**4.1 MR sensors in droplet-based millifluidics**

As seen in Section 2.2, millifluidics depicts the technology of precise control and manipulation of liquids in tubings with inner diameters from about 500 μm, connected via commercially available connectors. Despite being not as versatile as microfluidics with respect to complex liquid manipulation, millifluidics offer the advantage of quick prototyping of fluidic setups, since lithographically approaches are not mandatory to build a functional fluidic setup. In combination with MR sensors, the distance between sensor and liquids have to be minimized since they cannot be integrated into the tubes, *e.g.* achievable via careful grinding of the tubings [78] or selection of tubings with low difference in their inner and outer diameters. One of the first reports of MR sensors and millifluidics was demonstrated by Melzer and coworkers in 2012 [79]. In this work, GMR sensors on elastic substrates were wrapped around the tubing to assure isotropic detection of magnetic objects (1 mm-sized clusters of FeNdB particles). This conjunction was possible and strongly benefited from the realization of stretchable magnetic

field sensors in 2011 [80]. In addition, these clusters were detected in macro-sized quasi-droplets (with a tubing inner diameter of 1.5 mm and droplet volumes in microliter regime). The first conjunction of droplet millifluidics and MR sensors was demonstrated by Lin and coworkers in 2013 [32], demonstrating a droplet analyzer based on the integration of GMR-based sensors into millifluidic tubings. Water-based ferrofluid droplets from 120 nL to 270 nL were fabricated using a commercial T-junction connectors and guided over a GMR sensor platform (**Figure 8a**). Hence, both volume of fabricated ferrofluid droplets could be detected by full width at half maximum (FWHM) of passing droplets over the GMR platform and concentration of the ferrofluid via the amplitude signal of the droplets, giving rise to a multiparametric analysis (in the spirit of flow cytometry) of passing ferrofluid droplets (**Figure 8b**). Furthermore, the detection and characterization of ferrofluid droplets was also demonstrated using PHE sensors (**Figure 8d** and **e**). Schütt et al. demonstrated the integration of tubing-based ferrofluid droplets onto PHE sensor enabling contact-less measurement in artificial magnetic fields (up to 5 mT) down to earth magnetic field without any external magnetization of the ferrofluid droplets [81]. Doing so, the sensitivity of droplet-based magnetofluidics could be increased by a factor of 100 (**Figure 8c**–**e**).
