Taylor-Aris dispersion in microfluidic networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2002.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (leaves 172-183).This thesis constitutes the development and application of a theory for the lumped parameter, convective-diffusive-reactive transport of individual, non-interacting Brownian solute particles ("macromolecules") moving within spatially periodic, solvent-filled networks - the latter representing models of chip-based microfluidic devices, as well as porous media. The use of a lumped parameter transport model and network geometrical description affords the development of a discrete calculation scheme for computing the relevant network-scale (macrotransport) parameters, namely the mean velocity vector U*, dispersivity dyadic D* and, if necessary, the mean volumetric solute depletion rate K*. The ease with which these discrete calculations can be performed for complex networks renders feasible parametric studies of potential microfluidic chip designs, particularly those pertinent to biomolecular separation schemes. To demonstrate the computational and conceptual advantages of this discrete scheme, we consider: (i) a pair of straightforward examples, dispersion analysis of (non-reactive) pressure-driven flow in spatially periodic serpentine microchannels and reactive transport in an elementary geometric model of a porous medium; and (ii) a pair of case studies based upon the microfluidic separation techniques of vector chromatography and entropic trapping.(cont.) The straightforward examples furnish explicit proof that the present theory produces realistic results within the context of a simple computational scheme, at least when compared with the prevailing continuous generalized Taylor-Aris dispersion theory. In the case study on vector chromatography, we identify those factors which break the symmetry of the chip-scale particle mobility tensor, most importantly the hydrodynamic wall effects between the particles and the obstacle surfaces. In the entropic trapping case study, analytical expressions derived for the solute dispersiviy, number of theoretical plates, and separation resolution are shown to furnish results that accord, at least qualitatively, with experimental trends and data reported in the literature.by Kevin David Dorfman.Ph.D

Controlling effective dispersion within a channel with flow and active walls

Channels are fundamental building blocks from biophysics to soft robotics, often used to transport or separate solutes. As solute particles inevitably transverse between streamlines along the channel by molecular diffusion, the effective diffusion of the solute along the channel is enhanced - an effect known as Taylor dispersion. Here, we investigate how the Taylor dispersion effect can be suppressed or enhanced in different settings. Specifically, we study the impact of flow profile and active or pulsating channel walls on Taylor dispersion. We derive closed analytic expressions for the effective dispersion equation in all considered scenarios providing hands-on effective dispersion parameters for a multitude of applications. In particular, we find that active channel walls may lead to three regimes of dispersion: either dispersion decrease by entropic slow down at small Peclet number, or dispersion increase at large Peclet number dominated either by shuttle dispersion or by Taylor dispersion. This improves our understanding of solute transport e.g. in biological active systems such as blood flow and opens a number of possibilities to control solute transport in artificial systems such as soft robotics

Upstream swimming and Taylor dispersion of active Brownian particles

Locomotion of self-propelled particles such as motile bacteria or phoretic swimmers often takes place in the presence of applied flows and confining boundaries. Interactions of these active swimmers with the flow environment are important for the understanding of many biological processes, including infection by motile bacteria and the formation of biofilms. Recent experimental and theoretical works have shown that active particles in a Poiseuille flow exhibit interesting dynamics including accumulation at the wall and upstream swimming. Compared to the well-studied Taylor dispersion of passive Brownian particles, a theoretical understanding of the transport of active Brownian particles (ABPs) in a pressure-driven flow is relatively less developed. In this paper, employing a small wave-number expansion of the Smoluchowski equation describing the particle distribution, we explicitly derive an effective advection-diffusion equation for the cross-sectional average of the particle number density in Fourier space. We characterize the average drift (specifically upstream swimming) and effective longitudinal dispersion coefficient of active particles in relation to the flow speed, the intrinsic swimming speed of the active particles, their Brownian diffusion, and the degree of confinement. In contrast to passive Brownian particles, both the average drift and the longitudinal dispersivity of ABPs exhibit a nonmonotonic variation as a function of the flow speed. In particular, the dispersion of ABPs includes the classical shear-enhanced (Taylor) dispersion and an active contribution called the swim diffusivity. In the absence of translational diffusion, the classical Taylor dispersion is absent and we observe a giant longitudinal dispersion in the strong flow limit. Our continuum theory is corroborated by a direct Brownian dynamics simulation of the Langevin equations governing the motion of each ABP

Application of upscaling methods for fluid flow and mass transport in multi-scale heterogeneous media : A critical review

Physical and biogeochemical heterogeneity dramatically impacts fluid flow and reactive solute transport behaviors in geological formations across scales. From micro pores to regional reservoirs, upscaling has been proven to be a valid approach to estimate large-scale parameters by using data measured at small scales. Upscaling has considerable practical importance in oil and gas production, energy storage, carbon geologic sequestration, contamination remediation, and nuclear waste disposal. This review covers, in a comprehensive manner, the upscaling approaches available in the literature and their applications on various processes, such as advection, dispersion, matrix diffusion, sorption, and chemical reactions. We enclose newly developed approaches and distinguish two main categories of upscaling methodologies, deterministic and stochastic. Volume averaging, one of the deterministic methods, has the advantage of upscaling different kinds of parameters and wide applications by requiring only a few assumptions with improved formulations. Stochastic analytical methods have been extensively developed but have limited impacts in practice due to their requirement for global statistical assumptions. With rapid improvements in computing power, numerical solutions have become more popular for upscaling. In order to tackle complex fluid flow and transport problems, the working principles and limitations of these methods are emphasized. Still, a large gap exists between the approach algorithms and real-world applications. To bridge the gap, an integrated upscaling framework is needed to incorporate in the current upscaling algorithms, uncertainty quantification techniques, data sciences, and artificial intelligence to acquire laboratory and field-scale measurements and validate the upscaled models and parameters with multi-scale observations in future geo-energy research.© 2021 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)This work was jointly supported by the National Key Research and Development Program of China (No. 2018YFC1800900 ), National Natural Science Foundation of China (No: 41972249 , 41772253 , 51774136 ), the Program for Jilin University (JLU) Science and Technology Innovative Research Team (No. 2019TD-35 ), Graduate Innovation Fund of Jilin University (No: 101832020CX240 ), Natural Science Foundation of Hebei Province of China ( D2017508099 ), and the Program of Education Department of Hebei Province ( QN219320 ). Additional funding was provided by the Engineering Research Center of Geothermal Resources Development Technology and Equipment , Ministry of Education, China.fi=vertaisarvioitu|en=peerReviewed

