Robust Spatial Modeling of Thermodynamic Parameters in a Full-Scale Reverse Osmosis Membrane Channel.

Full-scale reverse osmosis (RO) units usually consist of a set of pressure vessels holding up to six (1 m long) membrane modules in series. Since process parameters and water composition change substantially along the filtration channel in full-scale RO units, relevant thermodynamic parameters such as the ion activities and the osmotic coefficient change as well. Understanding these changes will lead to more accurate fouling prediction and to improvement in process and equipment designs. In this article, a rigorous thermodynamic model for RO concentrates in a full-scale module is developed and presented, which is capable of accounting for such changes. The change in concentrate composition due to permeation of water and ions is predicted locally in the membrane filtration channel. The local ionic composition is used to calculate the local activity coefficient and osmotic coefficient along the membrane channel through the Pitzer model for each modeled anion and cation. The approach developed was validated against related literature data, showing that Pitzer coefficient predictions were satisfactory. The spatial variation model was verified experimentally. It was found under the modeled conditions of high recovery that individual solute activity coefficients could be diminished up to 65%, in our case for sulfate, from their initial value from the membrane inlet to the outlet, and the water osmotic coefficient increased 3% as concentrate salinity increased from the membrane inlet to the outlet. Modeled at moderate recovery, the sulfate still achieved a statistically significant drop of 34% and an opposing trend of a decrease of 0.5% for the osmotic coefficient. These variations in internal water chemistry along the channel can significantly impact predicted recovery, fouling propensity, and permeate quality. Fouling prediction with our approach was also assessed through a theoretical fouling index to demonstrate the significance of ion activity over concentration-based calculations. Additionally, data from a pilot plant RO filtration channel was used to carry out a sensitivity analysis to show the capability of the developed model.

Dielectrophoretic Microfluidic Device for Separating Microparticles Based on Size with Sub-Micron Resolution.

This article details the mathematical model of a microfluidic device aimed at separating any binary heterogeneous sample of microparticles into two homogeneous samples based on size with sub-micron resolution. The device consists of two sections, where the upstream section is dedicated to focusing of microparticles, while the downstream section is dedicated to separation of the focused stream of microparticles into two samples based on size. Each section has multiple planar electrodes of finite size protruding into the microchannel from the top and bottom of each sidewall; each top electrode aligns with a bottom electrode and they form a pair leading to multiple pairs of electrodes on each side. The focusing section subjects all microparticles to repulsive dielectrophoretic force, from each set of the electrodes, to focus them next to one of the sidewalls. This separation section pushes the big microparticles toward the interior, away from the wall, of the microchannel using repulsive dielectrophoretic force, while the small microparticles move unaffected to achieve the desired degree of separation. The operating frequency of the set of electrodes in the separation section is maintained equal to the cross-over frequency of the small microparticles. The working of the device is demonstrated by separating a heterogeneous mixture consisting of polystyrene microparticles of different size (radii of 2 and 2.25 µm) into two homogeneous samples. The mathematical model is used for parametric study, and the performance is quantified in terms of separation efficiency and separation purity; the parameters considered include applied electric voltages, electrode dimensions, outlet widths, number of electrodes, and volumetric flowrate. The separation efficiencies and separation purities for both microparticles are 100% for low volumetric flow rates, a large number of electrode pairs, large electrode dimensions, and high differences between voltages in both sections.

Modeling a Dielectrophoretic Microfluidic Device with Vertical Interdigitated Transducer Electrodes for Separation of Microparticles Based on Size.

This article conceptualizes and mathematically models a dielectrophoretic microfluidic device with two sets of interdigitated transducer vertical electrodes for separation of a binary heterogeneous mixture of particles based on size; each set of electrodes is located on the sidewalls and independently controllable. To achieve separation in the proposed microfluidic device, the small microparticles are subjected to positive dielectrophoresis and the big microparticles do not experience dielectrophoresis. The mathematical model consists of equations describing the motion of each microparticle, fluid flow profile, and electric voltage and field profiles, and they are solved numerically. The equations of motion take into account the influence of phenomena, such as inertia, drag, dielectrophoresis, gravity, and buoyancy. The model is used for a parametric study to understand the influence of parameters on the performance of the microfluidic device. The parameters studied include applied electric voltages, electrode dimensions, volumetric flow rate, and number of electrodes. The separation efficiency of the big and small microparticles is found to be independent of and dependent on all parameters, respectively. On the other hand, the separation purity of the big and small microparticles is found to be dependent on and independent of all parameters, respectively. The mathematical model is useful in designing the proposed microfluidic device with the desired level of separation efficiency and separation purity.

