stretching, such as chain interactions arising in entangled polymer solutions. We next conduct investigations of chain dynamics in obstacle-array based separation devices by means of coarse-grained stochastic modeling and Brownian dynamics simulation of a chain in a self-assembled array of magnetic beads, and predict the separation achievable among different chain sizes. We examine the influence of key parameters, namely, the applied electric field strength and the spacing between obstacles, on the separation resolution effected by the device. Our results elucidate the mechanisms of DNA dynamics in microfluidic separation devices, and are expected to aid in the design of DNA separation devices and the selection of parameters for their optimal operation.by Aruna Mohan.Ph.D

High resolution modeling of transport in porous media

This dissertation presents research on the pore-level modeling of transport in porous media. The focus of this work is on high-resolution modeling, a rigorous approach that represents detailed geometry and first-principle physics at the streamline scale. Three major topics are presented in this dissertation: an efficient approach for solving Stokes flow in essentially arbitrary disordered porous media, high-resolution versus network simulations of dispersion phenomena, and a stochastic model for solving interfacial mass transfer from source spheres in porous media. First an approach was developed for solving the Stokes flow problem in a comparatively large, very heterogeneous two-dimensional porous media with high efficiency using a combined domain decomposition and boundary element method. The second topic discussed in this dissertation is the high-resolution and network simulation of dispersion in the porous media for the purpose of evaluating network discretization effects for the hydrodynamic model and the nodal mixing assumption for the solute transport model. It was found that molecular diffusion is not resolved properly with the nodal mixing assumption in the high Peclet number range. The third topic was the development of a stochastic model for simulating interfacial mass transfer from the surface of a single source sphere in a heterogeneous porous medium, which is valid in both low and high Peclet number range

Nonlinear Dynamic Modeling, Simulation And Characterization Of The Mesoscale Neuron-electrode Interface

Extracellular neuroelectronic interfacing has important applications in the fields of neural prosthetics, biological computation and whole-cell biosensing for drug screening and toxin detection. While the field of neuroelectronic interfacing holds great promise, the recording of high-fidelity signals from extracellular devices has long suffered from the problem of low signal-to-noise ratios and changes in signal shapes due to the presence of highly dispersive dielectric medium in the neuron-microelectrode cleft. This has made it difficult to correlate the extracellularly recorded signals with the intracellular signals recorded using conventional patch-clamp electrophysiology. For bringing about an improvement in the signalto-noise ratio of the signals recorded on the extracellular microelectrodes and to explore strategies for engineering the neuron-electrode interface there exists a need to model, simulate and characterize the cell-sensor interface to better understand the mechanism of signal transduction across the interface. Efforts to date for modeling the neuron-electrode interface have primarily focused on the use of point or area contact linear equivalent circuit models for a description of the interface with an assumption of passive linearity for the dynamics of the interfacial medium in the cell-electrode cleft. In this dissertation, results are presented from a nonlinear dynamic characterization of the neuroelectronic junction based on Volterra-Wiener modeling which showed that the process of signal transduction at the interface may have nonlinear contributions from the interfacial medium. An optimization based study of linear equivalent circuit models for representing signals recorded at the neuron-electrode interface subsequently iv proved conclusively that the process of signal transduction across the interface is indeed nonlinear. Following this a theoretical framework for the extraction of the complex nonlinear material parameters of the interfacial medium like the dielectric permittivity, conductivity and diffusivity tensors based on dynamic nonlinear Volterra-Wiener modeling was developed. Within this framework, the use of Gaussian bandlimited white noise for nonlinear impedance spectroscopy was shown to offer considerable advantages over the use of sinusoidal inputs for nonlinear harmonic analysis currently employed in impedance characterization of nonlinear electrochemical systems. Signal transduction at the neuron-microelectrode interface is mediated by the interfacial medium confined to a thin cleft with thickness on the scale of 20-110 nm giving rise to Knudsen numbers (ratio of mean free path to characteristic system length) in the range of 0.015 and 0.003 for ionic electrodiffusion. At these Knudsen numbers, the continuum assumptions made in the use of Poisson-Nernst-Planck system of equations for modeling ionic electrodiffusion are not valid. Therefore, a lattice Boltzmann method (LBM) based multiphysics solver suitable for modeling ionic electrodiffusion at the mesoscale neuron-microelectrode interface was developed. Additionally, a molecular speed dependent relaxation time was proposed for use in the lattice Boltzmann equation. Such a relaxation time holds promise for enhancing the numerical stability of lattice Boltzmann algorithms as it helped recover a physically correct description of microscopic phenomena related to particle collisions governed by their local density on the lattice. Next, using this multiphysics solver simulations were carried out for the charge relaxation dynamics of an electrolytic nanocapacitor with the intention of ultimately employing it for a simulation of the capacitive coupling between the neuron and the v planar microelectrode on a microelectrode array (MEA). Simulations of the charge relaxation dynamics for a step potential applied at t = 0 to the capacitor electrodes were carried out for varying conditions of electric double layer (EDL) overlap, solvent viscosity, electrode spacing and ratio of cation to anion diffusivity. For a large EDL overlap, an anomalous plasma-like collective behavior of oscillating ions at a frequency much lower than the plasma frequency of the electrolyte was observed and as such it appears to be purely an effect of nanoscale confinement. Results from these simulations are then discussed in the context of the dynamics of the interfacial medium in the neuron-microelectrode cleft. In conclusion, a synergistic approach to engineering the neuron-microelectrode interface is outlined through a use of the nonlinear dynamic modeling, simulation and characterization tools developed as part of this dissertation research

