Building degradation is an important conservative issue. Among the principal causes of degradation of stone artefacts there is the crystallization of salts into the porous matrix, but also the presence of stains caused by iron compounds, responsible not only of exterior damages of lapideous artifacts but even in their structure. A new mathematical model describing the effect of phosphocitrate (PC) on sodium sulphate crystallization inside bricks is proposed [1]. A numerical fitting procedure of the parameters of model for both the case of the brick treated with PC and non treated case is implemented. Numerical results show the effectiveness of our method, since we obtain a low average error (around 12%) between measured data and simulated values. Moreover, here we present a preliminary study [2] of the phenomenon of the formation of Liesegang rings in porous materials in contact with iron sources. In order to describe the rings formation on Lecce stone found in laboratory experiments, we propose a modification of the classical Keller-Rubinow (K-R) model where the precipitation function is replaced by a smooth function to avoid instabilities of the model. In such a way, we are able to develop a simulation algorithm capturing the main features of phenomenon of Liesegang formation in the stone: the shape and the intensity of rings depends on the nearness to the iron source, as observed on the specimens used in the laboratory tests.
Mathematical Models for Cultural Heritage and Applications
Gabriella Bretti;Maurizio Ceseri;Roberto Natalini;Filippo Notarnicola
2018
Abstract
Building degradation is an important conservative issue. Among the principal causes of degradation of stone artefacts there is the crystallization of salts into the porous matrix, but also the presence of stains caused by iron compounds, responsible not only of exterior damages of lapideous artifacts but even in their structure. A new mathematical model describing the effect of phosphocitrate (PC) on sodium sulphate crystallization inside bricks is proposed [1]. A numerical fitting procedure of the parameters of model for both the case of the brick treated with PC and non treated case is implemented. Numerical results show the effectiveness of our method, since we obtain a low average error (around 12%) between measured data and simulated values. Moreover, here we present a preliminary study [2] of the phenomenon of the formation of Liesegang rings in porous materials in contact with iron sources. In order to describe the rings formation on Lecce stone found in laboratory experiments, we propose a modification of the classical Keller-Rubinow (K-R) model where the precipitation function is replaced by a smooth function to avoid instabilities of the model. In such a way, we are able to develop a simulation algorithm capturing the main features of phenomenon of Liesegang formation in the stone: the shape and the intensity of rings depends on the nearness to the iron source, as observed on the specimens used in the laboratory tests.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