Simulation of a microfluidic device employing dielectrophoresis for liquid biopsy.

This article details simulation based study of cell separation in a dielectrophoretic microfluidic device. The device consists of a narrow microchannel connected to a wide microchannel with several finite sized planar interdigitated transducer electrodes protruding into the narrow microchannel from one of its sidewalls. In the narrow microchannel, the circulating tumor cells are subjected to positive dielectrophoresis while the regular cells are subjected to negative dielectrophoresis to achieve separation and as all cells move in to the wide microchannel, the physical distance between the two types of cells increases thereby making their collection from the device easier. Equations describing motion, fluid field, electric field, and electric potential form the mathematical model and accounts for forces related to inertia, drag, and dielectrophoresis. Applied electric potential, electrode/gap length, and tumor cell diameter have a positive effect on the performance metrics while velocity of the medium and microchannel width have negative effect on the performance metrics. The model presented in this article is beneficial in realizing liquid biopsy with the desired performance metrics using the proposed microfluidic device.

Nozzle-Shaped Electrode Configuration for Dielectrophoretic 3D-Focusing of Microparticles.

: An experimentally validated mathematical model of a microfluidic device with nozzle-shaped electrode configuration for realizing dielectrophoresis based 3D-focusing is presented in the article. Two right-triangle shaped electrodes on the top and bottom surfaces make up the nozzle-shaped electrode configuration. The mathematical model consists of equations describing the motion of microparticles as well as profiles of electric potential, electric field, and fluid flow inside the microchannel. The influence of forces associated with inertia, gravity, drag, virtual mass, dielectrophoresis, and buoyancy are taken into account in the model. The performance of the microfluidic device is quantified in terms of horizontal and vertical focusing parameters. The influence of operating parameters, such as applied electric potential and volumetric flow rate, as well as geometric parameters, such as electrode dimensions and microchannel dimensions, are analyzed using the model. The performance of the microfluidic device enhances with an increase in applied electric potential and reduction in volumetric flow rate. Additionally, the performance of the microfluidic device improves with reduction in microchannel height and increase in microparticle radius while degrading with increase in reduction in electrode length and width. The model is of great benefit as it allows for generating working designs of the proposed microfluidic device with the desired performance metrics.

Dielectrophoresis-based 3D-focusing of microscale entities in microfluidic devices.

This article presents a validated mathematical model of a dielectrophoresis (DEP)-based microfluidic device capable of 3D-focusing microscale entities at any lateral location inside the microchannel. The microfluidic device employs planar, independently controllable, interdigitated transducer (IDT) electrodes on either side of the microchannel. The developed model is used for understanding the influence of different geometric and operating parameters on 3D focusing, and it comprises of motion equation, Navier-Stokes equation, continuity equation, and electric potential equation (Laplace equation). The model accounts for forces associated with inertia, gravity, buoyancy, virtual mass, drag, and DEP. The model is solved using finite difference method. The findings of the study indicate that the 3D focusing possible with the proposed microfluidic device is independent of microscale entity's size and initial position, microchannel height, and volumetric flow rate. In contrast, 3D focusing achievable with the microfluidic device is dependent on the applied electric potential, protrusion width of electrodes, and width of electrode/gap. Additionally, the lateral position of 3D focused can be controlled by varying the applied electric potential. The advantage of the proposed microfluidic device is that it is simple to construct while capable of achieving 3D focusing at any lateral location inside the microchannel.

Microfluidics Based Magnetophoresis: A Review.

Magnetophoresis, the manipulation of trajectory of micro-scale entities using magnetic forces, as employed in microfluidic devices is reviewed at length in this article. Magnetophoresis has recently garnered significant interest due to its simplicity, in terms of implementation, as well as cost-effectiveness while being efficient and biocompatible. Theory associated with magnetophoresis is illustrated in this review along with different sources for creating magnetic field gradient commonly employed in microfluidic devices. Additionally, this article reviews the state-of-the-art of magnetophoresis based microfluidic devices, where positive- and negative-magnetophoresis are utilized for manipulation of micro-scale entities (cells and microparticles), employed for operations such as trapping, focusing, separation, and switching of microparticles and cells. The article concludes with a brief outlook of the field of magnetophoresis.