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The role of viscous forces coupled with Brownian forces in momentum -conserving computer simulations is studied here in the context of their contribution to the total average pressure of a simple fluid as derived from the virial theorem, in comparison with the contribution of the conservative force to the total pressure. The specific mesoscopic model used is the one known as dissipative particle dynamics, although our conclusions apply to similar models that obey the fluctuation -dissipation theorem for short range interactions and have velocity -dependent viscous forces. We find that the average contribution of the random and dissipative forces to the pressure is negligible for long simulations, provided these forces are appropriately coupled and when the finite time step used in the integration of the equation of motion is not too small. Finally, we study the properties of the fluid when the random force is made equal to zero and find that the system freezes as a result of the competition of the dissipative and conservative forces.

We review briefly the concept of colloidal dispersions, their general properties, and some of their most important applications, as well as the basic molecular interactions that give rise to their properties in equilibrium. Similarly, we revisit Brownian motion and hydrodynamic interactions associated with the concept of viscosity of colloidal dispersion. It is argued that the use of modern research tools, such as computer simulations, allows one to predict accurately some macroscopically measurable properties by solving relatively simple models of molecular interactions for a large number of particles. Lastly, as a case study, we report the prediction of rheological properties of polymer brushes using state-of-the-art, coarse-grained computer simulations, which are in excellent agreement with experiments.

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The connection between fundamental interactions acting in molecules in a fluid and macroscopically measured properties, such as the viscosity between colloidal particles coated with polymers, is studied here. The role that hydrodynamic and Brownian forces play in colloidal dispersions is also discussed. It is argued that many -body systems in which all these interactions take place can be accurately solved using computational simulation tools. One of those modern tools is the technique known as dissipative particle dynamics, which incorporates Brownian and hydrodynamic forces, as well as basic conservative interactions. A case study is reported, as an example of the applications of this technique, which consists of the prediction of the viscosity and friction between two opposing parallel surfaces covered with polymer chains, under the influence of a steady flow. This work is intended to serve as an introduction to the subject of colloidal dispersions and computer simulations, for lastyear undergraduate students and beginning graduate students who are interested in beginning research in soft matter systems. To that end, a computational code is included that students can use right away to study complex fluids in equilibrium.