Colloid Transport in Porous Media: A Review of Classical Mechanisms and Emerging Topics

To celebrate the tenth anniversary of InterPore, we present an interdisciplinary review of colloid transport through porous media. This review aims to explore both classical colloid transport and topics that fall outside that purview and thus offer transformative insights into the physics governing transport behavior. First, we discuss the unique colloid characteristics relative to molecules and larger particles. Then, the classical advection?dispersion?filtration models (both conceptual and mathematical) of colloid transport are introduced as well as anomalous transport behaviors. Next, the forces of interaction between colloids and porous media surfaces are discussed. Fourth, applications that are interested in maximizing the transport of colloids through porous media are considered. Then the concept of motile, active biocolloids is introduced, and finally, colloid swarming as a newly recognized mode of transport is summarized.Fil: Molnar, Ian L.. York University; CanadáFil: Pensini, Erica. School Of Engineering; CanadáFil: Asad, Md Abdullah. York University; CanadáFil: Mitchell, Chven A.. Department Of Physics And Astronomy; Estados UnidosFil: Nitsche, Ludwig C.. College Of Engineering; Estados UnidosFil: Pyrak-Nolte, Laura J.. Department Of Physics And Astronomy; Estados UnidosFil: Miño, Gastón Leonardo. Universidad Nacional de Entre Ríos. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática - Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática; ArgentinaFil: Krol, Magdalena M.. York University; Canad

Multiphase flow through spatially periodic models of porous media

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 1989.Includes bibliographical references (leaves 242-273).by Ludwig C. Nitsche.Ph.D

Secondary cohesion and chemical potential models for diffuse interfaces

A recent paper [L. C. Nitsche, A. Nguyen and G. Evans, Chem. Phys. Lett., 397, 417-421 (2004).] developed a cohesive chemical potential (referred to here as "primary" cohesion) for treating liquid-liquid interfaces, which yielded the correct free-surface evolution of drops while seeming to circumvent the characteristic properties of interfacial tension. Diffusion of miscible interfaces was interpreted as a consequence of the same driving force, acting through a different propagator. In this work we refine the chemical potential formulation by semi-analytically subtracting out, at each point within a drop, the corresponding potential for a flat interface at the same distance. The new "secondary" cohesive potential is shown to be consistent with the usual interfacial stress-jump boundary condition, while allowing interfacial "information" to be spread over a significant volume of the drop(s). In other words, the numerically defined interfacial layer need not be "thin". Reduction of parasytic currents in computer simulations is considered. Secondary cohesion is contrasted with (i) two prevailing volumetric versions of interfacial tension, as used in volume-of-fluid and front-tracking numerics, and (ii) the diffuse interface method [D. M. Anderson, G. B. McFadden & A. A. Wheeler, Ann. Rev. Fluid Mech., 30, 139-165 (1998)]. Morphological energy penalties and representations of diffusion associated with the various interfacial chemical potentials are compared. In particular, the double-well mixing energy density of the diffuse interface model can be simplified for certain modeling purposes. Numerical simulations based upon swarms of fuzzy Stokeslets are compared with experiments involving trailing drops and surfaces

Stokes flow singularity at the junction between impermeable and porous walls

For two-dimensional, creeping flow in a half-plane, we consider the singularity that arises at an abrupt transition in permeability from zero to a finite value along the wall, where the pressure is coupled to the seepage flux by Darcy's law. This problem represents the junction between the impermeable wall of the inflow section and the porous membrane further downstream in a spiral-wound desalination module. On a macroscopic, outer length scale the singularity appears like a jump discontinuity in normal velocity, characterized by a non-integrable 1/r divergence of the pressure. This far-field solution is imposed as the boundary condition along a semicircular arc of dimensionless radius 30 (referred to the microscopic, inner length scale). A preliminary numerical solution (using a least-squares variant of the method of fundamental solutions) indicates a continuous normal velocity along the wall coupled with a weaker 1/root r singularity in the pressure. However, inconsistencies in the numerically imposed outer boundary condition indicate a very slow radial decay. We undertake asymptotic analysis to: (i) understand the radial decay behaviour; and (ii) find a more accurate far-field solution to impose as the outer boundary condition. Similarity solutions (involving a stream function that varies like some power of r) are insufficient to satisfy all boundary conditions along the wall, so we generalize these by introducing linear and quadratic terms in log r. By iterating on the wall boundary conditions (analogous to the method of reflections), the outer asymptotic series is developed through second order. We then use a hybrid computational scheme in which the numerics are iteratively patched to the outer asymptotics, thereby determining two free coefficients in the latter. We also derive an inner asymptotic series and fit its free coefficient to the numerics at r = 0.01. This enables evaluation of the singular flow field in the limit as r -> 0. Finally, a uniformly valid fit is obtained with analytical formulas. The singular flow field for a solid-porous abutment and the general Stokes flow solutions obtained in the asymptotic analysis are programmed in Fortran for future use as local basis functions in computational schemes. Numerics are required for the intermediate-r regime because the inner and outer asymptotic expansions do not extend far enough toward each other to enable rigorous asymptotic matching. The logarithmic correction terms explain why the leading far-field solution (used in the preliminary numerics) was insufficient even at very large distances

