Ronald F. Probstein

Coagulation in turbulent flow: Theory and experiment

Abstract The coagulation of colloidal particles in turbulent flows is investigated theoretically and experimentally. A coagulation model is developed for destabilized particles in an isotropic turbulent flow. Simple binary collision mean-free path concepts are employed and for mono-disperse systems coagulation rate relations are derived for particle sizes less than and larger than the Kolmogorov microscale of turbulence. Polydisperse systems are also considered and some general results concerning their behavior are obtained. Coagulation experiments are reported on inside fully developed turbulent pipe flows using an approximately monodisperse UCAR latex dispersion in which the particle sizes are less than the Kolmogorov microscale. The flow rate, destabilizer concentration and volume fraction of the dispersed phase were varied in these experiments. The experimental results for destabilized particles are shown to agree very well with the theoretical predictions. Brownian motion coagulation experiments for partially destabilized systems are compared with the corresponding turbulent motion experiments and the results indicate that the coagulation efficiency does not appear to depend on the particle transport mode.

Colloidal fouling of reverse osmosis membranes

Abstract A theoretical model of the fouling of reverse osmosis membranes by colloidal material has been developed for laminar flow and compared with the experimental results of fouling of cellulose acetate membranes by colloidal ferric hydroxide. The model is one-dimensional, based on the empirical observation that laminar flow does not affect the foulant growth behavior. A fast initial reaction-dominated fouling regime is predicted, followed very shortly in time by a much slower flux-driven deposition, as confirmed experimentally by a slow linear flux decline. The data have also shown that if the ferric hydroxide is stabilized, the flux decline rate is linear in the feed concentration, as predicted by the model. An unstable solution leads to a nonlinear dependence of foulant deposition on foulant feed concentration. An important experimental finding is that there exists a threshold transmembrane velocity, on the order of 5 × 10−4 cm/s, below which no flux decline or fouling is observed. The origin of this threshold velocity is believed to result from surface charge and double layer interactions. The important conclusion is that in reverse osmosis systems, fouling may be prevented simply by stabilizing the colloid solution and operating below the threshold permeation velocity.

EDTA-enhanced electroremediation of metal-contaminated soils

Precipitation and sorption of heavy metals reduce their mobility and limit the effectiveness of in-situ remediation technologies. In electroremediation, metal mobility can be further impeded by the development of regions of elevated pH near the collecting electrodes. This paper investigates the feasibility of mobilizing precipitated heavy metals by delivering complexing agents into soils by ionic migration. Two metals, lead and zinc, were selected as contaminants, and EDTA, a widely available non-toxic chelating agent, was selected as the complexing agent. It was found that EDTA added to the catholyte can be readily delivered into a sandy soil where it solubilizes the precipitated metals. The resulting complexes are then transported to the anode with metal removal efficiencies, for the spiked laboratory samples, approaching 100%. The poor ligand utilization obtained in the tests is attributed to the low dissolution rate of the metals. Modifying the operating conditions to increase the concentration and the residence time of the ligand in the soil is expected to improve the utilization efficiency of the complexing agent.

Development of an integrated microfluidic platform for dynamic oxygen sensing and delivery in a flowing medium

This paper describes a platform for real-time sensing of dissolved oxygen in a flowing microfluidic environment using an oxygen-sensitive luminescent dye (platinum octaethylporphyrin ketone) integrated into a micro-oxygenator device. Using a phase-based detection method, the luminescent decay lifetime of the dye was consistent with the linear Stern-Volmer relationship using both gaseous and aqueous samples. Maximum sensor resolution varied between 120-780 ppb across a range of dissolved oxygen (DO) concentrations ranging from 0-42.5 ppm. The sensor was subsequently used to determine the convective mass-transfer characteristics of a multi-layer polydimethylsiloxane (PDMS) microfluidic oxygenator. The membrane-based oxygenator showed excellent agreement with an analytical convection model, and the integrated oxygen sensor was accurate across a wide range of tested flow rates (0.05-5 mL min(-1)). The device is unique for its ease of fabrication and highly flexible configuration, as well as the novel incorporation of oxygen delivery and detection in a single micro-device. Potential applications include tissue engineering, cell culturing, and miniaturized bio-assays that require the delivery and/or detection of precise quantities of oxygen within a microfluidic construct.

