Simplified one-way coupling approaches are often used to model transport properties of diluted particle suspensions for predicting the performance of microcapillary hydrodynamic chromatography (MHDC). Recently, a one-way coupling approach was exploited to optimize the geometry and operating conditions of an unconventional double-channel geometry with a square cross section, where a Brownian sieving mechanism acting alongside the MHDC separation drive (BS-MHDC) is enforced to boost separation resolution. In this article, a cylindrical geometry enforcing the same BS-MHDC separation drive is thoroughly investigated by following a two-way coupling, fully three-dimensional approach, and results are compared with those obtained enforcing the one-way coupling analysis. Device geometry and operating conditions are optimized by maximizing the separation resolution. The effective velocity and dispersion coefficient of spherical, finite-sized particles of different diameters are computed, and two-phase effects are discussed in detail. Similar to the square channel device, the cylindrical double-channel geometry allows for a sizable reduction in the column length and in the analysis time (a factor above 12 for the length and a factor larger than 3 for the processing time) when compared to the standard MHDC configuration ensuring the same separation resolution. As expected, the one-way coupling approach overestimates the separation performance of both the BS-MHDC and the standard MHDC devices with respect to the two-way coupling analysis. But, surprisingly, 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.

This article develops a modal expansion (in terms of functions exponentially decaying with time) of the force acting on a micrometric particle and stemming from fluid inertial effects (usually referred to as the Basset force) deriving from the application of the time-dependent Stokes equation to model fluid–particle interactions. One of the main results is that viscoelastic effects induce the regularization of the inertial memory kernels at t=0, eliminating the 1/t-singularity characterizing Newtonian fluids. The physical origin of this regularization stems from the finite propagation velocity of the internal shear stresses characterizing viscoelastic constitutive equations. The analytical expression for the fluid inertial kernel is derived for a Maxwell fluid, and a general method is proposed to obtain accurate approximations of it for generic complex viscoelastic fluids, characterized by a spectrum of relaxation times.

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The equivalence between parabolic transport equations for solute concentrations and stochastic dynamics for solute particle motion represents one of the most fertile correspondences in statistical physics originating from the work by Einstein on Brownian motion. In this article, we analyze the problems and the peculiarities of the stochastic equations of motion in microfluidic confined systems. The presence of solid boundaries leads to tensorial hydrodynamic coefficients (hydrodynamic resistance matrix) that depend also on the particle position. Singularity issues, originating from the non-integrable divergence of the entries of the resistance matrix near a solid no-slip boundary, determine some mass-transport paradoxes whenever surface phenomena, such as surface chemical reactions at the walls, are considered. These problems can be overcome by considering the occurrence of non vanishing slippage. Added-mass effects and the influence of fluid inertia in confined geometries are also briefly addressed.

For isothermal liquid flows, the condition of incompressibility provides a useful simplification for describing their mechanical properties. Nevertheless, it overlooks acoustic effects, and it provides the unpleasant shortcoming of infinite propagation speed of velocity perturbations, no matter the type of constitutive equation for the shear stresses is adopted. In this paper, we provide a derivation of a new formulation of the Navier–Stokes equations for liquid flows that overcomes the above issues. The pressure looses its ancillary status of mere gauge variable (or equivalently Lagrange multiplier of the incompressibility condition) enforcing the solenoidal nature of the velocity field, and attains the proper physical meaning of hydrodynamic field variable characterized by its own spatiotemporal evolution. From the experimental evidence of sound attenuation, related to the occurrence of a non-vanishing bulk viscosity, the evolution equation for pressure in out-of-equilibrium conditions is derived without introducing any adjustable parameters. The connection between compressibility and memory effects in the propagation of internal stresses is established. Normal mode analysis and some preliminary simulations are also discussed.