Groundwater remediation by anionic surfactant micelles - an innovative double layer model applied to Na+ and Mg2+ association with dodecylsulfate micelles

1998 ◽  
Vol 38 (7) ◽  
pp. 99-106 ◽  
Author(s):  
Ching Yuan ◽  
Chung-Hsuang Hung ◽  
Chad T. Jafvert
Keyword(s):  
Anionic Surfactant ◽  
Groundwater Remediation ◽  
Electrical Potential ◽  
Binding Constants ◽  
High Concentration ◽  
Experimental Conditions ◽  
Counterion Binding ◽  
Double Layer Model ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

The association reactions involving counterions, Na+ and Mg2+, and micelles composed of the anionic surfactant, dodecylsulfate (DS−), were investigated in ultrafiltration experiments. To access the data, an innovative model was developed that considered specific counterion binding within a Stern layer, with binding constant dependent upon the electrical potential as derived by the Poisson-Boltzmann equation and with calculation of the cmc as a function of counterion binding (or association). The experimental and model results both show that magnitude of counterion binding is greater for divalent species, Mg2+, than that for the monovalent species, Na2+. However, high concentration of Na+ compete for surface area diminishing the ability of the DS− to bind either divalent species. At experimental conditions from 0 to 100 mM NaCl addition, the binding ratio (BR) varied only from 0.58 to 0.63. The optimum binding constants, KMg and KNa, were determined to be 0.4 and 1.0 L mol−1, respectively, for the model. The experimental data and model calculated results were generally in good agreement.

scholarly journals Review and Modification of Entropy Modeling for Steric Effects in the Poisson-Boltzmann Equation

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 632
Author(s):  
Tzyy-Leng Horng
Keyword(s):  
Free Energy ◽  
Lattice Gas ◽  
Steric Effect ◽  
Mean Field ◽  
Boltzmann Distribution ◽  
Experimental Conditions ◽  
Ion Concentrations ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Ion Size

The classical Poisson-Boltzmann model can only work when ion concentrations are very dilute, which often does not match the experimental conditions. Researchers have been working on the modification of the model to include the steric effect of ions, which is non-negligible when the ion concentrations are not dilute. Generally the steric effect was modeled to correct the Helmholtz free energy either through its internal energy or entropy, and an overview is given here. The Bikerman model, based on adding solvent entropy to the free energy through the concept of volume exclusion, is a rather popular steric-effect model nowadays. However, ion sizes are treated as identical in the Bikerman model, making an extension of the Bikerman model to include specific ion sizes desirable. Directly replacing the ions of non-specific size by specific ones in the model seems natural and has been accepted by many researchers in this field. However, this straightforward modification does not have a free energy formula to support it. Here modifications of the Bikerman model to include specific ion sizes have been developed iteratively, and such a model is achieved with a guarantee that: (1) it can approach Boltzmann distribution at diluteness; (2) it can reach saturation limit as the reciprocal of specific ion size under extreme electrostatic conditions; (3) its entropy can be derived by mean-field lattice gas model.

A 2D Electric Double Layer Model for Biological Nanochannels

2006 ◽  
Author(s):  
Fuzhi Lu ◽  
Daniel Y. Kwok
Keyword(s):  
Double Layer ◽  
Surface Potential ◽  
Electric Double Layer ◽  
Classical Model ◽  
Time Dependent ◽  
Layer Model ◽  
End Effects ◽  
Double Layer Model ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

We developed a 2D electric double layer model for biological nanochannels based on the linearlized Poisson-Boltzmann equation with arbitrary surface potential. Time dependent adsorption kinetics was used in the model to examine the variation of electric double layer distribution and compare with that from the classical model. Based on the 2D model, EDL interaction for heavily patched arbitray surface potential was found to be much weaker in such biological nanochannels. Channel end effects are also found to be significant and not negligible.

Unsteady Rotating Electroosmotic Flow Through a Slit Microchannel

2016 ◽  
Vol 32 (5) ◽  
pp. 603-611 ◽  
Author(s):  
D.-Q. Si ◽  
Y.-J. Jian ◽  
L. Chang ◽  
Q.-S. Liu
Keyword(s):  
Flow Rate ◽  
Electroosmotic Flow ◽  
Volume Flow Rate ◽  
Electrical Potential ◽  
Velocity Fields ◽  
Volume Flow ◽  
Half Height ◽  
Poisson Boltzmann ◽  
Flow Through ◽  
Poisson Boltzmann Equation

AbstractUsing the method of Laplace transform, an analytical solution of unsteady rotating electroosmotic flow (EOF) through a parallel plate microchannel is presented. The analysis is based upon the linearized Poisson-Boltzmann equation describing electrical potential distribution and the Navies Stokes equation representing flow field in the rotating coordinate system. The discrepancy of present problem from classical EOF is that the velocity fields are two-dimensional. The rotating EOF velocity profile and flow rate greatly depend on time t, rotating parameter ω and the electrokinetic width K (ratio of half height of microchannel to thickness of electric double layer). The influence of the above dimensionless parameters on transient EOF velocity, volume flow rate and EO spiral is investigated.

scholarly journals Peristaltically Induced Electroosmotic Flow of Jeffrey Fluid with Zeta Potential and Navier-Slip at the Wall

2019 ◽  
Vol 8 (10) ◽  
pp. 1324-1329
Keyword(s):  
Zeta Potential ◽  
Electrical Potential ◽  
Slip Boundary Condition ◽  
Jeffrey Fluid ◽  
Long Wavelength ◽  
Navier Slip ◽  
Slip Boundary ◽  
Fluid Parameter ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

