Peristaltic flow of electrically conducting nanofluid under the action of Joule and radiative heat within an asymmetric microchannel

The proposed mathematical model is based upon the peristaltic flow of an electrical conducting nanofluid within an asymmetric microchannel. The flow takes place under the action of dissipative heat energy due to the occurrence of the magnetic field that is basically known as Joule heating and radiative heat proposed as thermal radiation along with the additional heat source. Moreover, the impact of upper/lower wall zeta potential and the expression for the electric potential is presented using the Poisson Boltzmann equation and Debey length approximation. The well-known numerical practice is used for distorted governing equations with appropriate boundary conditions. Further, computation of the pressure gradient is obtained for the associated physical parameters. The graphical illustration shows the characteristics of the pertinent parameters on the flow problem and the tabular result represents the simulated values for the rate coefficients. In the significant examination, the study reveals that the mobility parameter due to the occurrence of the electric field vis-à-vis time parameter encourages the velocity distribution within the center of the channel furthermore significant retardation occurs near the wall region.

The pH-dependent Swelling of Weak Polyelectrolyte Hydrogels Modeled at Different Levels of Resolution

The swelling of polyelectrolyte hydrogels has been often explained using simple models derived from the Flory-Rehner model. While these models qualitatively predict the experimentally observed trends, they also introduce strong approximations and neglect some important contributions. Consequently, they sometimes incorrectly ascribe the observed trends to contributions which are of minor importance under the given conditions. In this work, we investigate the swelling properties of weak (pH-responsive) polyelectrolyte gels at various pH and salt concentrations, using a hierarchy of models, gradually introducing various approximations. For the first time, we introduce a three-dimensional particle-based model which accounts for the topology of the hydrogel network, for electrostatic interactions between gel segments and small ions and for acid-base equilibrium coupled to the Donnan partitioning of small ions. This model is the most accurate one, therefore, we use it as a reference when assessing the effect of various approximations. As the first approximation, we introduce the affine deformation, which allows us to replace the network of many chains by a single chain, while retaining the particle-based representation. In the next step, we use the mean-field approximation to replace particles by density fields, combining the Poisson-Boltzmann equation with elastic stretching of the chain. Finally, we introduce an ideal gel model by neglecting the electrostatics while retaining all other features of the previous model. Comparing predictions from all four models allows us to understand which contributions dominate at high or low pH or salt concentrations. We observe that the field-based models overestimate the ionization degree of the gel because they underestimate the electrostatic interactions. Nevertheless, a cancellation of effects on the electrostatic interactions and Donnan partitioning causes that both particle-based and field-based models consistently predict the swelling of the gels as a function of pH and salt concentration. Thus, we can conclude that any of the employed models can rationalize the known experimental trends in gel swelling, however, only the particle-based models fully account for the true effects causing these trends. The full understanding of differences between various models is important when interpreting experimental results in the framework of existing theories and for ascribing the observed trends to particular contributions, such as the Donnan partitioning of ions, osmotic pressure or electrostatic interactions.

Ionization equilibrium in a highly imperfect smoke plasma

The ionization equilibrium in a heterogeneous strongly nonideal smoky plasmas containing condensed particles and an easily ionized addition of cesium atoms in the gas phase is considered. To determine the charges of particles, the nonlinear Poisson-Boltzmann equation was used, and for the ionization of atoms of the gas phase, the Saha equation taking into account the effect of the displacement of the ionization equilibrium. The dependences of the concentration of electrons and particle charges, as well as the interface between the regions of positive and negative charges of particles, on the concentration of cesium atoms and the concentration of aluminum oxide particles are obtained.

A Deep Neural Network based on ResNet for Predicting Solutions of Poisson–Boltzmann Equation

The Poisson–Boltzmann equation (PBE) arises in various disciplines including biophysics, electrochemistry, and colloid chemistry, leading to the need for efficient and accurate simulations of PBE. However, most of the finite difference/element methods developed so far are rather complicated to implement. In this study, we develop a ResNet-based artificial neural network (ANN) to predict solutions of PBE. Our networks are robust with respect to the locations of charges and shapes of solvent–solute interfaces. To generate train and test sets, we have solved PBE using immersed finite element method (IFEM) proposed in (Kwon, I.; Kwak, D. Y. Discontinuous bubble immersed finite element method for Poisson–Boltzmann equation. Communications in Computational Physics 2019, 25, pp. 928–946). Once the proposed ANNs are trained, one can predict solutions of PBE in almost real time by a simple substitution of information of charges/interfaces into the networks. Thus, our algorithms can be used effectively in various biomolecular simulations including ion-channeling simulations and calculations of diffusion-controlled enzyme reaction rate. The performance of the ANN is reported in the result section. The comparison between IFEM-generated solutions and network-generated solutions shows that root mean squared error are below 5·10−7. Additionally, blow-ups of electrostatic potentials near the singular charge region and abrupt decreases near the interfaces are represented in a reasonable way.

Mean-field theory of the interaction of the magnesium ion with biopolymers: the case of lysozyme

A statistical theory is presented of the magnesium ion interacting with lysozyme under conditions where the latter is positively charged. Temporarily assuming magnesium is not noncovalently bound to the protein, I solve the nonlinear Poisson–Boltzmann equation accurately and uniformly in a perturbative fashion. The resulting expression for the effective charge, which is larger than nominal owing to overshooting, is subtle and cannot be asymptotically expanded at high ionic strengths that are practical. An adhesive potential taken from earlier work together with the assumption of possibly bound magnesium is then fitted to be in accord with measurements of the second virial coefficient by Tessier et al. The resulting numbers of bound magnesium ions as a function of MgBr$$_2$$ 2 concentration are entirely reasonable compared with densitometry measurements.