Debye Huckel Research Articles

Enhancement efficiency of flow and irreversibility system for MHD Buongiorno's nanofluid in complex peristaltic tapered channel with electroosmosis forces

Abstract Magnetohydrodynamic flow efficiency and irreversibility improvement research are multiple problems that arise when electroosmosis forces affect Buongiorno's nanofluid in a complicated peristaltic tapered channel. Thermal energy and temperature gradients cause nanoparticles to migrate randomly, affecting flow efficiency and irreversibility. Sometimes the Infected veins generate complex peristaltic waves on its walls. The mathematical model that characterizes the motion of Jeffrey magnetohydrodynamic Buongiorno's nanofluid inside a complex tapered peristaltic channel, considering the effects of electroosmotic forces is discussed. The long wavelength and low Reynolds numbers approximation is considered. The approximate solution of the nonlinear system of partial differential formulas is obtained using the Adomian decomposition method. Also, the irreversibility of the system and entropy generation are being studied. Flow characteristics with biophysical and thermal parameters are plotted and discussed. The improvement in the interstitial distances between the molecules that make up the nanofluid, which in turn works to enhance the Bejan numbers. So, one important result is by growing in both Brownian motion and thermophoresis, the Bejan numbers rise clearly. Both the Jeffrey parameter and Debye–Huckel parameter work to upsurge the loss of kinetic energy within the molecules, which reduces the temperatures inside the nanofluid and thus reduces the entropy rate, in contrast to the rest of the parameters that raise the kinetic energy inside the molecules that make up the nanofluid.

Multiphase flow and reactive transport benchmark for radioactive waste disposal

AbstractCompacted bentonite is part of the multi-barrier system of radioactive waste repositories. The assessment of the long-term performance of the barrier requires using reactive transport models. Here we present a multiphase flow and reactive transport benchmark for radioactive waste disposal. The numerical model deals with a 1D column of unsaturated bentonite through which water, dry air and $${\hbox {CO}_{2{(g)}}}$$ CO 2 ( g ) may flow and with the following reactions; aqueous complexation, calcite and gypsum dissolution/precipitation, cation exchange and gas dissolution. INVERSE-FADES-CORE V2, $$\hbox {DuMu}^X$$ DuMu X , TOUGHREACT and iCP were benchmarked with 6 test cases of increasing complexity, starting with conservative tracer transport under variably unsaturated conditions and ending with water flow, gas diffusion, minerals and cation exchange. The solutions of all codes exhibit similar trends. Small discrepancies are found in conservative tracer transport due to differences in hydrodynamic dispersion. Computed $${\hbox {CO}_{2{(g)}}}$$ CO 2 ( g ) pressures agree when a sufficiently refined grid is used. Small discrepancies in $${\hbox {CO}_{2{(g)}}}$$ CO 2 ( g ) and pH are found near the no-flow boundary at early times which vanish later. Discrepancies are due differences in the formulations used for gas flow at nearly water-saturated conditions. Computed $${\hbox {CO}_{2{(g)}}}$$ CO 2 ( g ) pressures show a fluctuation between $$10^{-4}$$ 10 - 4 and $$10^{-3}$$ 10 - 3 years which slows down the in-diffusion of $${\hbox {CO}_{2{(g)}}}$$ CO 2 ( g ) . This fluctuation is associated with chemical reactions involving $${\hbox {CO}_{2}}$$ CO 2 . There are discrepancies in solute concentrations due to differences in the Debye–Hückel (DH) formulation. They are overcome when all codes use the same DH formulation. The results of this benchmark will contribute to increase the confidence on multiphase reactive transport models for radioactive waste disposal.

