scholarly journals Dissociation and recombination in the electrolyte flow model

2021 ◽  
Vol 2090 (1) ◽  
pp. 012076
Author(s):  
A Shobukhov ◽  
H Koibuchi
Keyword(s):  
Flow Model ◽  
Numerical Solutions ◽  
Stable Equilibrium ◽  
Steady State Solution ◽  
System Of Equations ◽  
Constant Flow ◽  
Dimensional Model ◽  
Electrolyte Flow ◽  
One Dimensional ◽  
Dilute Aqueous Solution

Abstract We propose a one-dimensional model for the dilute aqueous solution of NaCl which is treated as an incompressible fluid placed in the external electric field. This model is based on the Poisson-Nernst-Planck system of equations, which also contains the constant flow velocity as a parameter and considers the dissociation and the recombination of ions. We study the steady-state solution analytically and prove that it is a stable equilibrium. Analyzing the numerical solutions, we demonstrate the importance of dissociation and recombination for the physical meaningfulness of the model.

BATCH DOUGH VISCOSITY INFLUENCE ON FLOW-PRESSURE CHARACTERISTICS OF THE KNEADING MACHINE

2019 ◽  
Author(s):  
В.С. РУБАН ◽  
В.И. АЛЕШИН ◽  
Д.С. БЕЗУГЛЫЙ
Keyword(s):  
Batch Process ◽  
System Of Equations ◽  
Systems Of Equations ◽  
The Finite Element Method ◽  
Dimensional Model ◽  
Symmetric Form ◽  
Pressure Function ◽  
One Dimensional ◽  
Flow Pressure ◽  
Transport Problems

Рассмотрены уравнения баланса и концентрационных потоков, базирующихся на моделях, позволяющих анализировать одноименные модели реологии течения в канале шнека блока замеса тестомесильной машины. Анализ процесса транспортировки и замеса на основе одномерной модели выявил необходимость использования сигмоидальной функции коэффициента напоропроводности от давления. Переход от одномерных задач к многомерным задачам переноса связан с преобразованием систем уравнений к симметричному виду. Полученные системы уравнений после использования теоремы Грина могут быть решены методом конечных элементов. The balance equation and concentration flows based on the models which make it possible to analyze the eponymous models of flow rheology in the block screw channel in a dough mixing machine has been considered. The analysis of the transportation and batch process based on one-dimensional model proved the necessity to apply sigmoidal coefficient of pressure function. The transition from one-dimensional problems to multidimensional transport problems is associated with the transformation of systems of equations to a symmetric form. The resulting system of equations after using Green’s theorem can be solved by the finite element method.

A simple calculation method for estimating the flow velocity on the roof of a train running through a tunnel using an unsteady incompressible flow model

2019 ◽  
Vol 234 (7) ◽  
pp. 734-748
Author(s):  
Katsuhiro Kikuchi ◽  
Satoru Ozawa ◽  
Yuhei Noguchi ◽  
Shinya Mashimo ◽  
Takanobu Igawa
Keyword(s):  
Boundary Layer ◽  
Flow Velocity ◽  
Calculation Method ◽  
Model Experiment ◽  
Flow Model ◽  
Simple Calculation ◽  
Dimensional Model ◽  
One Dimensional ◽  
Calculation Results ◽  
Tunnel System

Predicting the aerodynamic phenomena in a train-tunnel system is important for increasing the speed of railway trains. Among these phenomena, many studies have focused on the effects of pressure; however, only a few studies have examined the effects of flow velocity. When designing train roof equipment such as a pantograph and an aerodynamic braking unit, it is necessary to estimate the flow velocity while considering the influence of the boundary layer developed on the train roof. Until now, numerical simulations using a one-dimensional model have been utilized to predict the flow velocity around a train traveling through a tunnel; however, the influence of the boundary layer cannot be taken into consideration in these simulations. For this purpose, the authors have previously proposed a simple calculation method based on a steady incompressible tunnel flow model that can take into account the influence of the boundary layer, but this method could not incorporate the unsteadiness of the flow velocity. Therefore, in this study, the authors extend the previous simple calculation method such that it can be used for an unsteady incompressible tunnel flow. The authors compare the calculation results obtained from the extended method with the results of a model experiment and a field test to confirm its effectiveness.

scholarly journals Mathematical Model for the Electrokinetic Instability of Electrolyte Flow

2019 ◽  
Vol 224 ◽  
pp. 02003
Author(s):  
Andrey Shobukhov
Keyword(s):  
Electric Potential ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Steady State Solution ◽  
Stability Loss ◽  
Navier Stokes ◽  
Ion Distribution ◽  
Navier Stokes Equations ◽  
Dilute Aqueous Solution