Porous media drying and two-phase flow studies using micromodels

In this thesis, we report an investigation of porous media drying and steady-state two-phase flow behaviour at the pore scale using micromodels based on thin section images of real rocks. Fluid distributions (and the deposition of solid salt in the case of drying) were imaged in real-time using optical microscopy. Computer simulations of the two-phase flow was initially compared to micromodel experiments and then used to predict behaviour in geometries not available in the lab. We performed evaporation experiments on a 2.5D etched-silicon/glass micromodel based on a thin section image of a sucrosic dolomite carbonate rock at different wetting conditions. NaCl solutions from 0 wt% (deionized water) to 36 wt% (saturated brine) were evaporated by passing dry air through a channel in front of the micromodel matrix. For deionized water in a water-wet model, we observed the three classical periods of evaporation: the constant rate period (CRP) in which liquid remains connected to the matrix surface, the falling rate period (FRP) and the receding front period (RFP), in which the capillary connection is broken and water transport becomes dominated by vapour diffusion. The length of the deionized water CRP was much shorter for a uniformly oil-wet model, but mixed wettability made little difference to the drying process. For brine systems in water-wet and mixed-wet micromodels, the evaporation rate became linear with the square root of time after a short CRP. Although this appears similar to the RFP for water, salt continued to be deposited at the external surface of the matrix during this period indicating that a capillary connection was maintained. The reduction of evaporation rate appears to be due to the deposited salt acting as a partial barrier to hydraulic connectivity, perhaps allowing dry patches to grow on the evaporating surface. The mechanism causing the square root time behaviour is therefore unlike the case of deionized water where capillary disconnection from the fracture channel is followed by a diffusion controlled process. In completely oil-wet micromodels capillary disconnection prevented salt deposition in the fracture. The resulting permeability impairment was also measured, for the water-wet model, we observed two regions of a linear downward trend in the matrix and fracture permeability measurements. A similar trend was observed for the mixed-wet systems. However, for the oil-wet systems, fracture permeability only changes slightly even for 360g/L brine, a result of the absence of salt deposits in the fracture caused by the early rupture of the liquid wetting films needed to aid hydraulic connectivity. Overall, matrix permeability for all wetting conditions decreased with increasing brine concentration and was almost total for the 360g/L brine. Furthermore, drying with air was compared with drying with CO2 gas, with the latter having important applications in CO2 sequestration processes. We observed that using CO2 rather than air as carrier gas makes the brine phase somewhat more wetting especially in the deionized water case, with the result that hydraulic connectivity was maintained for longer in the CO2 case compared to dry-out with air. Steady-state two-phase flow experiments were also conducted to study the effect of viscosity ratio, flow rate and capillary number on flow regimes and displacement processes using a 2.5D etched-silicon/glass micromodel based on a thin section image of a Berea sandstone rock. Of particular interest here was a new type of pore-scale behaviour, termed dynamic connectivity, previously identified in steady-state two-phase flow experiments in real rocks at the transition to ganglia flow by X-ray tomography. Micromodels have the potential to resolve the dynamics of these displacement processes due to the high speed resolution of optical techniques. Depending on the mean-size, prevalence, and connectivity of the non-wetting phase, four flow regimes were identified: connected pathway flow (CPF), big ganglia flow (BGF), big-small ganglia flow (BSGF) and small ganglia flow (SGF). These flow regimes move from CPF to SGF as the capillary-viscous balance of the system is altered by increasing the total flow rate of the system. The boundaries of the flow regimes are indistinct, however the domain of the BGF increases (and/or SGF decreases) with a decrease in the viscosity ratio of the system. That is the BGF regime persisted to higher capillary number for the water/squalane system than the water/decane system because it is harder for big blobs to split into smaller blobs at low viscosity ratio. However, dynamic connectivity was not observed in these micromodel experiments even after replicating the experiments with the same fluid pair (Nitrogen/Deionized water) used in the real porous media experiment. Therefore, we speculate that the constant depth of the micromodel used in this study does not provide a suitable geometry for dynamic connectivity to develop. One potential reason for this is the compressed range of capillary pressures due to the single etch depth. Hence, a multi-depth non-repeat micromodel was designed based on a single confocal image of a Bentheimer sandstone. Prototypes of small sections of the multi-depth model were produced by 3D printing but it was not possible to fabricate a functioning model due to time constraints. Simulation was therefore used to explore the multiphase flow behaviour of the new geometry. Initially a Lattice Boltzmann code (developed in another project) was applied to simulate flow in a small region of the single depth geometry and compared to the experimental results as a validation step. The LB model was then used to predict flow behaviour in the multi-depth geometry, however only connected pathway and ganglia flow regimes were seen unambiguously. It is therefore likely that the lack of 3D connectivity rather than capillary pressure limitations prevent the appearance of dynamic connectivity.Open Acces