Electroosmotic peristaltic transport of magnetohydrodynamic Casson nanofluid in a non-uniform wavy porous asymmetric micro-channel

Magnetohydrodynamics (MHD) have numerous engineering and biomedical applications such as sensors, MHD pumps, magnetic medications, MRI, cancer therapy, astronomy, cosmology, earthquakes, and cardiovascular devices. In view of these applications and current developments, we investigate the magnetohydrodynamic MHD electro-osmotic flow of Casson nanofluid during peristaltic movement in a non-uniform porous asymmetric channel. The effect of thermal radiation, heat source, and Hall current on the Casson fluid peristaltic pumping in a porous medium is taken into consideration. The effect of chemical reactions is also considered. The mass, momentum, energy, and concentration equations were constructed using the proper transformations and dimensionless variables to make them easier for non-Newtonian fluids. A lubricating strategy is used to make the system less complicated. The Boltzmann distribution of electric potential over an electric double layer is studied using the Debye–Huckel approximation. The temperature and concentration equations are addressed using the homotopy perturbation method (HPM), while the exact solution is determined for the velocity field. The study examines the performance of velocity, pressure rise, temperature, concentration, streamlines, Nusselt, and Sherwood numbers for the involved parameters using graphical illustrations and tables. Asymmetric channels exhibit varying behavior, with velocity declining near the left wall and accelerating towards the right wall while enhancing the Casson fluid parameter. The pumping rate boosts in the retrograde region due to the evolution of the permeability parameter value, while it declines in the augment region. The temperature profile optimizes as the value of the heat source parameter gets higher. The concentration profile significantly falls as the chemical reaction parameter rises. The size of the trapped bolus strengthens with a spike in the parameter for the Casson fluid.

Comment on "Binding Debye-Hückel theory for associative electrolyte solutions" [J. Chem. Phys. 159, 154503 (2023)

It is argued that the Binding Debye-Hückel (BiDH) model proposed by Naseri Boroujeni et al. [J. Chem. Phys. 159, 154503 (2023)] might not be appropriate for the description of Monte Carlo simulation data obtained for primitive model electrolytes. The first reason is that the original Debye-Hückel (DH) theory is of low accuracy for describing deviations from ideality in concentrated solutions of strong salts. The DH framework is thus a poor basis for building a model including association. The second reason is that the mean-spherical approximation, without assumption of association, apparently predicts Monte Carlo (MC) data for primitive electrolytes better than BiDH. Thus, the BiDH model seems to be simply a way of compensating for the deficiencies of DH theory by assuming association.

Response to "Comment on 'Binding Debye-Hückel theory for associative electrolyte solutions'" [J. Chem. Phys. 159, 154503 (2023)

This Response addresses critiques raised about the Binding Debye-Hückel (BiDH) theory [Naseri Boroujeni et al., J. Chem. Phys. 159, 154503 (2023)] by Simonin and Bernard [J.-P. Simonin and O. Bernard, J. Chem. Phys. (2024)]. The critiques questioned the foundational framework of the Debye-Hückel (DH) theory, the relevance of ion pairing in primitive model fluids, and the accuracy of the BiDH model compared to mean spherical approximation model. Through a systematic rebuttal, supported by extensive literature review and comparison with Monte Carlo simulation data, this Response addresses these concerns. It demonstrates the efficacy of DH theory in describing real electrolyte solutions, validates the relevance of ion pairing in primitive model fluids, and establishes the BiDH model's accuracy in describing electrolyte properties.

Effects of axial electric and transverse magnetic fields on a rotating electro-osmotic flow in micro-parallel plates

This paper explores the combined influence of an axial electric field and a perpendicular magnetic field imposed on rotating micro-parallel plates immersed in an electrolyte solution. A specialized computer program was developed to solve the velocity as well as the EDL potential fields using the finite difference method, employing the Debye-Hückel (DH) approximation to linearization the EDL potential. The study examines the influence of various non-dimensional parameters, including rotational speed (ω), Hartmann number (Ha), Debye-Hückel parameter (κ), and the non-dimensional parameter ‘S’, on axial, and transverse velocities, wall shear stress, and net flow rate. Results demonstrate that, both velocity components decrease with increased rotational speed and Hartmann number, while the net flow rate increases with the Debye-Hückel parameter for both rotating and non-rotating systems. The impact of these parameters on shear stress was also analyzed. Analysis of Ekmann spirals in the velocity plane revealed closed spirals at a higher rotational speed and open spirals at lower speeds, with spiral size reducing as rotational speed increases.

