TY - JOUR
T1 - Etching of Mass, Surface, and Porous Fractal Solids
AU - Gavrilov, C.
AU - Sheintuch, M.
PY - 1997/8
Y1 - 1997/8
N2 - To study fractal aspects of reactive etching, we consider three types of solids with surface, mass, and pore fractality. An analytical solution for etching of the solid boundary in the form of a Koch curve demonstrates that in the absence of diffusion resistance bifractal structures are formed due to screening effects. Over a certain domain the surface area scales like t1-Df. Stochastic simulation of etching of solid clusters, obtained by diffusion-limited aggregation (DLA), shows that the dynamics strongly depend on the value of fractal dimension. Analytical approximation for the dynamics of etching based on the DLAs density distribution was obtained, showing that the mass scales like (1 - Kt)Df, where K is a certain constant, and was in excellent agreement with the simulation. The simulation of etching of a Sierpinski-gasket fractal and the corresponding uniform-pore object of the same size, porosity, and reactive area demonstrates the combined influence of diffusion resistance optimization and fractal geometry on the character of etching. The etching of fractal structures is significantly faster in the regions of strong and moderate diffusion resistance. In the region of strong diffusion resistance the rates of etching declined monotonically with time. The reaction occurred in a narrow penetration layer, and fractality did not break. No simple scaling is evident in this case.
AB - To study fractal aspects of reactive etching, we consider three types of solids with surface, mass, and pore fractality. An analytical solution for etching of the solid boundary in the form of a Koch curve demonstrates that in the absence of diffusion resistance bifractal structures are formed due to screening effects. Over a certain domain the surface area scales like t1-Df. Stochastic simulation of etching of solid clusters, obtained by diffusion-limited aggregation (DLA), shows that the dynamics strongly depend on the value of fractal dimension. Analytical approximation for the dynamics of etching based on the DLAs density distribution was obtained, showing that the mass scales like (1 - Kt)Df, where K is a certain constant, and was in excellent agreement with the simulation. The simulation of etching of a Sierpinski-gasket fractal and the corresponding uniform-pore object of the same size, porosity, and reactive area demonstrates the combined influence of diffusion resistance optimization and fractal geometry on the character of etching. The etching of fractal structures is significantly faster in the regions of strong and moderate diffusion resistance. In the region of strong diffusion resistance the rates of etching declined monotonically with time. The reaction occurred in a narrow penetration layer, and fractality did not break. No simple scaling is evident in this case.
UR - http://www.scopus.com/inward/record.url?scp=0031199596&partnerID=8YFLogxK
U2 - 10.1021/ie960605x
DO - 10.1021/ie960605x
M3 - 文章
AN - SCOPUS:0031199596
SN - 0888-5885
VL - 36
SP - 2915
EP - 2923
JO - Industrial and Engineering Chemistry Research
JF - Industrial and Engineering Chemistry Research
IS - 8
ER -