We study a one-dimensional model of the dilute aqueous solution of KCl in the electric field. Our model is based on a set of Nernst-Planck-Poisson equations and includes the incompressible fluid velocity as a parameter. We demonstrate instability of the linear electric potential variation for the uniform ion distribution and compare analytical results with numerical solutions. The developed model successfully describes the stability loss of the steady state solution and demonstrates the emerging of spatially non-uniform distribution of the electric potential. However, this model should be generalized by accounting for the convective movement via the addition of the Navier-Stokes equations in order to substantially extend its application field.

scholarly journals One-dimensional model for a laser-ablated slab under acceleration

2004 ◽  
Vol 22 (2) ◽  
pp. 183-188 ◽  
Author(s):  
J. RAMÍREZ ◽  
R. RAMIS ◽  
J. SANZ
Keyword(s):  
Subsonic Flow ◽  
Numerical Solutions ◽  
Critical Surface ◽  
Slab Surface ◽  
Dimensional Model ◽  
Initial Value ◽  
Sonic Point ◽  
One Dimensional ◽  
Ablation Pressure ◽  
Simple Dependence

A one-dimensional model for a laser-ablated slab under acceleration g is developed. A characteristic value gc is found to separate two solutions: Lower g values allow sonic or subsonic flow at the critical surface; for higher g the sonic point approaches closer and closer to the slab surface. A significant reduction in the ablation pressure is found in comparison to the g = 0 case. A simple dependence law between the ablation pressure and the slab acceleration, from the initial value g0 to infinity, is identified. Results compared well with fully hydrodynamic computer simulations with Multi2D code. The model has also been found a key step to produce indefinitely steady numerical solutions to study Rayleigh–Taylor instabilities in heat ablation fronts, and validate other theoretical analysis of the problem.

scholarly journals A one-dimensional model for the interaction between cell-to-cell adhesion and chemotactic signalling

2011 ◽  
Vol 22 (4) ◽  
pp. 291-316 ◽  
Author(s):  
K. ANGUIGE
Keyword(s):  
Cell Adhesion ◽  
Discrete Model ◽  
Continuum Limit ◽  
Numerical Solutions ◽  
Problem Formulation ◽  
Dimensional Model ◽  
One Dimensional ◽  
Spatial Oscillations ◽  
Cell To Cell Adhesion ◽  
The Continuum

We develop and analyse a discrete, one-dimensional model of cell motility which incorporates the effects of volume filling, cell-to-cell adhesion and chemotaxis. The formal continuum limit of the model is a non-linear generalisation of the parabolic-elliptic Keller–Segel equations, with a diffusivity which can become negative if the adhesion coefficient is large. The consequent ill-posedness results in the appearance of spatial oscillations and the development of plateaus in numerical solutions of the underlying discrete model. A global-existence result is obtained for the continuum equations in the case of favourable parameter values and data, and a steady-state analysis, which, amongst other things, accounts for high-adhesion plateaus, is carried out. For ill-posed cases, a singular Stefan-problem formulation of the continuum limit is written down and solved numerically, and the numerical solutions are compared with those of the original discrete model.

Transient Response in a One-Dimensional Model of Thermoelastic Contact

1996 ◽  
Vol 63 (3) ◽  
pp. 575-581 ◽  
Author(s):  
Z. S. Olesiak ◽  
Yu. A. Pyryev
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Problem ◽  
Transient Response ◽  
Computational Simulation ◽  
Linear Equations ◽  
Numerical Results ◽  
System Of Equations ◽  
Dimensional Model ◽  
One Dimensional ◽  
Method Of Solution

We consider two layers of different materials with the initial gap between them in the field of temperature with imperfect boundary conditions in Barber’s sense. The model we discuss is that of two contacting rods (Barber and Zhang, 1988) which in the case of a single rod was devised and discussed by Dundurs and Comninou (1976, 1979). In this paper we try to make a step further in the investigation of the essentially nonlinear problem. Though we consider a system of the linear equations of thermoelasticity the nonlinearity is induced by the boundary conditions dependent on the solution. We present an algorithm for solving the system of equations based on Laplace’s transform technique. The method of solution can be used also in the dynamical problems with inertial terms taken into account. The numerical results have been obtained by a kind of computational simulation.

scholarly journals Extended stable equilibrium invaded by an unstable state

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Camila Castillo-Pinto ◽  
Marcel G. Clerc ◽  
Gregorio González-Cortés
Keyword(s):  
Domain Walls ◽  
Stable Equilibrium ◽  
Energy State ◽  
Front Propagation ◽  
Unstable State ◽  
Dimensional Model ◽  
One Dimensional ◽  
First Order ◽  
Contagious Diseases ◽  
Pattern Forming