Interaction of Multiple Drops and Formation of Toroidal-Spiral Particles

In the development of drug delivery technologies for treating complex diseases, encapsulating multiple compounds and manipulating their sustained-release kinetics independently (for optimal therapeutic effect) can be challenging. Toward this goal, we previously developed a fluid-dynamic technology based on multi-drop interactions to produce solid toroidal-spiral (TS) particles. During sedimentation in a miscible, viscous liquid, polymeric drops self-assemble into a reproducible and controllable TS structure, which can be solidified into particles by photo-initiated cross-linking of the polymer. The goal of encapsulating multiple drops of different physical properties (such as size and density) generally requires complicated and time-consuming laboratory iteration on the starting conditions, because all satellite drops (containing drugs) must catch up and coalesce simultaneously with the main drop that forms the surrounding matrix upon solidification. In this paper we consider a model system for multi-drop entrainment that features a main drop followed by three smaller satellite drops arranged in a horizontal, triangular array. Experiments visualized with a high-speed camera are used to validate computer simulations based upon a swarm-of-Stokeslets method. The simulations accurately track complex drop configurations involving intertwined interfaces. Replacing the actual starting drop shapes with suitably positioned, volume-equivalent spheres yields very similar configurations: the crucial deformations and interactions occur during sedimentation, as opposed to during the initial injection of the drops. The simulations are then used to formulate two robust rules of thumb by which further trial-and-error (whether in the laboratory or by computation) can be avoided toward encapsulating multiple satellite drops with different properties. The first rule applies to satellite drops of different properties but symmetric starting positions, and establishes the single-drop Hadamard-Rybczynski (HR) sedimentation velocity as the crucial parameter. The second rule makes use of a universal entrainment map by which three satellite drops of the same radius but different densities and asymmetric starting positions can all be encapsulated at an arbitrarily prescribed distance of sedimentation. Two final simulations demonstrate how both rules can be combined to successfully design an (asymmetric) injection geometry to encapsulate three satellite drops of different radii and densities, at an arbitrarily prescribed distance of sedimentation. Understanding fundamental hydrodynamics of interaction between multiple drops could lead to potential scale-up of production of TS particles and also impact applications of mixing and printing in general

Toroidal-Spiral Particles for Codelivery of Anti-VEGFR‑2 Antibody and Irinotecan: A Potential Implant to Hinder Recurrence of Glioblastoma Multiforme

Heterogeneous toroidal-spiral particles (TSPs) were generated by polymer droplet sedimentation, interaction, and cross-linking. TSPs provide a platform for encapsulation and release of multiple compounds of different sizes and physicochemical properties. As a model system, we demonstrate the encapsulation and independently controlled release of an anti-VEGFR-2 antibody and irinotecan for the treatment of glioblastoma multiforme. The anti-VEGFR-2 antibody was released from the TS channels and its binding to HUVECs was confirmed by confocal microscopy and flow cytometry, suggesting active antibody encapsulation and release. Irinotecan, a small molecule drug, was released from the dense polymer matrix of poly­(ethylene glycol) diacrylate (MW ∼ 700 g/mol; PEGDA 700). Released irinotecan inhibited the proliferation of U251 malignant glioma cells. Since the therapeutic compounds are released through different pathways, specifically diffusion through the polymer matrix versus TS channels, the release rate can be controlled independently through the design of the structure and material of particle components