A reactive system's slow dynamic behavior is approximated well by evolution on manifolds of dimension lower than that of the full composition space. This work addresses the construction of one-dimensional slow invariant manifolds for dynamical systems arising from modeling unsteady spatially homogeneous closed reactive systems. Additionally, the relation between the systems' slow dynamics, described by the constructed manifolds, and thermodynamics is clarified. It is shown that other than identifying the equilibrium state, traditional equilibrium thermodynamic potentials provide no guidance in constructing the systems' actual slow invariant manifolds. The construction technique is based on analyzing the composition space of the reactive system. The system's finite and infinite equilibria are calculated using a homotopy continuation method. The slow invariant manifolds are constructed by calculating attractive heteroclinic orbits which connect appropriate equilibria to the unique stable physical equilibrium point. Application of the method to several realistic reactive systems, including a detailed hydrogen-air kinetics model, reveals that constructing the actual slow invariant manifolds can be computationally efficient and algorithmically easy.

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We have used a dissipative particle dynamics (DPD) model to study the movement of microparticles in a microfluidic device at extremely low Reynolds number (Re). The particles, immersed in a medium, are transported in the microchannel by a flow force and deflected transversely by an external force along the way. An in-house Fortran code is developed to simulate a two-dimensional fluid flow using DPD at Re ≥ 0.0005, which is two orders of magnitude less than the minimum Re value previously reported in the DPD literature. The DPD flow profile is verified by comparing it with the exact solution of Hagen-Poiseuille flow. A bioparticle based on a rigid spring-bead model is introduced in the DPD fluid, and the employed model is verified via comparing the velocity profile past a stationary infinite cylinder against the profile obtained via the finite element method. Moreover, the drag force and drag coefficient on the stationary cylinder are also computed and compared with the reported literature results. Dielectrophoresis (DEP) is investigated as a case study for the proposed DPD model to compute the trajectories of red blood cells in a microfluidic device. A mapping mechanism to scale the external deflecting force from the physical to DPD domain is performed. We designed and built our own experimental setup with the aim to compare the experimental trajectories of cells in a microfluidic device to validate our DPD model. These experimental results are used to investigate the dependence of the trajectory results on the Reynolds number and the Schmidt number. The numerical results agree well with the experiment results, and it is found that the Schmidt number is not a significant parameter for the current application; Reynolds numbers combined with the DEP-to-drag force ratio are the only important parameters influencing the behavior of particles inside the microchannel.