移动Liesegang图案的数值模拟

Numerical Simulation of Moving Liesegang Pattern

基于数学模型对移动Liesegang斑图进行动态模拟发现,不同比例的内外电解质浓度能形成3种不同沉淀图案:单根带,完全分散的多根带,以及两种共存的图案。相同模拟条件下,内电解质浓度的变化对图案外形有较大影响,出现多根沉淀带与单根沉淀带的转化。计算表明,移动Liesegang带出现的位置和时间满足时间定律(X_(n)~t_(n)^(1/2)),不过Liesegang带移动速度随内电解质浓度增加而减慢,随外电解质浓度增加而增加,相同浓度比下同一时刻沉淀位置相同。对特定浓度下产生的超级带进行分析发现,这些细纹也符合Liesegang图案的空间定律,当K值逐渐增大,沉淀细条纹数变少,条纹间距变大。

In the same conditions of simulation,initial concentration of inner electrolyte play a important role in altering the bang morphology,transforming from a simple moving precipitation pulse to moving precipitation bands.Our calculation further illustrates that the location of X n of the moving band and its time of formation satisfies time law,X_(n)~t_(n)^(1/2).With the increasing of inner electrolyte concentration,the speeds of the precipitation pulse decrease,in the reverse case increasing the concentration of the outer electrolyte results in a faster motion.Location of bands was fixed under the same concentration ratio of the inner electrolyte and the outer electrolyte.We find that these fine structure of super bands is also in line with the space law of Liesegang pattern under a specific concentration,fewer bands are formed with increasing band spacing when value of K increases.The work performed in this paper is useful for further understanding Liesegang pattern formation and also provides guidance to future experiments.