## 1 Introduction
The analytical method for multiphase fluid is represented by Navier-Stokes (N-S) equations coinciding with those of an incompressible fluid, where the numerical solutions show the desired phenomenon. These expressions lead to the continuity and balance equations of momentum for a two-phase fluid [29]. Multiphase fluids can be studied by simplifying N-S equations and adapting to the requirements of the case. Current computer capabilities require reducing the error when writing codes for the development of mathematical models that are increasingly simpler to process. There are great exponents that suggest simplified methods for given physical conditions of the fluid. On the one hand, [PERSON]'s approach proposes that, considering the particle density and the gas volume faction, each phase of the fluid can be studied separately if it is assumed that each phase can be represented as continuous and inter-penetrating. In addition, they coexist, separated by an interface [30]. On the other hand, the bubble fluid method is a simplification of [PERSON]'s, since it considers that the density of the gas present is less than 10% of the total volume of the fluid. Both phases are subjected to the same pressure field. Unlike other models, this treatment allows for an efficient study of a two-phase fluid as if it were one, that is to say, one set of N-S equations is used and subsequently the volume fraction is split in two, for each phase [31]. If the need is to study the average phase concentration, the assumption that the density of each phase is constant allows for use of the mixing method. It is very similar to the bubble fluid method, with the difference that the mixing method also covers liquid or solid drops immersed in the fluid. The theoretical knowledge and the previous experimental studies on magnetic fields in biological systems enables the development of methodologies for biotechnological applications. Accordingly, the aim of the research is as follows. This work focuses on cell cultures inside a glass flask, containing a liquid medium in which air is introduced through a tube, and affected by external SMFs. We consider that magnetic fields can affect water properties as well as biological media by means of modifying the equilibrium between ROSs and antioxidant molecules, promoting either beneficial or negative conditions. Therefore, cells can activate their defensive system in response to an external agent. In this context, this research relates physical properties of the medium with the magnetic field, discusses the effects of the magnetic field by evaluating solutions, and performs experimental measurements quantifying the production of antioxidants. Finally, the cell cultures used in this work correspond to the _Scenedesmus obliquus_ and _Nanochloropsis gaditana_ microalgae. These model species feature a known structure, functionality, and rapid growth. These characteristics can provide effectiveness regarding the effects of SMFs. They present biotechnological potential for the generation of antioxidant biomolecules such as \(\beta\)-carotenes in _S. obliquus_ or the high accumulation of polyunsaturated fatty acids (PUFAs) in _N. gaditana_.