In this work, the dynamics of the bioconvection process of gravitactic microorganisms enclosed in a rectangular cavity, is analyzed. The dimensionless cell and energy conservation equations are coupled with the vorticity-stream function formulation. Then, the effects of the bioconvection Rayleigh number and the heating source on the dynamics of microorganisms are discussed. The results based in streamlines, concentration and temperature contours are obtained through numerical simulations considering eight different configurations of symmetrical and asymmetrical heat sources. It is concluded that microorganisms accumulate in the warmer regions and swim through the cooler regions to reach the surface. They form cells for each heat source, but at high concentrations, they form a single stable cell. The results presented here can be applied to control and to understand the dynamics of microorganisms with discrete heat sources.

In the present work, an analytical approximate solution of mixed electroosmotic/pressure driven flow of viscoelastic fluids between a parallel plates microchannel is reported. Inserting the Oldroyd, Jaumann, or both time derivatives into the Maxwell model, important differences in the velocity profiles were found. The presence of the shear and normal stresses is only close to the wall. This model can be used as a tool to understand the flow behavior of low viscosity fluids, as most of them experiment on translation, deformation and rotation of the flow. For practical applications, the volumetric flow rate can be controlled with two parameters, namely the gradient pressure and the electrokinetic parameter, once the fluid has been rheologically characterized.

The multiscale modeling of complex fluids under small and large amplitude oscillatory shear flow using non-linear kinetic and transient network models is presented. The kinetics of microstates is analogous to chemical kinetics, which defines the physical macromolecule interaction in a Newtonian fluid, and the concentration of microstates defines a variable maximum length of extension for each microstate. The effect of important parameters like viscosity ratio, chain length, viscoelasticity, kinetic rate constants, for different initial entanglement scenarios (entangled, disentangled and aleatory) are analyzed. The Lissajous curves for the shear stress and the first normal stress difference versus the instantaneous strain or strain-rate are shown. The self-intersection of the Lissajous curves or secondary loops is shown to depend on the kinetic rate constants, the maximum extension length, and the elasticity.

The results of numerical simulations of gravitactic bioconvection influenced by nanoparticles suspended in water are analyzed. In this work, two cases are established which consider the removal of nanometric particles suspended in wastewater. The competence among the bioconvection of Paramecium caudatum, natural convection and buoyancy of nanoparticles phenomena in an aqueous suspension is presented. The position of a thermal source to control the orientation of microorganisms when swimming is analyzed. Numerical simulations are carried out using the finite difference method in an ADI scheme, employing stream-vorticity formulations and equations for microorganisms, nanoparticle concentration, and energy. The percentage of nanoparticles is considered using the Rayleigh number, which includes the effect of Brownian and thermophoretic parameters. At low values of the Brownian parameter ${\delta }_{Bm}=0.1$, thermophoretic parameter ${\delta }_{Tm}=0.1$, and the nanoparticles Rayleigh number $0.005<R{a}_n<0.015$, the swimming of microorganisms contributed to streamlines across which nanoparticles traveled in response to a thermal control source. Thus, the results obtained suggest an alternative approach to the removal of solids such as heavy metals in polluting waters. The development of this type of technology will help in the bioremediation of wastewater.