A hydrodynamic theory of desalination by electrodialysis

Abstract A hydrodynamic theory of demineralization by electrodialysis has been developed for a multichannel system with steady laminar flow between plane, parallel membranes. The modeling of the system is found to be governed by four basic similarity parameters: (i) a dimensionless applied potential, (ii) the product of the channel aspect ratio and the inverse Peclet number, (iii) the ratio of brine and dialysate inlet concentrations, and (iv) a parameter measuring membrane resistance. For sufficiently long channels it is shown that there are two distinct regions: a “developing” region where the concentration diffusion layers are growing, and a “developed” region where the diffusion layers fill the channel. Parabolic and uniform velocity profiles are considered and self-consistent solutions are derived for the distributions of salt concentration, electric field and current density in the system, as well as for the total current. An integral method of solution is used. In the limits of low and high polarization analytic solutions are obtained which when matched at their point of equality closely approximate the complete numerical solutions. It is found that under a wide range of operating conditions, the solution for the total current is represented by the empirical formula I ^ = [ 1 − exp ( − Ψ ^ 3 ) ] 1 / 3 , where I and Ψ ^ are, respectively, a dimensionless current and potential embodying the four similarity parameters mentioned. Comparison is made of the calculated limiting total current with experiment.

Model and experiments on soil remediation by electric fields

Abstract The dominant transport process for removing charged species from soils by electric fields is electromigration. In the case of heavy metals, the polarity and magnitude of the charge depends on the pH. Positive ions are generally stable at low pH and negatively charged complexes dominate at high pH. The transport is further complicated by the strong dependence of solubility on pH, with many heavy metals being virtually insoluble in moderately alkaline conditions. It was found experimentally that under certain conditions, strong pH gradienis can develop in the soil trapping the metals by a process of isoelectric focusing, A numerical model of the transport and electrochemical processes was extended for the first time to incorporate complexation and precipitation reactions and was found to closely reproduce the experimental findings. The model demonstrates the role played by background ions and electroneutrality in governing the distribution of species, and how the concomitant variations in the elect...

Ultrafiltration of macromolecular solutions at high polarization in laminar channel flow

Abstract The limiting flux for the ultrafiltration of a macromolecular solute is obtained by a boundary layer integral method for a laminar channel flow with a concentration dependent diffusivity. A simple analytic expression is obtained for this flux which closely parallels the widely used formula of Michaels but with the diffusivity evaluated at the gelling concentration rather than the bulk concentration. Comparison of values given by the analytic result with numerical solutions and experiments show excellent agreement. Flux augmentation experiments carried out with strip type promoters show that at the same flow rate limiting fluxes can be increased to about 3 times the empty channel values.

Structure of a Plasma Shock Wave

The one‐dimensional, steady‐state structure of a shock wave in a fully ionized plasma is investigated in the absence of external applied magnetic or electric fields. The structure is assumed to be described by the Navier‐Stokes equations written for the electron and ion fluids, together with Poissons equation for the self‐induced electric field. When the Debye length downstream of the shock (λD2) is small compared to the ion‐ion mean free path there (l2), the plasma remains essentially neutral and the equations governing the charge separation and electric field can be uncoupled from the system. The remaining equations are reduced by a boundary layer type analysis, which uses the fact that different dissipative mechanisms are important over different length scales, and an integration in phase space is carried out. It is found that when the free stream Mach number M1 is less than 1.12, the plasma behaves like a single fluid and there is only one shock layer whose thickness is proportional to l2/e, where e ...

Kinetic Theory Approach to Electrostatic Probes

A spherical electrostatic (Langmuir) probe in a slightly ionized plasma is studied from a kinetic theory point of view. The two‐sided distribution function method of Lees, which embodies the Mott‐Smith approach, is used. The velocity space is divided into two regions along the straight cone tangent to the spherical probe, and different distribution functions are defined in the two regions. On satisfying the two relevant moments of the distribution function (continuity and number density flux) three simultaneous ordinary nonlinear differential equations, which are appropriate to all values of the Debye length, collision mean free path and probe potential, are obtained for determining the ion and electron number densities, and the potential. These equations reduce to the usual linear flux equations when the mean free path is much shorter than the probe radius and the Debye length. The equations are first linearized and solved for the case of small probe potential. Explicit solutions are given for the curren...

Self‐Similar Strong Shocks with Radiation in a Decreasing Exponential Atmosphere

The self‐similar one‐dimensional flow behind a plane shock propagating upward into an exponentially decreasing atmosphere is considered. The flow is taken to be isothermal in view of the large radiation mean free paths associated with high altitudes and the intense radiation heat transfer accompanying the high temperatures characteristic of an accelerating shock wave. The equations of motion are formulated in Lagrangian coordinates and are integrated exactly for all values of the shock density ratio. Solutions are presented for the cases where the boundary conditions at the shock correspond to a Hugoniot shock and to a Chapman‐Jouguet shock. A significant result of the analysis is that in both of these cases the shock propagates much faster than for the case of adiabatic flow.