## 1 Introduction  
Biological systems and functions usually occur in water. Thus, water is the medium where chemical reactions take place supporting life and its evolution. In addition, flows are made of fluids, which can be aqueous solutions with ions in suspension, and play a role by transporting macromolecules, among other features. Fluids can be subjected to a variety of conditions, which can be intrinsic or can be imposed perturbations. In the case of man-made externally applied forces, they are justified for practical uses either for industry in general, for biotechnological applications, or purely for research purposes. One of these external influences can be the magnetic field. Flows when coupled with magnetic or more general electromagnetic fields are described in terms of magnetohydrodynamics (MHD), which can be used for any kind of applications where fluid motion, heat, levitation, or any other effects need to be controlled. Furthermore, it provides a basis for studying the terrestrial magnetic field because of fluid motion or of magnetic field found in the sun and stars, to mention some examples. The present work involves a case study of a two-phase flow subjected to static magnetic fields (SMFs)for biotechnological applications. In the following, a brief description regarding the existence of magnetic fields in biological systems and flows is provided. Magnetic fields in biological systems appear in several ways. For instance, magnetostatic bacterium, due to chains of single-domain biogenic magnetite, aligns its body according to Earth's magnetic field [1]. It has been shown that birds can orient themselves to Earth's magnetic field lines allowing their migration across long distances [2]. There are studies related to practical applications of both electric and magnetic fields in biology. For instance, cells can exhibit directional migration or alignment upon exposure to static electric fields [3]. Authors have differentiated cells by applying external magnetic fields established by permanent magnets [4]. This is based on the equilibrium between the magnetic gradient force and gravity, and on the magnetic fingerprint of each type of cell. In addition, a magnetic trap for living cells in a buffer has been developed. To obtain the movement of cells towards zones of magnetic field minima, the original medium was enriched with a paramagnetic fluid to achieve a magnetic susceptibility much higher than that of the cells [5]. Further procedures to supervise cells have been developed; for instance, researchers have created nanomushroom structures as labelfree nano sensors for long-term cell proliferation detection [6]. In more detail, magnetic fields can participate at several levels, ranging among the tissue, cell, membrane, and molecular levels [7]. In this regard, it has been stated that magnetic fields can alter the rate, yield, and product distribution of chemical reactions [8]. Reviewing the effects of SMFs on cellular systems, authors point out that the radical pair recombination and the diamagnetic anisotropy can lead to changes and subsequent effects on the susceptibility of biomolecules, intracellular structural modifications, and changes in the enzymatic reactions [9]. To elucidate how fields act on cells, main processes in cells must be understood first. The main physiological processes in cells generate reactive oxygen species (ROSs). In case of microalgae, ROSs are generated by mitochondria, chloroplasts, and peroxisomes [10; 11]. ROSs can oxidize essential macromolecules, as they are highly reactive. Cells exhibit an antioxidant defense system that neutralizes or metabolizes ROSs. This defense system comprises antioxidant enzymes, such as catalase, superoxide dismutase, ascorbate peroxidase, and glutathione peroxidase, among others, and low-molecular-weight metabolites such as glutathione, ascorbic acid, carotenes, phenols, and flavonoids [12].