My research field is in **Soft Condensed Matter (Materia Condensada Suave)**,
exemplified through some of my present research projects:
**colloids** such as ferrofluids,
** surface dynamics** at the interface of a vapor and liquid crystal, or polymeric solution, and electrolytes .

Confined electrolyte between electrically charged surfaces; for the problem of the effective electric interaction (due to charge's correlated fluctuations) between charged membranes (such as those present in biological cells) and surfaces (of colloids) in polyvalent electrolytes in material science.
Here we study how this interaction is determined by solvent characteristics (dielectric constant, molecular structure, pH) and surface properties.
See: O.González-Amezcua et al, Electrostatic correlation force of
discretely charged membranes. Phys.Rev.E,64(2001)041603-1.

on the stability of biomolecular materials used in gene therapy.
Statistical mechanics theories allow to study the thermodynamic properties and stability of the electrostatic Liposome-DNA complex, a self-assembled
micro-structure that is obtained with castionic vesicles and DNA in water.
M.Hernández-Contreras, Materiales biomoleculares,
Avance y perpectiva, Vol.19(2000)263.

and on the surface dynamics present at interfaces of vapor and liquid crystals.
We have determined that both Smectics and Nematics can develop Faraday waves on their surface. These waves result from the vertical movement of a vessel containing the liquid,
which it develops stationary surface waves for a given frequency and acceleration of the
shaker. We investigate with existing hydrodynamic theories based on Navier-Stokes equations, the appeareance of nonlinear waves as has been observed in other complex fluids. This is an important system that allows us to study in a macroscopic enviroment nonlinear effects in a clearly controlled way. Similarly, we have studied the
thermal surface wave at the interface on air-polymer solution, which is of interest to
understand the dynamical behavior of many real systems such as biological cells, or
on coatings with paints and microrhelogy of these liquids in tribology problems.

We have determined that Smectic A and Nematics liquid crystals can develop Faraday waves at their interface with a vapor. Therefore, its quite possible that they also may sustain nonlinear waves of some symmetric structure as has been observed in other complex fluids (polymer and micellar solutions, simple liquids and ferrofluids). Thus, our work now focuses to investigate these nonlinear waves both with low viscocity hydrodynamic perturbation theories and assisted with computer simulations of the full numerical solution of the Navier-Stokes equation. M. Hernandez Contreras. J. Phys. Condens. Matter 22, 035106, 2010, Phys. Rev. E 88, 062311, 2013.

Microestructure and dynamical properties of colloidal suspensions and ferrofluids.
There is a growing interest to study ferrocolloids since they have important applications as magnetic vehicles for hyperthermic cancer treatment, in magnetic drug targeting, in cooling applications, in waste disposal, as frictionless seals, to name a few.
Thus, in order to have a better control of this material in all of these applications it is important to know its basic phase behavior under applied external magnetic fields, temperature, concentration and colloidal particle's interactions. We are developing
a wide range of studies on their dynamical properties (collective and single particle
diffusion coefficients, rheological behavior) and their thermodynamic phase behavior under external fields.
For this purpose we use static and dynamical density statistical theories, liquid theory approaches, and
computer simulations (brownian dynamics, molecular and monte carlo simulations).

M. Hernández-Contreras, Rotational diffusion in a ferrocolloid.
Developments in mathematical and experimental physics Vol.B: statistical
physics and beyond. Edit.Macias et al
Kluwer Academic 2003.
For the static properties we use Liquid theory, density functional theory

For the dynamical properties we use mesoscopic nonequilibrium thermodynamic theory and Langevin equation
approach

Also for the problem of the diffusion of macromolecules in bulk electrolyte solutions
we study the effect of added salts in solution on the tracer diffusion of model rod-like colloidal particles

Our main interest is to study the thermodynamic microstruture and dynamical processes occurring in complex fluids formed by several species: mainly colloidal ferrofluids, surface dynamics on liquid crystals, and inhomogeneous electrolytes.