Effects of multiple relaxation times in the annular flow of pulsatile electro-osmotic flow of a complex biological fluid: blood with low and high cholesterol

This study investigates the electro-osmotic flow of a biological fluid (blood with varying cholesterol levels) in annular flow to simulate a first approximation to arterial occlusion. The fluid´s rheology is characterized by a multi-modal convected Maxwell model equation. The charge density follows the Boltzmann distribution, governing the electrical field. Mathematically, this scenario can be modeled by the Poisson–Boltzmann partial differential equation. Assuming a small zeta potential (less than 25 mV) using the Debye–Huckel approximation and considering a pulsatile electrical field, analytical solutions are derived using the Fourier transform formalism. These solutions, expressed in terms of the modified Bessel function, provide transfer functions for axial velocity and volumetric flow as functions of material parameters represented by characteristic dimensionless numbers. This study further analyzes thermal, electric, inertial, viscoelastic, and various interactions within the plasma, hematocrit, hematocrit–cholesterol, and cholesterol–cholesterol as well as weight concentration through numerical simulations. Finally, the flow and rheology predictions are validated using experimental data on human blood with varying cholesterol levels. The obtained transfer functions reveal that the electric–thermal–viscoelastic effects and the multiple geometric relationships contribute to the dynamic response of the interactions between the input electrical field and output volumetric flow and shear stress functions, leading to and evolution of resonance curves. It is noteworthy that electro-osmotic flow in blood with pathologies associated with low and high cholesterol has been scarcely reported in the literature on rheology. Thus, this work represents a significant contribution to the field.

Photoionization process of the hydrogenlike carbon ion embedded in warm and hot dense plasmas.

Complicated many-body interactions between ions and surrounding particles exist in warm and hot dense plasmas. It will significantly alter the atomic structures and dynamic properties of the embedded ions. Recently, the atomic-state-dependent (ASD) screening model has been proposed and shown to be valid for investigating the screening effect in warm and hot dense plasmas over a wide range of electron densities and temperatures. By employing the ASD model, we investigate the photoionization process for the hydrogenlike carbon ion embedded in warm and hot dense plasmas with corresponding Coulomb coupling parameter ranges of 0.05 ≤ Γ ≤ 1.16, where Γ characterizes the ratio of the average potential to thermal energy. It is found that there are stronger plasma screening effects on the ionization energy and photoionization cross section due to the negative-energy electron distributions considered in the ASD model compared to those considering only free electrons. The present results from the ASD model show reasonable agreement with the classical Debye-Hückel (DH) model in weakly coupled plasmas. However, significant deviations of the ionization energy and cross section between these two models are observed in moderately and strongly coupled plasmas, due to the approximate treatment of the plasma-electron density distribution of the DH model. In the region of low photoelectron energies, the positions of the shape resonance peaks of the cross sections obtained from the ASD model differ significantly from those of the DH model due to the different screening effects.

Systematic Incorporation of Ionic Hard-Core Size into the Debye-Hückel Theory via the Cumulant Expansion of the Schwinger-Dyson Equations.

The Debye-Hückel (DH) formalism of bulk electrolytes equivalent to the Gaussian-level closure of the electrostatic Schwinger-Dyson identities without the interionic hard-core (HC) coupling is extended via the cumulant treatment of these equations augmented by HC interactions. By comparing the monovalent ion activity and pressure predictions of our cumulant-corrected DH (CCDH) theory with hypernetted-chain results and Monte Carlo simulations from the literature, we show that this rectification extends the accuracy of the DH formalism from submolar to molar salt concentrations. In the case of internal energies or the general case of divalent electrolytes mainly governed by charge correlations, the improved accuracy of the CCDH theory is limited to submolar ion concentrations. Comparison with experimental data from the literature shows that, via the adjustment of the hydrated ion radii, CCDH formalism can equally reproduce the nonuniform effect of salt increment on the ionic activity coefficients up to molar concentrations. The inequality satisfied by these HC sizes coincides with the cationic branch of the Hofmeister series.

