Effect of Erosion Damage on Diffusion of Sulfate Ions in Concrete

2011 ◽  
Vol 243-249 ◽  
pp. 4683-4686 ◽  
Author(s):  
Chao Sun ◽  
Jian Kang Chen
Keyword(s):  
Differential Equation ◽  
Diffusion Equation ◽  
Numerical Method ◽  
Nonlinear Diffusion ◽  
Damage Evolution ◽  
Sulfate Attack ◽  
Nonlinear Diffusion Equation ◽  
Second Law ◽  
Sulfate Ions ◽  
Erosion Damage

Based on Fick’s second law and the damage evolution due to sulfate attack, a new model is proposed to analyze the diffusion of sulfate ions in concrete. The relation between erosion damage and erosion time, as well as the concentration of sulfate ions is firstly investigated by virtue of the ultrasonic experimental results. Furthermore, the damage evolution is treated as the increase of porosity, and a new nonlinear differential equation on the diffusion of sulfate ions is established by substituting such an increasing porosity into Fick’s law. The nonlinear diffusion equation is then solved by numerical method. It is found that the erosion damage can significantly affect the diffusion of sulfate ions in concrete.

scholarly journals Nonlinear diffusivity dependence on dimensions

2015 ◽  
Vol 56 ◽  
Author(s):  
Arvydas Juozapas Janavičius ◽  
Sigita Turskienė ◽  
Kęstutis Žilinskas
Keyword(s):  
Diffusion Equation ◽  
Nonlinear Diffusion ◽  
Diffusion Processes ◽  
Three Dimensional ◽  
Nonlinear Diffusion Equation ◽  
Classical Solutions ◽  
Second Law ◽  
Tail Region ◽  
Linear Diffusion ◽  
Good Coincidence

The nonlinear diffusion equation corresponds to the diffusion processes which can occur with a finite velocity. This statement is not satisfied in Fick’s second law or linear diffusion equation. The processes by which different materials mix in the result of the random Brownian motions of atoms, molecules and ions can be exactly described only with presented nonlinear equation. It was important in practice that theoretically profiles fit with the experimental profiles tail region, but get good coincidence between diffusion experiments and the classical solutions is impossible. By using obtained theoretical solutions for two and three-dimensional cases we can provide more exact modeling of all the stages of a planar transistor formation.

NONLINEAR DIFFUSION EQUATION WITH A PERTURBED CONVECTIONTERM: POTENTIAL SYMMETRIES WITH RESPECT TO THE SECOND CONSERVATION LAW

2021 ◽  
Vol 10 (5) ◽  
pp. 2611-2624
Author(s):  
O.K. Narain ◽  
F.M. Mahomed
Keyword(s):  
Diffusion Equation ◽  
Conservation Law ◽  
Nonlinear Diffusion ◽  
Nonlinear Diffusion Equation ◽  
The Other ◽  
Linear Case ◽  
Exact Equation ◽  
Convection Term ◽  
Potential Symmetries ◽  
Perturbed Equation

We consider the nonlinear diffusion equation with a perturbed convection term. The potential symmetries for the exact equation with respect to the second conservation law are classified. It is found that these exist only in the linear case. It is further shown that no nontrivial approximate potential symmetries of order one exists for the perturbed equation with respect to the other conservation law.

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