Blob Sizes Research Articles

On the hydrodynamic limit of Ginzburg‐Landau wave vortices

AbstractIn this paper, we study the hydrodynamic limit of the finite Ginzburg‐Landau wave vortices, which was established in [16]. Unlike the classical vortex method for incompressible Euler equations, we prove here that the densities approximated by the vortex blob method associated with the Ginzburg‐Landau wave vortices tend to the solutions of the pressure‐less compressible Euler‐Poisson equations. The convergence of such approximation is proved before the formation of singularities in the limit system as the blob sizes and the grid sizes tend to zero in appropriate rates. © 2002 John Wiley & Sons, Inc.

On the use of the activation energy concept to investigate analyte and network deformations in entangled polymer solution capillary electrophoresis of synthetic polyelectrolytes.

The activation energy associated with the electrophoretic migration of an analyte under given electrolyte conditions can be accessed through the determination of the analyte electrophoretic mobility at various temperatures. In the case of the electrophoretic separation of polyelectrolytes in the presence of an entangled polymer network, activation energy can be regarded as the energy needed by the analyte to overcome the obstacles created by the separating network. Any deformation undergone by the analyte or the network is expected to induce a decrease in the activation energy. In this work, the electrophoretic mobilities of poly(styrenesulfonates) (PSSs) of various molecular weights (Mr 16 x 10(3) to 990 x 10(3)) were determined in entangled polyethylene oxide (PEO) solutions as a function of temperature (in the 17-60 degrees C range) and the PSS activation energies were calculated. The influences of the PSS molecular weight, blob sizes zetab of the separating network (related to the PEO concentration), ionic strength of the electrolyte and electric field strength (75-600 V/cm) were investigated. The results were interpreted in terms of analyte and network deformations and were confronted with those previously obtained for DNA migration in polymer solutions and chemical gels. For a radius of gyration Rg<zetab the activation energy increases with the PSS molecular mass, while the reverse is true for Rg>zetab, suggesting PSS and network deformations in the latter case. Increasing ionic strength resulted in an increase in the PSS activation energy, because of the decrease of their radii of gyration, which makes them less deformable. Finally, the activation energies of all the PSSs are a decreasing function of field strength and at high field strength tend to reach a constant value close to that for a small molecule.

A distributed-site model for non-equilibrium dissolution of multi-component residually trapped NAPL

An approach for modeling the dissolution of residually-trapped multi-component non-aqueous phase liquids (NAPLs) from a physically heterogeneous porous medium is presented. The Distributed-Site (DS) model presented uses the beta probability density function to characterize the initial distribution of residual NAPL blob volumes. Mass transfer from the trapped idealized NAPL blobs is simulated using as a basis a correlation for mass transfer coefficients, a linear concentration driving force, and multi-component partitioning. The main advantage of the approach outlined in this work is that by using reasonable assumptions the Distributed-Site model is able to model the mass transfer behavior of a complex dissolution phenomena using fewer fitted parameters than current multi-site models. Application of this model to column experimental data for the dissolution of benzene, toluene, and m-xylene from a tridecane NAPL source is presented. The incorporation of several NAPL blob sizes (and corresponding mass transfer rate coefficients) was able to account for the behavior of the effluent concentrations as they passed through the exponential decay and into the asymptotic region, an important feature lacking in the two-site modeling approach. When fitted to data for benzene, the DS model was found to predict experimental data satisfactorily for the dissolution of toluene and m-xylene from tridecane without adjustment of the parameters. This indicates that the dissolution process can be generalized for various compounds even when mass transfer limitations are present and that dissolution data obtained for one compound can be useful for predicting the long term dissolution history.

Detachment of a coalesced-phase blod from a circular obstacle in a Hele-Shaw cell

Two-phase flow through porous media has many important applications in chemical industry, e.g. enhanced oil recovery and filtration separation of dispersion. To elucidate the basic processes occurring in such porous media, Moses and Ng (1985) conducted visual studies on a model porous structure, which consisted of cylinders arranged in a centered hexagonal pattern between two parallel plates. By using an emulsion of silicone oil-in-water (containing electrolyte), they showed that small drops adhere to the cylinder near the stagnation point and coalesce there to form larger blobs. Through these observations, they were able to qualitatively explain the behaviour of actual porous media in terms of the electrical properties of the system. Their study was qualitative, and did not address the issue of the detachment of accumulated dispersed phase blob from the cylinder. The prediction of the detached blob sizes would be an important factor for overall flow behaviour of porous media since the structure of porous media is repetitive in nature.

Phenomenological models for transient NAPL-water mass-transfer processes

A phenomenological model for transient NAPL dissolution, referred to as the “sphere” model, is developed. In this model, the mass-transfer coefficient and specific surface areas are quantified independently. The unique aspect of this work is the assumption that the complex distribution of NAPL blob shapes and sizes can be represented by a set of spheres with a range of diameters. The sphere diameter distributions are determined through the entrapment, polymerization and characterization of styrene blobs in sandy media. Mass-transfer coefficients are estimated from experimental measurements of the dissolution of naphthalene emplaced as solid spheres within sandy media. The phenomenological model describing NAPL dissolution rates is incorporated into a solute transport equation and solved with a numerical simulator. Simulations show that the sphere model can be calibrated to experimental NAPL dissolution data from column studies presented previously. The inclusion of a range of sphere sizes resulted in a model which represents experimental data better than a model based on mono-size spheres. The sphere model also adequately predicts dissolution for NAPL's with a range of solubilities provided the NAPL blob size distributions can be adequately estimated. The primary limitation of the sphere model is the qiantity of input data required to describe the distribution of effective sphere sizes. While these data requirements are extensive, the ability to define the NAPL blob distribution within the model makes the sphere model much more versatile for extrapolation to heterogeneous systems than other available dissolution models.

Theoretical study of the significance of nonequilibrium dissolution of nonaqueous phase liquids in subsurface systems

The objective of this work is to assess the potential significance of deviations from local equilibrium for the exchange of mass between residual nonaqueous phase liquids and the aqueous phase in the saturated groundwater zone. A one‐dimensional convection‐dispersion mass balance equation incorporating a first‐order interphase mass transfer rate relationship and temporal changes in blob configuration is used to model this system. Analytical and numerical methods are employed to examine the steady state and transient behavior of the system under a variety of hypothetical aquifer conditions and pumping remediation schemes. Sensitivity of the model to several parameters including mass transfer coefficient, blob size and shape, and Darcy velocity is explored. Results of the theoretical assessment indicate that nonequilibrium effects could play a significant role in some contamination scenarios, primarily for large blob sizes and relatively high velocities. Design of soil flushing techniques will be impacted by these conclusions. Uncertainty in several parameter values used in this analysis indicate the need for further experimental investigation of this process.