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The Langevin description of Brownian motion in inhomogeneous suspensions is here revisited. Inhomogeneous suspensions are, characterized by a position-dependent friction coefficient, which can significantly influence the dynamics of the suspended particles. Outstanding examples are suspensions in confinement or in the presence of a temperature gradient. The Langevin approach in inhomogeneous systems encounters a fundamental difficulty related to the interpretation of the multiplicative noise induced by the position-dependent friction. We show that the so-called Ito-Stratonovich dilemma is originated by the violation of the macroscopic force balance condition in the traditional procedure of eliminating the fast variables. Repairing this deficit, we rederive the extended overdamped Langevin equation directly from the infradamped Langevin equation. This is without invoking the Fokker-Planck formalism, such that the self-completeness of the Langevin framework is restored. Furthermore, we derive the generalized forms of the drift-force relation and the Smoluchowski equation for inhomogeneous suspensions in a straightforward manner. [ABSTRACT FROM AUTHOR]

In contrast to most real fluids, angular momentum is not a locally conserved quantity in some mesoscopic simulation methods. Here we quantify the importance of this conservation in the flow fields associated with different colloidal systems. The flow field is analytically calculated with and without angular momentum conservation for the multiparticle collision dynamics (MPC) method, and simulations are performed to verify the predictions. The flow field generated around a colloidal particle moving under an external force with slip boundary conditions depends on the conservation of angular momentum, and the amplitude of the friction force is substantially affected. Interestingly, no dependence on the angular momentum conservation is found for the flow fields generated around colloids under the influence of phoretic forces. Moreover, circular Couette flow between a no-slip and a slip cylinder is investigated, which allows us to validate one of the two existing expressions for the MPC stress tensor. [ABSTRACT FROM AUTHOR]