Numerical entropy analysis of MHD electro-osmotic flow of peristaltic movement in a nanofluid

The present study investigates the MHD electro-osmotic flow of entropy generation analysis for peristaltic movement in a nanofluid with temperature-dependent viscosity. Long wavelengths, i.e., The magnitude of a wave's energy corresponds directly to its frequency while being inversely related to its wavelength in terms of velocity, temperature, and concentration, govern and confine the flow stream in the laminar region. Ohmic heating and hall effects are also included. Graphs are used to obtain and examine numerical solutions for axial velocity, temperature, concentration, Bejan number, and entropy generation. The effects of this research can help to improve pumping and gastrointestinal movements in different engineering devices. Debye–Huckel and lubrication approximations are studied to access the Boltzmann distribution of electric potential across an electric double layer. The investigations of an existing model are important in illuminating the microfluidics machinery used at the micro level for various transport phenomena in which fluids as well as particles are transported together. The current study has many applications and can be further extended to a three-dimensional profile with appropriate modifications and assumptions. When studying entropy generation, it is essential to examine the irreversible factors, while also taking into account the velocity and thermal slip conditions at channel boundaries. Moreover, the concept of entropy generation holds significant importance in comprehending various biological phenomena. Hence, the current research holds promising implications for both industrial and medical fields. The entropy generation is minimum at left wall of the channel for negative values of Helmholtz-Smoluchowski velocity.

Energy Shift of the Atomic Emission Lines of He-like Ions Subject to Outside Dense Plasma

We present an extension of our study of the energy shift of the atomic emissions subject to charged-neutral outside dense plasma following the good agreement between the experimental measurements and our recent theoretical estimates for the α and β emission lines of a number of H-like and He-like ions. In particular, we are able to further demonstrate that the plasma-induced transition energy shift could indeed be interpolated by the simple quasi-hydrogenic picture based on the application of the Debye–Hückel (DH) approximation for the n=3 to n=2 transitions of the He-like ions. Our theoretically estimated redshifts of those emissions may offer the impetus for additional experimental measurement to facilitate the diagnostic efforts in the determination of the temperature and density of the dense plasma.

Peristalsis of Carreau–Yasuda nanofluid possessing variable thermal conductivity regulated by electroosmosis via an expanding asymmetric channel

Peristalsis of non-Newtonian nanofluid via a non-uniform conduit has several applications in physiology and industry. This study proposes a mathematical model as well as exploration of the impacts of entropy generation for peristalsis of magneto nanofluid with temperature-dependent thermal conductivity via an expanding asymmetric channel. Buongiorno’s model for study of nanofluid flow has been adopted. Rheological aspects are accounted using the Carreau–Yasuda model due to its experimentally validated significance. Impacts of applied electric and magnetic fields have been taken into account. Thermophoresis, ohmic heating, viscous heating and Brownian motion effects are incorporated in the model. Numerical method is used via NDSolve in Mathematica after implementing the lubrication approach and Debye–Huckel linearization. The effects of embedded parameters on the flow, heat transfer, entropy generation and Bejan number are studied using graphical depictions. Outcomes indicate that a rise in electroosmotic parameter enhances heat transfer rate, whereas it reduces entropy generation and mass transfer rate at the boundary. Therefore, this study can provide basics to study nanofluidic systems which has applications in drug delivery. Increasing trends for temperature, heat transfer rate and entropy generation, while declining trends in the concentration of the particles are noted for higher joule heating.

Self-consistent electrostatic formalism of bulk electrolytes based on the asymmetric treatment of the short- and long-range ion interactions.

We predict the thermodynamic behavior of bulk electrolytes from an ionic hard-core (HC) size-augmented self-consistent formalism incorporating asymmetrically the short- and long-range ion interactions via their virial and cumulant treatment, respectively. The characteristic splitting length separating these two ranges is obtained from a variational equation solved together with the Schwinger-Dyson (SD) equations. Via comparison with simulation results from the literature, we show that the asymmetric treatment of the distinct interaction ranges significantly extends the validity regime of our previously developed purely cumulant-level Debye-Hückel (DH) theory. Namely, for monovalent solutions with typical ion sizes, the present formalism can accurately predict up to molar concentrations the liquid pressure dominated by HC interactions, the internal energies driven by charge correlations, and the local ion distributions governed by the competition between HC and electrostatic interactions. We evaluate as well the screening length of the liquid and investigate the deviations of the macromolecular interaction range from the DH length. In fair agreement with simulations and experiments, our theory is shown to reproduce the overscreening and underscreening effects occurring respectively in submolar mono- and multivalent electrolytes.

