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Open AccessArticle

# Numerical Modelling of Effects of Biphasic Layers of Corrosion Products to the Degradation of Magnesium Metal In Vitro

by 1,* and
1
Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, UK
2
Department of Mechanical, Electrical and Manufacturing Engineering, Loughborough University, Loughborough LE11 3TU, UK
*
Author to whom correspondence should be addressed.
Materials 2018, 11(1), 1; https://doi.org/10.3390/ma11010001
Received: 1 November 2017 / Revised: 6 December 2017 / Accepted: 14 December 2017 / Published: 21 December 2017
(This article belongs to the Special Issue Constitutive Modelling of Biological Tissues and Biomaterials)
Magnesium (Mg) is becoming increasingly popular for orthopaedic implant materials. Its mechanical properties are closer to bone than other implant materials, allowing for more natural healing under stresses experienced during recovery. Being biodegradable, it also eliminates the requirement of further surgery to remove the hardware. However, Mg rapidly corrodes in clinically relevant aqueous environments, compromising its use. This problem can be addressed by alloying the Mg, but challenges remain at optimising the properties of the material for clinical use. In this paper, we present a mathematical model to provide a systematic means of quantitatively predicting Mg corrosion in aqueous environments, providing a means of informing standardisation of in vitro investigation of Mg alloy corrosion to determine implant design parameters. The model describes corrosion through reactions with water, to produce magnesium hydroxide Mg(OH) $2$ , and subsequently with carbon dioxide to form magnesium carbonate MgCO $3$ . The corrosion products produce distinct protective layers around the magnesium block that are modelled as porous media. The resulting model of advection–diffusion equations with multiple moving boundaries was solved numerically using asymptotic expansions to deal with singular cases. The model has few free parameters, and it is shown that these can be tuned to predict a full range of corrosion rates, reflecting differences between pure magnesium or magnesium alloys. Data from practicable in vitro experiments can be used to calibrate the model’s free parameters, from which model simulations using in vivo relevant geometries provide a cheap first step in optimising Mg-based implant materials. View Full-Text
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MDPI and ACS Style

Ahmed, S.K.; Ward, J.P.; Liu, Y. Numerical Modelling of Effects of Biphasic Layers of Corrosion Products to the Degradation of Magnesium Metal In Vitro. Materials 2018, 11, 1.

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