Abstract Coexistence of states is an indispensable feature in the observation of domain walls, interfaces, shock waves or fronts in macroscopic systems. The propagation of these nonlinear waves depends on the relative stability of the connected equilibria. In particular, one expects a stable equilibrium to invade an unstable one, such as occur in combustion, in the spread of permanent contagious diseases, or in the freezing of supercooled water. Here, we show that an unstable state generically can invade a locally stable one in the context of the pattern forming systems. The origin of this phenomenon is related to the lower energy unstable state invading the locally stable but higher energy state. Based on a one-dimensional model we reveal the necessary features to observe this phenomenon. This scenario is fulfilled in the case of a first order spatial instability. A photo-isomerization experiment of a dye-dopant nematic liquid crystal, allow us to observe the front propagation from an unstable state.

Quasi-one-dimensional model equations for plasma flows in high-pressure discharges in ablative capillaries

1992 ◽  
Vol 48 (2) ◽  
pp. 215-227 ◽  
Author(s):  
D. Zoler ◽  
S. Cuperman
Keyword(s):  
High Pressure ◽  
Numerical Solutions ◽  
Experimental Information ◽  
Dimensional System ◽  
System Of Equations ◽  
Two Dimensional ◽  
One Dimensional ◽  
Pressure Discharge ◽  
Model Equations ◽  
Energy Equations

Quasi-one dimensional hydrodynamic continuity, momentum and energy equations describing the plasma flow in high-pressure-discharge ablative capillaries are derived. To overcome the formidable difficulties arising in the solution of a fully two-dimensional system of equations, experimental information on the structure (geometry) of the generated plasma is used. Thus the two-dimensional hydrodynamic equations are averaged over the cross-section of the capillary to obtain a quasi-one-dimensional system of equations in which, however, the essential two-dimensional features are present. These include the radial outwards radiative transfer of energy and the radial inwards ablative mass flow. Some particular cases, including their thermodynamical aspects, are discussed. Illustrative analytical and numerical solutions of the equations are also presented.

MATHEMATICAL AND NUMERICAL ANALYSIS OF A THREE-DIMENSIONAL FLUID FLOW MODEL IN GLACIOLOGY

2005 ◽  
Vol 15 (01) ◽  
pp. 37-52 ◽  
Author(s):  
JACQUES RAPPAZ ◽  
ADRIAN REIST
Keyword(s):  
Flow Model ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Ice Sheets ◽  
Tetrahedral Mesh ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Piecewise Polynomial Functions ◽  
Theoretical Results

The main goal of this article is to analyze a three-dimensional model for stress and velocity fields in grounded glaciers and ice sheets including the role of normal deviatoric stress gradients. This model leads to a nonlinear system of stationary partial differential equations for the velocity with a viscosity depending on the stress–tensor but which is not explicitly depending on the velocity. The existence and uniqueness of a weak solution corresponding to this model is established by using the calculus of variations. The approximation of this model is made by a finite element method with piecewise polynomial functions of degree 1 on a tetrahedral mesh and error analysis is performed. Numerical solutions show that the theoretical results we have obtained are almost optimal.

scholarly journals Enhanced models for the nonlinear bending of planar rods: localization phenomena and multistability

2020 ◽  
Vol 476 (2242) ◽  
pp. 20200455
Author(s):  
Matteo Brunetti ◽  
Antonino Favata ◽  
Stefano Vidoli
Keyword(s):  
Dimensional Reduction ◽  
Compatibility Condition ◽  
Stable Equilibrium ◽  
Thin Shells ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Nonlinear Bending ◽  
One Dimensional ◽  
Equilibrium Configurations ◽  
Dimensional Models

We deduce a one-dimensional model of elastic planar rods starting from the Föppl–von Kármán model of thin shells. Such model is enhanced by additional kinematical descriptors that keep explicit track of the compatibility condition requested in the two-dimensional parent continuum, that in the standard rods models are identically satisfied after the dimensional reduction. An inextensible model is also proposed, starting from the nonlinear Koiter model of inextensible shells. These enhanced models describe the nonlinear planar bending of rods and allow to account for some phenomena of preeminent importance even in one-dimensional bodies, such as formation of singularities and localization (d-cones), otherwise inaccessible by the classical one-dimensional models. Moreover, the effects of the compatibility translate into the possibility to obtain multiple stable equilibrium configurations.

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