Effects of Non-Thermal Plasma on the Transition from Nano-Crystalline to Amorphous Structure in Water and Subsequent Effects on Viscosity

Recent studies have demonstrated that the physical properties of water treated with non-thermal plasma, or plasma-activated water (PAW), significantly differ from those of distilled water. For example, contrary to expectation, the viscosity of PAW becomes lower than that of distilled water at certain temperatures. This study developed a model to explain these differences by combining the two-state model of ordinary water, which describes water as a combination of nano-crystalline clusters and amorphous, free-floating molecules, using the Debye–Huckel theory for a fluid containing ions. A model for the viscosity of PAW was then developed from the general model. It explains how PAW has a lower viscosity than distilled water as the temperature decreases and why this effect is stronger than the colligative effect for ideal solutions. Finally, the viscosity model is compared to the experimental measurements of PAW treated with gliding arc plasma, showing that the data match the predicted values quite well. The model of PAW developed here can be used to understand other physical properties beyond viscosity, such as the surface tension, contact angle, electric conductivity, heat capacity, isothermal compressibility, and density, potentially facilitating new applications of PAW.

Impact of Ionic Strength and Charge Density on Donnan Potential in the NaCl-Cation Exchange Membrane System

This work aims to theoretically investigate the effect of both the fixed charge density of ion exchange membranes and the ionic strength of the treated aqueous NaCl solution on the generated Donnan potential at thermodynamic equilibrium conditions. The direct objective of our work is to calculate the equilibrium concentration of the Cl− co-ion inside a swelled cation-exchange membrane equilibrated with a water/NaCl system. Two activity coefficient models are employed, i.e., the Debye–Huckel (DH) model (as a reference model) and the Meissner model, which is known for its applicability in treating concentrated solutions. Experimental data available in the literature for Donnan potential are used to verify model predictions. Our study confirms that a high fixed charge density is required to counterbalance the deterioration in membrane selectivity encountered in high-salinity systems. The DH model can be safely used to predict the Donnan potential for feed compositions up to 0.1 M. At higher compositions, the DH model significantly overestimates the predicted (absolute) Donnan potential compared to the Meissner model. The osmotic pressure resulting from the difference in ionic concentration between the membrane phase and the feed phase is found to have insignificant effects on the Donnan potential. The equilibrium computations and methodology are presented in a general way that enables handling multivalent electrolyte systems such as CaCl2.

Contribution of electromagnetism in lowering entropy in microchannel

The study examined how entropy can be reduced in an asymmetric microchannel with sinusoidal walls by analyzing the flow of an incompressible micropolar fluid that is electrokinetically driven. The study takes into account the effects of Ohmic and viscous dissipation of energy in a magnetohydrodynamic environment. To model electroosmotic phenomena, the Poisson equation and Nernst–Planck equation were used, which were simplified using Debye–Huckel linearization and a small ionic Peclet number. The energy, rotational momentum, mass, and momentum equations for the micropolar fluid were constructed and linearized using a lubrication approach before being solved analytically. The resulting expressions for velocity microrotation and temperature were then used to compute the Bejan number and the formation of entropy number The study also examined the effects of various thermophysical parameters and discussed their potential applications in fields such as biomedical engineering, pharmaceuticals, energy conservation, cancer treatment, and manufacturing. The findings suggest that entropy generation can be reduced by increasing the micropolar coupling number and temperature difference parameter This study provides a theoretical guide for the operation and thermal control of flow actuation systems with asymmetric geometry.

Binding Debye-Hückel theory for associative electrolyte solutions.