Comparative Study of Uniform and Graded Meshes for Solving Convection-Diffusion Equation with Quadratic Source

Due to its fundamental nature, the problems of convection-diffusion are discussed in various aviation, science and engineering applications. Among major applications are in the study of the dynamics of aircraft wake vortex and its interaction with turbulent jet which is a very serious hazard in aviation. Other applications include those in the investigation of intrusive sampling of jet engine exhaust gases, and the effectiveness of hot fluid injection in the removal of ice on aircraft wings. The numerical solutions of convection-diffusion require proper meshing schemes. Among major meshes in computational fluid dynamics are those of uniform, piecewise-uniform, graded, and hybrid over which the solutions of discretized governing equations are found. Bad solutions as spurious fluctuations, over- or under-predictions, and excessive computation time might be the results of unwitting application of the meshes. Accentuating comparative effectiveness of two meshes, namely uniform mesh and graded mesh with mesh expansion factor, this paper takes the solution of a convection-diffusion equation with quadratic source term into account. The problem is solved by assigning several values of mesh expansion factor to graded mesh, while mesh number is kept constant. The factors are calculated based on the generalization of their logarithmically linear relationship with low Peclet numbers derived in previous work. Based on the values of Peclet number, five test cases are considered. Graded mesh is proven relatively more robust, particularly due the solution on the mesh being free from spurious fluctuation. Furthermore, the accuracy level of the solution of up to two order of magnitude higher is obtained. The mesh expansion factor therefore contributes to a stable and highly accurate solution corresponding to all interested Peclet numbers

Efficient simulation of non-crossing fibers and chains in a hydrodynamic solvent

An efficient simulation method is presented for Brownian fiber suspensions, which includes both uncrossability of the fibers and hydrodynamic interactions between the fibers mediated by a mesoscopic solvent. To conserve hydrodynamics, collisions between the fibers are treated such that momentum and energy are conserved locally. The choice of simulation parameters is rationalised on the basis of dimensionless numbers expressing the relative strength of different physical processes. The method is applied to suspensions of semiflexible fibers with a contour length equal to the persistence length, and a mesh size to contour length ratio ranging from 0.055 to 0.32. For such fibers the effects of hydrodynamic interactions are observable, but relatively small. The non-crossing constraint, on the other hand, is very important and leads to hindered displacements of the fibers, with an effective tube diameter in agreement with recent theoretical predictions. The simulation technique opens the way to study the effect of viscous effects and hydrodynamic interactions in microrheology experiments where the response of an actively driven probe bead in a fiber suspension is measured.Comment: 12 pages, 2 tables, 5 figure

Lattice-Boltzmann coupled models for advection–diffusion flow on a wide range of Péclet numbers

