## 1 Introduction  
_Arthrospira platensis_, commonly known as spirulina, is a photosynthetic filamentous cyanobacterium considered one of the most commercially important algal species [1]. Due to its high protein content, up to 70%, and several other reported health benefits, its biomass has found multiple applications as a nutritional supplement or food additive [2]. Besides its nutritional properties, spirulina, like many cyanobacteria, has attracted interest due to its capacity to synthesise phycobiliproteins (PBP) [3]. This class of relatively stable proteins can be divided into three main groups, namely, phycocyanin (PC), allophycocyanin (APC), and phycoerythrin (PE), based on their inherent colour, structure, and light-qualityabsorption [4]. _A. platensis_ biomass is considered one of the most excellent sources of PC, as, depending on the growing conditions, this pigment can accumulate in high amounts [5; 6]. These accessory light-harvesting pigment complexes, especially PC, have also attracted scientific interest because of their reported antioxidant, anti-tumour, immunomodulatory, anti-inflammatory, neuro- and hepato-protective effects [7]. Moreover, owing to their fluorescent properties, they have high market value and are extensively commercialised as fluorescent probes in clinical and immunological assays [6]. Furthermore, because most synthetic pigments and colours are hazardous, these naturally deriving blue pigments, particularly PC, have found excellent application as food and cosmetic product colourants [8]. In fact, both _A. platensis_ extracts and PC are listed in the European Commission's database for cosmetic ingredients (CosIng), which contains information on cosmetic ingredients and substances found in the cosmetics regulations (No. 1223/2009) of the European Parliament and the Council [9]. Specifically, _A. platensis_ extract is listed in the database as an ingredient with antioxidant, hair conditioning, humectant, skin conditioning, and protecting functions. Moreover, algal-derived PC is also listed in the database (EC# 234-348-8) as an antioxidant, colourant, and light stabiliser [10; 11]. However, the application of PC heavily relies on its purity, determined by the ratio between the \(\lambda\)max of the pigment at 620 nm and specific absorbance at 280 nm, with PC higher than 0.7, 1.5, 3.9, and 4.0 considered to be food-grade, cosmetic grade, reactive grade, and analytical grade, respectively [12]. Nevertheless, recent reviews highlight that, among other factors, stability and mainly cost-effective extraction and purification processes are essential to increase their application potential [13; 14]. PBP extraction depends on multiple parameters with moderate temperatures (<50 \({}^{\circ}\)C), pH values ranging from 6 to 8, and preventing light contact, favouring high recoveries of PC while assuring stability. Moreover, efficient recovery of PBP relies on the applied cell disruption method [15; 16; 17]. The literature suggests multiple techniques, with conventional approaches, such as freezing and thawing, maceration and homogenisation, and bead milling, standing out [16], or emerging advanced techniques, such as pulsed electric fields [18], ultrasound [19], microwave [20], and high-pressure homogenisation [21] that have also been suggested, as alternatives. Besides an efficient extraction and cell disruption process, downstream processing of PBP necessitates purification, at least by one step and to a certain degree, before incorporation into a final product/formulation, especially if the final application is not food [22]. PC purification is a rather complex and time-consuming process that, with multiple purification protocols involving precipitation, centrifugation, or dialysis, has been suggested as an initial purification step [23; 24].