## 1 Introduction  
The availability of synchrotron and X-ray free-electron laser (XFEL) radiation sources enables time-resolved studies of structural changes in biomolecules to be carried out with atomic resolution [1]. A key challenge with performing these types of experiments is how to efficiently deliver molecules to the X-ray beam and then rapidly trigger dynamic changes on the relevant molecular timescales. In order to address the first problem, devices capable of forming liquid micro-jets have been developed which offer precise control over the size of the interaction region and produce minimal background signal [2, 3, 4, 5, 6]. For the second problem of triggering a reaction, microfluidics offers a number of advantages in terms of efficiently and homogeneously mixing reactants such that the subsequent molecular dynamics can be probed by illuminating different points on the liquid jet with the X-ray beam. Benefits of using microfluidic devices for studying molecular dynamics include the ability to combine multiple fluidic components on a single chip, the flexibility of the geometries that can be produced, and the reproducibility in terms of fabrication. The use of microfluidics also enables a high surface-to-volume ratio to be used, enhancing heat and mass transfer whilst ensuring a low Reynolds number, i.e., the laminar flow regime. In this scenario, the viscous forces dominate over the inertial forces within the flow, which dampens any flow irregularities that might occur in the fluid [7]. However, in the laminar flow regime, there is a requirement for comparatively long mixing channels, as mixingpredominantly occurs via low-efficiency diffusion, which limits the temporal resolution than can be achieved using diffusion-based micromixers. A promising method to overcome the limitations imposed by mixing in straight microchannels is to employ passive mixing techniques, which are able to enhance mixing by inducing chaotic behaviours that are not present in linear channels [7; 8]. A typical approach to enhanced passive mixing is exploiting unusual geometries in the mixing channels to achieve a chaotic advection effect. The chaotic effect increases the effective contact surface area and overall contact time between the reactants, which results in an improved mixing efficiency compared to just a straight microchannel [9]. Examples of enhanced passive mixing strategies employed in micromixers include the use of intersecting channels [10; 11; 12; 13; 14; 15], the addition of curvatures [16; 17; 18], and the inclusion of obstacles or barriers to the liquid flow [19; 20; 21; 22; 23]. For example, [PERSON] et al. [24] conducted a numerical study comparing the mixing efficiencies of wavy and straight T-junction micromixers. They reported higher mixing efficiencies for the wavy micromixer because a chaotic flow regime could be induced. This is consistent with the fact that the chaotic advection effect increases at higher Reynolds numbers, making wavy micromixers more efficient at higher flow rates. In a related study, [PERSON] et al. [25] carried out a series of COMSOL [26] finite element method (FEM) simulations comparing the efficiency of standard zig-zag micromixers to a topologically optimised zig-zag micromixer, including additional obstacles. Their results show that additional blocks to the liquid flow create more secondary flow and chaotic effects within the mixer, resulting in higher efficiencies. However, the use of obstacles negatively impacts the width of the microchannels, which can result in a higher rate of blockage within the device. For example, working with micro-crystals or even biomolecules means that there is often debris or organic material within the liquid flow, which can become trapped against any barriers or obstacles which may exist.