## 1 Introduction
For instance, natural fibres such as jute [17] and hemp [18] have been combined with PBAT to produce biodegradable composites suitable for packaging and other engineering applications. Additionally, nanoscale particles like cellulose nanocrystals [19] and titania nanoparticles [20] have been integrated into PBAT matrices to optimise processability and improve thermal and mechanical properties. A recent study has shown that PBAT can be combined with agricultural waste, such as rice husks [21] and wheat straw [22], presenting a sustainable solution for waste valorisation while reducing the environmental impact through the use of biodegradable polymers. These innovations demonstrate the potential of PBAT-based composites as a solution for sustainable composite manufacturing while contributing to a circular economy. Inspired by this, the team identified a research gap regarding incorporating alum sludge into PBAT composites to establish a novel industrial waste valorisation strategy. The aim of the work was to investigate the feasibility of using alum sludge as a functional filler in biodegradable composite manufacturing, converting undervalued industrial waste into useful products. The work firstly examined how alum sludge particle size influences the mechanical properties and biodegradation behaviour of the composites. Smaller particle sizes are reported to provide larger surface areas per unit volume, enabling more uniform stress transfer, which is critical for improving both mechanical properties and biodegradation performance [23]. Additionally, research suggests that a polydisperse mixture of particles can significantly affect the elastic modulus [24], highlighting the potential of optimised size distributions in enhancing composite performance. In this study, the alum sludge was pre-treated and categorised into two size distributions before being incorporated into PBAT to form composite samples. These composites were characterised for their mechanical properties and biodegradation behaviours; the latter were assessed through a composting test, in which the composites were buried in soil for 60 days. This methodological approach not only evaluates degradation over time but also provides insights into the lifecycle performance of biodegradable materials. The results highlight the role of alum sludge, in different size distributions, in influencing both the degradation rate and mechanical performance, aiding in the optimisation of composite formulations for improved environmental sustainability. Moreover, composite samples with varying alum sludge concentrations were also prepared and characterised to evaluate how the loading of sludge particles affects composites' mechanical, thermal, and crystallographic properties, as well as their moisture adsorption behaviour. The findings contribute to the development of an innovative composite material that incorporates valorised waste materials, offering enhanced functionality and economic viability. By demonstrating a sustainable approach to utilising industrial byproducts in composite manufacturing, this work addresses key challenges in material sustainability and underscores the broader potential of waste-derived materials in high-performance applications.