This paper concern with the electro-osmotically modulated peristaltic of Jeffrey fluid with zeta potential and Navier-slip boundary condition at the channel wall. The Poisson-Boltzmann equation for electrical potential distribution is assumed to accommodate the electrical double layer. Poisson-Boltzmann equations are simplified by using Debye-Huckel linearization approximation. The closed form analytical solutions are calculated by using low Reynolds number and long wavelength assumptions. Influence of various parameters like electro-osmotic, Jeffrey fluid parameter, Slip parameter and Zeta potential on the flow are discussed through the nature of graphs

scholarly journals Electrothermal Transport in Biological Systems: An Analytical Approach for Electrokinetically Modulated Peristaltic Flow

2017 ◽  
Vol 9 (4) ◽  
Author(s):  
Dharmendra Tripathi ◽  
Ashish Sharma ◽  
O. Anwar Bég ◽  
Abhishek Tiwari
Keyword(s):  
Joule Heating ◽  
Body Force ◽  
Electrical Potential ◽  
Debye Length ◽  
Planck Equation ◽  
Volumetric Flow Rate ◽  
Flow And Heat Transfer ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
The Impact

A mathematical model is presented to study the combined viscous electro-osmotic (EO) flow and heat transfer in a finite length microchannel with peristaltic wavy walls in the presence of Joule heating. The unsteady two-dimensional conservation equations for mass, momentum, and energy conservation with viscous dissipation, heat absorption, and electrokinetic body force, are formulated in a Cartesian co-ordinate system. Both single and train wave propagations are considered. The electrical field terms are rendered into electrical potential terms via the Poisson–Boltzmann equation, Debye length approximation, and ionic Nernst Planck equation. A parametric study is conducted to evaluate the impact of isothermal Joule heating and electro-osmotic velocity on axial velocity, temperature distribution, pressure difference, volumetric flow rate, skin friction, Nusselt number, and streamline distributions.

Examining sharp restart in a Monte Carlo method for the linearized Poisson–Boltzmann equation

2020 ◽  
Vol 26 (3) ◽  
pp. 223-244
Author(s):  
W. John Thrasher ◽  
Michael Mascagni
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Monte Carlo Algorithm ◽  
Significant Bias ◽  
Poisson Boltzmann ◽  
Electrostatic Free Energy ◽  
Poisson Boltzmann Equation ◽  
The Stability ◽  
Potential Methods ◽  
The Individual

AbstractIt has been shown that when using a Monte Carlo algorithm to estimate the electrostatic free energy of a biomolecule in a solution, individual random walks can become entrapped in the geometry. We examine a proposed solution, using a sharp restart during the Walk-on-Subdomains step, in more detail. We show that the point at which this solution introduces significant bias is related to properties intrinsic to the molecule being examined. We also examine two potential methods of generating a sharp restart point and show that they both cause no significant bias in the examined molecules and increase the stability of the run times of the individual walks.

scholarly journals Explanation of the Formation of Complexes between Representatives of Oxazolidinones and HDAS-β-CD Using Molecular Modeling as a Complementary Technique to cEKC and NMR

2021 ◽  
Vol 22 (13) ◽  
pp. 7139
Author(s):  
Wojciech Bocian ◽  
Elżbieta Bednarek ◽  
Katarzyna Michalska
Keyword(s):  
Molecular Dynamics ◽  
Molecular Modeling ◽  
Computational Methods ◽  
Chiral Separation ◽  
Structural Information ◽  
Binding Constants ◽  
Nmr Studies ◽  
Thermodynamics Of Complexation ◽  
Poisson Boltzmann ◽  
Explicit Water

Molecular modeling (MM) results for tedizolid and radezolid with heptakis-(2,3-diacetyl-6-sulfo)-β-cyclodextrin (HDAS-β-CD) are presented and compared with the results previously obtained for linezolid and sutezolid. The mechanism of interaction of chiral oxazolidinone ligands belonging to a new class of antibacterial agents, such as linezolid, tedizolid, radezolid, and sutezolid, with HDAS-β-CD based on capillary electrokinetic chromatography (cEKC), nuclear magnetic resonance (NMR) spectroscopy, and MM methods was described. Principles of chiral separation of oxazolidinone analogues using charged single isomer derivatives of cyclodextrin by the cEKC method were presented, including the selection of the optimal chiral selector and separation conditions, complex stoichiometry, and binding constants, which provided a comprehensive basis for MM studies. In turn, NMR provided, where possible, direct information on the geometry of the inclusion complexes and also provided the necessary structural information to validate the MM calculations. Consequently, MM contributed to the understanding of the structure of diastereomeric complexes, the thermodynamics of complexation, and the visualization of their structures. The most probable mean geometries of the studied supramolecular complexes and their dynamics (geometry changes over time) were determined by molecular dynamics methods. Oxazolidinone ligands have been shown to complex mainly the inner part of cyclodextrin, while the external binding is less privileged, which is consistent with the conclusions of the NMR studies. Enthalpy values of binding of complexes were calculated using long-term molecular dynamics in explicit water as well as using molecular mechanics, the Poisson–Boltzmann or generalized Born, and surface area continuum solvation (MM/PBSA and MM/GBSA) methods. Computational methods predicted the effect of changes in pH and composition of the solution on the strength and complexation process, and it adapted the conditions selected as optimal during the cEKC study. By changing the dielectric constant in the MM/PBSA and MM/GBSA calculations, the effect of changing the solution to methanol/acetonitrile was investigated. A fairly successful attempt was made to predict the chiral separation of the oxazolidinones using the modified cyclodextrin by computational methods.

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