Upstream swimming and Taylor dispersion of active Brownian particles

Locomotion of self-propelled particles such as motile bacteria or phoretic swimmers often takes place in the presence of applied flows and confining boundaries. Interactions of these active swimmers with the flow environment are important for the understanding of many biological processes, including infection by motile bacteria and the formation of biofilms. Recent experimental and theoretical works have shown that active particles in a Poiseuille flow exhibit interesting dynamics including accumulation at the wall and upstream swimming. Compared to the well-studied Taylor dispersion of passive Brownian particles, a theoretical understanding of the transport of active Brownian particles (ABPs) in a pressure-driven flow is relatively less developed. In this paper, employing a small wave-number expansion of the Smoluchowski equation describing the particle distribution, we explicitly derive an effective advection-diffusion equation for the cross-sectional average of the particle number density in Fourier space. We characterize the average drift (specifically upstream swimming) and effective longitudinal dispersion coefficient of active particles in relation to the flow speed, the intrinsic swimming speed of the active particles, their Brownian diffusion, and the degree of confinement. In contrast to passive Brownian particles, both the average drift and the longitudinal dispersivity of ABPs exhibit a nonmonotonic variation as a function of the flow speed. In particular, the dispersion of ABPs includes the classical shear-enhanced (Taylor) dispersion and an active contribution called the swim diffusivity. In the absence of translational diffusion, the classical Taylor dispersion is absent and we observe a giant longitudinal dispersion in the strong flow limit. Our continuum theory is corroborated by a direct Brownian dynamics simulation of the Langevin equations governing the motion of each ABP

Lattice Kinetic Monte Carlo Simulations of Platelet Aggregation and Deposition

Platelet aggregation is an essential process in forming a stable clot to prevent blood loss. The response of platelets to a complex signal of pro-clotting agonists determines the stability and size of the resulting clot. An underdeveloped clot represents a bleeding risk, while an overdeveloped clot can cause vessel occlusion, which can lead to heart attack or stroke. A multiscale model was developed to study the integration of platelet signaling within the complex phenomena driven by flow. The model is built upon a lattice kinetic Monte Carlo algorithm (LKMC) to track platelet motion and binding. First, a new method for including flow-driven particle motion in LKMC was derived from a timescale analysis of particle motion. Simple methods for simulating flow-driven motion were found to exhibit concentration dependent velocities violating the assumptions in the model. The nature of the error was analyzed mathematically and resolved by considering the chain length distribution on the lattice. The accuracy of the method was found to scale linearly with the lattice spacing. Second, the LKMC method was extended to study particle aggregation in complex flows. The LKMC results for simple flows were compared directly to a continuum population balance equation (PBE) approach. A contact time model was introduced to capture nonideal collisions in the LKMC model and a connection to the continuum collision efficiency was derived. The particle size distribution for a baffled geometry with regions of standing vortices and squeezing flows was determined using the LKMC method for varying baffle heights. Finally, the LKMC method was incorporated within a multiscale model to simulate platelet aggregation including platelet signaling (neural network model), blood flow (lattice Boltzmann method), and the release of soluble platelet agonists (finite element method). The neural network model for platelet signaling was trained on patient-specific, experimental measurements of intracellular calcium enabling patient-specific predictions of platelet function in flow. The model accurately predicted the order of potency for three antiplatelet therapies, donor-specific aggregate size, and donor-specific response to antiplatelet therapy as compared to microfluidic experiments of platelet aggregation

Investigation of drift phenomena at the pore-scale during flow and transport in porous media

Acknowledgments: We express our appreciation to the Petroleum Technology Development Fund, Nigeria (PTDF), for funding this research project.Peer reviewedPublisher PD

Channel modeling for diffusive molecular communication - a tutorial review

Molecular communication (MC) is a new communication engineering paradigm where molecules are employed as information carriers. MC systems are expected to enable new revolutionary applications such as sensing of target substances in biotechnology, smart drug delivery in medicine, and monitoring of oil pipelines or chemical reactors in industrial settings. As for any other kind of communication, simple yet sufficiently accurate channel models are needed for the design, analysis, and efficient operation of MC systems. In this paper, we provide a tutorial review on mathematical channel modeling for diffusive MC systems. The considered end-to-end MC channel models incorporate the effects of the release mechanism, the MC environment, and the reception mechanism on the observed information molecules. Thereby, the various existing models for the different components of an MC system are presented under a common framework and the underlying biological, chemical, and physical phenomena are discussed. Deterministic models characterizing the expected number of molecules observed at the receiver and statistical models characterizing the actual number of observed molecules are developed. In addition, we provide channel models for timevarying MC systems with moving transmitters and receivers, which are relevant for advanced applications such as smart drug delivery with mobile nanomachines. For complex scenarios, where simple MC channel models cannot be obtained from first principles, we investigate simulation-driven and experiment-driven channel models. Finally, we provide a detailed discussion of potential challenges, open research problems, and future directions in channel modeling for diffusive MC systems