**5. Conclusions**

A chaotic model of Brownian motion was theoretically analyzed and simulated using Maple software. The chaotic model was mapped and control parameter *p* was introduced, which depends on the viscosity coefficient and particle mass and size, in analogy with the Langevin equation. The ferrofluid in the gravitational field without the presence of an external magnetic field in a two-dimensional mathematical model was observed. It performed 400 collisions with fluid molecules.

Computer simulation showed that nanoparticles can exhibit deterministic patterns in a chaotic model for certain material properties of the particles (and the surrounding fluid, as well as their interrelated properties) that could result in the controlled nanofluid behavior. Trajectory shapes were significantly changed for slight changes in the parameter *p*: a value of 1 resulted in a fully linear trajectory, while a value of 0.9 produced a fully random path. The lowest value of p (0.5) introduced patterns of linearity within chaotic motion, with noticed changes in the shape and density of trajectories. Since parameter *p* is related to the fluid viscosity and particle radius and mass, it could be assumed that such transitional behavior with changes in the parameter *p* can be attributed to a complex phenomenon underlining dependencies between viscosity and volume fractions of particles in nanofluids. For values of p in between the designated numbers (Equation (31)), fully random trajectories were generated by simulation. Accordingly, we could tailor the trajectory path of the particle in the liquid, regardless of the exogenous power propulsion strategy (e.g., external magnetic field), by tailoring the values of the parameter *p*, which is related to viscosity and volume fractions of nanoparticles in a fluid.

Fine tailoring of the Brownian motion can produce different desired effects, including tailoring of the time and amount of the drug release. Patterns of deterministic trajectories can be designed by predefined values of the parameter *p* in a computer simulation, which can further lead to the design of the nanoparticle system for targeted drug delivery without an exogenous power propulsion strategy (e.g., external magnetic field). However, complex relations between different influential factors need further study, including further development of the theoretical model that will consider magnetic properties of the nanoparticles in a ferrofluid.

**Author Contributions:** Conceptualization, S.N., J.R., F.Ž., M.V.J. and N.G.; methodology, S.N., J.R., F.Ž., A.M. and N.G.; software, S.N., M.V.J. and N.G.; validation, S.N., F.Ž. and Ž.J.P.; formal analysis, J.R., F.Ž., A.M., M.V.J. and N.G.; investigation, S.N., J.R. and F.Ž.; resources, S.N., F.Ž. and Ž.J.P.; data curation, S.N., F.Ž. and Ž.J.P.; writing—original draft preparation, S.N., F.Ž., A.M. and Ž.J.P.; writing—review and editing, S.N., J.R., F.Ž., A.M., Ž.J.P., M.V.J. and N.G.; visualization, S.N., F.Ž. and A.M.; supervision, J.R., F.Ž. and N.G.; funding acquisition, F.Ž. All authors have read and agreed to the published version of the manuscript.

**Funding:** This paper is funded through the EIT's HEI Initiative SMART-2M project, supported by EIT RawMaterials, funded by the European Union.

**Data Availability Statement:** Not applicable. **Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.