Traditional Lattice-Boltzmann modelling of advection–diffusion flow is affected by numerical instability if the advective term becomes dominant over the diffusive (i.e., high-Péclet flow). To overcome the problem, two 3D one-way coupled models are proposed. In a traditional model, a Lattice-Boltzmann Navier–Stokes solver is coupled to a Lattice-Boltzmann advection–diffusion model. In a novel model, the Lattice-Boltzmann Navier–Stokes solver is coupled to an explicit finite-difference algorithm for advection–diffusion. The finite-difference algorithm also includes a novel approach to mitigate the numerical diffusivity connected with the upwind differentiation scheme. The models are validated using two non-trivial benchmarks, which includes discontinuous initial conditions and the case Pe$_{g}$->$\infty$ for the first time, where Pe$_{g}$ is the grid Péclet number. The evaluation of Pe$_{g}$ alongside Pe is discussed. Accuracy, stability and the order of convergence are assessed for a wide range of Péclet numbers. Recommendations are then given as to which model to select depending on the value Pe$_{g}$ - in particular, it is shown that the coupled finite-difference/Lattice-Boltzmann provide stable solutions in the case Pe->$\infty$, Pe$_{g}$->$\infty

A review on reactive transport model and porosity evolution in the porous media

This work comprehensively reviews the equations governing multicomponent flow and reactive transport in porous media on the pore-scale, mesoscale and continuum scale. For each of these approaches, the different numerical schemes for solving the coupled advection–diffusion-reactions equations are presented. The parameters influenced by coupled biological and chemical reactions in evolving porous media are emphasised and defined from a pore-scale perspective. Recent pore-scale studies, which have enhanced the basic understanding of processes that affect and control porous media parameters, are discussed. Subsequently, a summary of the common methods used to describe the transport process, fluid flow, reactive surface area and reaction parameters such as porosity, permeability and tortuosity are reviewed

Saturation in Liquid/Gas Coalescence

The problem was to construct a mathematical model for a liquid/gas coalescer, in order that the model could be analyzed to find combinations of parameters that would minimize the effects of saturation. The team has developed three complementary models, each with different strengths and weaknesses so that, depending on the information desired, one model may be more useful than another. The three models are: 1. A continuum model giving a macroscopic description of the filter. The governing equations are derived from first-principle consider- ations of conservation of mass and momentum. Constitutive relations for this model are derived by considering the processes going on in the filter at a microscopic level. 2. A stochastic model based on a Markov Decision Process. Each droplet is modelled as a single entity that can merge or move stochastically. This leads to a Markov simulation of the filter and the computation of average quantities. 3. A Lattice-Boltzmann model. The droplets are modelled to interact with each other and with the filter, using a Boltzmann distribution for their speed. This simulates the hydrodynamic behaviour of the droplet inside the filter

Numerical modeling of free surface and rapid solidification for simulation and analysis of melt spinning

The work provides methodologies for studying, designing, and optimizing melt spinning processes of fiber manufacture. Amorphous metallic materials can be created through melt spinning processes, in which a highly spinning wheel undercools a jet of molten metal or alloy below the equilibrium melting and the nucleation temperatures. Free-jet melt spinning employs a larger nozzle-wheel gap compared to planar flow casting. The instability of melt pool formation in a free-jet melt spinning will allow the variability of ribbon production. In general, a stable delivery of amorphous materials depends simultaneously on various control parameters, such as wheel speed, molten flow viscosity, surface tension force, and heat transfer. To analyze dynamical and thermodynamical characteristics of a free-jet melt spinning, two mathematical models, free surface and rapid solidification, have been established by means of Computational Fluid Dynamics. Based on the nucleation theory, I have predicted the nucleation temperature and the critical cooling rate for an alloy Fe75-Si10-B15 (at.%). The applications of these crystalline solidification properties in the simulation and analysis help the researchers gain insight into the processes. The research focuses on a novel simple and second-order accurate algorithm for computing surface normal and curvature in the Volume of Fluid method; it reconstructs the continuum surface force model to eliminate spurious currents. A computer program has been developed with the enhanced numerical schemes and the capability of heat transfer for two-dimensional laminar Newtonian surface flows. It conducted numerical simulations of impingement of a melt stream against a highly rotating wheel, and explains the complicated processes with numerical results of velocity and temperature in melt pools. The analytical estimates of ribbon thickness presented in the thesis agree with the experimental observation of the alloy. An in-depth investigation of the melt spinning process was performed to develop benchmarks of process variables for amorphous material production