This study presents a new equation of state (EOS) for charged hard sphere fluids that incorporates ion-ion association. The EOS is developed using the Debye-Hückel (DH) theory, reference cavity approximation, and Wertheim's theory. Predictive accuracy is evaluated by comparing the model's predictions with Monte Carlo simulations for various charged hard-sphere fluids. The assessment focuses on mean ionic activity coefficient, individual ionic activity coefficient, and osmotic coefficients. The results demonstrate good agreement between the model and simulations, indicating its success for different electrolyte systems. Incorporating ion-ion association improves accuracy compared to the DH theory. The importance of the cavity function and ion-dipole interactions is emphasized in accurately representing structural properties. Overall, the developed EOS shows promising predictive capabilities for charged hard sphere fluids, providing validation and highlighting the significance of ion-ion association in thermodynamic predictions of electrolyte solutions.

Modeling the effects of salt concentration on aqueous and organic electrolytes

Understanding the thermodynamic properties of electrolyte solutions is of vital importance for a myriad of physiological and technological applications. The mean activity coefficient γ± is associated with the deviation of an electrolyte solution from its ideal behavior and may be obtained by combining the Debye-Hückel (DH) and Born (B) equations. However, the DH and B equations depend on the concentration and temperature-dependent static permittivity of the solution εr(c, T) and the size of the solvated ions ri, whose experimental data is often not available. Here, we use a combination of molecular dynamics and density functional theory to predict εr(c, T) and ri, which enables us to apply the DH and B equations to any technologically relevant aqueous and nonaqueous electrolyte at any concentration and temperature of interest.

Entropy generation optimization for the electroosmotic MHD fluid flow over the curved stenosis artery in the presence of thrombosis

The present study deals with the entropy generation analysis on the flow of an electrically conductive fluid (Blood) with hbox {Al}_2hbox {O}_3-suspended nanoparticles through the irregular stenosed artery with thrombosis on the catheter. The fluid flow can be actuated by the interactions of different physical phenomena like electroosmosis, radiation, Joule heating and a uniform radial magnetic field. The analysis of different shapes and sizes of the nanoparticle is considered by taking the Crocine model. The velocity, temperature, and concentration distributions are computed using the Crank–Nicholson method within the framework of the Debye–Huckel linearization approximation. In order to see how blood flow changes in response to different parameters, the velocity contour is calculated. The aluminium oxide nanoparticles employed in this research have several potential uses in biomedicine and biosensing. The surface’s stability, biocompatibility, and reactivity may be enhanced by surface engineering, making the material effective for deoxyribonucleic acid sensing. It may be deduced that the velocity profile reduces as the nanoparticle’s size grows while depicts the reverse trend for the shape size. In a region close to the walls, the entropy profile decreases, while in the region in the middle, it rises as the magnetic field parameter rises. The present endeavour can be beneficial in biomedical sciences in designing better biomedical devices and gaining insight into the hemodynamic flow for treatment modalities.

A mathematical model for cilia actuated transport of Gold–Silver hybrid nanofluid EMHD flow with activation energy phenomena

The advancement of nanobiotechnology is happening with leap and bound and the maneuvering in application of nanofluids in medical field is emerged as major research topic in recent times. Motivated by key applications in this direction, the current investigation embarks to explore the hybrid nanofluid dynamics in a ciliated inclined microchannel with various physical impacts, electromagnetohydrodynamic (EMHD), gyrotactic microorganisms, activation energy, and solar radiation. The pertinent equations of motion are tackled with low Reynolds number, long wavelength, and Debye–Huckel linearization approximations. The resulting equations of motion after simplifications tackled with the implementation numerical computations in Mathematica. The variations of pivotal physical parameters on the flow dynamics and thermal axiom are exhibited with graphical illustrations. It is worth mention here that the Hartmann, Grashof, electroosmotic, buoyancy, bioconvection parameters surged the hybrid nanofluid velocity adjacent to right wall. The temperature goes down with the thermal radiation and thermophoresis parameters. The radiation, Brownian motion, thermophoresis parameters reinforce the nanoparticle volume fraction, and motile microorganisms. The reported investigation has great significance for physiological fluid transport in the gastrointestinal tract, managing the bleeding by manipulating the magnetic field and in drug infusion mechanism.