Titolo della tesi: On the effect of particle size and inertia, wall hydrodynamic confinement and surface adsorption/desorption on particle motion in microfluidic devices.
The analysis of dispersion properties, evaluated with local and integral moment analysis, is here used to quantify the effect of particle size and inertia, wall hydrodynamic confinement and surface adsorption/desorption on particle motion in microfluidic devices.
The inertial regime of non-interacting Brownian particles in the washboard potential is investigated, when the overdamped approximation does not yield accurate predictions. Different reduced models of increasing complexity, improving the overdamped approximation, are developed starting from the basic assumption that the velocity variable can be split into an "almost" deterministic and a fully stochastic contribution. The almost deterministic velocity term can be estimated from a fully deterministic or from a stochastic slow inertial manifold.
The effective particle velocity field, described by a slow/inertial manifold, is estimated for the dynamics of finite-sized particles with large inertia in steady and time-dependent open and closed flows. The numerical solution of the invariance equation describing the space-time evolution of the inertial manifold allows for an accurate reconstruction of the effective particle divergence field controlling clustering/dispersion features of particles, for which a perturbative approach is inaccurate or even not convergent. The effect of inertia is quantified in terms of the rate of contraction/expansion of volume elements along a particle trajectory and of the maximum Lyapunov exponent for systems exhibiting chaotic orbits.
The hydrodynamic effects on finite-size particles are evaluated in the Brownian Sieving Microcapillary Hydrodynamic Chromatography device (BS-MHDC), an unconventional double-channel device. The separation performance is investigated adopting a two-way coupling approach, and results are compared with those obtained with the one-way coupling (excluded volume) analysis. The latter overestimates the separation performance with respect to the two-way coupling analysis, but, the enhancement factor of the BS-MHDC over the standard MHDC is underestimated by the single-phase approximation as it doubles when wall/particle interactions are properly accounted for with a two-phase description.
Dispersion properties of point-size particles are also investigated when an adsorption/desorption process occurs at the device walls. As a first case of study, the separation performance in Open-Tubular Liquid Chromatography is evaluated in the presence of transversal flows, possessing regular or chaotic streamlines, thus showing that the presence of cross-flows can lower sensitively the dependence of the column length on the P\'{e}clet number. Flows possessing chaotic streamlines prove the most efficient choice at large eluent velocities and low values of the column adsorption constant.
The dispersion of an analyte in a sinusoidal channel with adsorbing/desorbing walls and in the retentive pillar array column for liquid chromatography are taken as case studies for the exact local and integral moment approach, representing a significant improvement of the classical Brenner's theory as it allows to investigate the temporal evolution of effective dispersion properties of solute particles in periodic media possessing impermeable walls as well as absorbing/desorbing walls. The transient analysis of dispersion properties shows that the adsorption/desorption process strongly amplifies the phenomenon of the overshoot for the effective dispersion coefficient. Moreover, the method proposed allows for a detailed analysis of the temporal evolution of the skewness of the marginal distribution of the analyte along the main stream direction, thus permitting an accurate and reliable estimate of the time-scale for achieving the macro-transport regime, that implies a Gaussian (symmetric) marginal pdf.