Fabio Garofalo

Laminar dispersion at high Péclet numbers in finite-length channels: Effects of the near-wall velocity profile and connection with the generalized Leveque problem

This article develops the theory of laminar dispersion in finite-length channel flows at high Peclet numbers, completing the classical Taylor–Aris theory which applies for long-term, long-distance properties. It is shown, by means of scaling analysis and invariant reformulation of the moment equations, that solute dispersion in finite length channels is characterized by the occurrence of a new regime, referred to as the convection-dominated transport. In this regime, the properties of the dispersion boundary layer and the values of the scaling exponents controlling the dependence of the moment hierarchy on the Peclet number are determined by the local near-wall behavior of the axial velocity. Specifically, different scaling laws in the behavior of the moment hierarchy occur, depending whether the cross-sectional boundary is smooth or nonsmooth (e.g., presenting corner points or cusps). This phenomenon marks the difference between the dispersion boundary layer and the thermal boundary layer in the classical Leveque problem. Analytical and numerical results are presented for typical channel cross sections in the Stokes regime.

Convection-dominated dispersion regime in wide-bore chromatography: A transport-based approach to assess the occurrence of slip flows in microchannels

This article develops the theoretical analysis of transport and dispersion phenomena in wide-bore chromatography at values of the Peclet number Pe beyond the upper bound of validity of the Taylor-Aris theory. It is shown that for Poiseuille flows in cylindrical capillaries the average residence time grows logarithmically with the Peclet number, while the variance of the outlet chromatogram scales as the power 1/3 of Pe. In the presence of slip boundary conditions, both the mean and the variance of the outlet chromatograms saturate at high Pe, and this phenomenon provides an indirect transport-based way to detect slip flow conditions at the solid walls and, more generally, flow distributions in channel flows.

An intra-droplet particle switch for droplet microfluidics using bulk acoustic waves

To transfer cell- and bead-assays into droplet-based platforms typically requires the use of complex microfluidic circuits, which calls for methods to switch the direction of the encapsulated particles. We present a microfluidic chip where the combination of acoustic manipulation at two different harmonics and a trident-shaped droplet-splitter enables direction-switching of microbeads and yeast cells in droplet microfluidic circuits. At the first harmonic, the encapsulated particles exit the splitter in the center daughter droplets, while at the second harmonic, the particles exit in the side daughter droplets. This method holds promises for droplet-based assays where particle-positioning needs to be selectively controlled.

Characterization of stationary mixing patterns in a three-dimensional open Stokes flow: Spectral properties, localization and mixing regimes

This article analyses stationary scalar mixing downstream an open flow Couette device operating in the creeping flow regime. The device consists of two coaxial cylinders of finite length Lz, and radii κR and R (<1), which can rotate independently. At relatively large values of the aspect ratioα = Lz/R 1, and of the Pclet number Pe, the stationary response of the system can be accurately described by enforcing the simplifying assumption of negligible axial diffusion. With this approximation, homogenization along the device axis can be described by a family of generalized one-dimensional eigenvalue problems with the radial coordinate as independent variable. A variety of mixing regimes can be observed by varying the geometric and operating parameters. These regimes are characterized by different localization properties of the eigenfunctions and by different scaling laws of the real part of the eigenvalues with the Pclet number. The analysis of this model flow reveals the occurrence of sharp transitions between mixing regimes, e.g. controlled by the geometric parameter. The eigenvalue scalings can be theoretically predicted by enforcing eigenfunction localization and simple functional equalities relating the behaviour of the eigenvalues to the functional form of the associated eigenfunctions. Several flow protocols corresponding to different geometric and operating conditions are considered. Among these protocols, the case where the inner and the outer cylinders counter-rotate exhibits a peculiar intermediate scaling regime where the real part of the dominant eigenvalue is independent of Pe over more than two decades of Pe. This case is thoroughly analysed by means of scaling analysis. The practical relevance of the results deriving from spectral analysis for fluid mixing problems in finite-length Couette devices is addressed in detail. (Less)

Performance Study of Acoustophoretic Microfluidic Silicon-Glass Devices by Characterization of Material- and Geometry-Dependent Frequency Spectra

The mechanical and electrical response of acoustophoretic microfluidic devices attached to an ac-voltage-driven piezoelectric transducer is studied by means of numerical simulations. The governing equations are formulated in a variational framework that, introducing Lagrangian and Hamiltonian densities, is used to derive the weak form for the finite element discretization of the equations and to characterize the device response in terms of frequency-dependent figures of merit or indicators. The effectiveness of the device in focusing microparticles is quantified by two mechanical indicators: the average direction of the pressure gradient and the amount of acoustic energy localized in the microchannel. Further, we derive the relations between the Lagrangian, the Hamiltonian and three electrical indicators: the resonance Q-value, the impedance and the electric power. The frequency response of the hard-to-measure mechanical indicators is correlated to that of the easy-to-measure electrical indicators, and by introducing optimality criteria, it is clarified to which extent the latter suffices to identify optimal driving frequencies as the geometric configuration and the material parameters vary.

Dispersion-induced mixing in simple flows : evidence for new anomalous scaling laws in the mixing boundary layer beyond the Lèvêque theory

We investigate the mixing layer thickness, δ(ξ), along the streamwise coordinate ξ of a straight channel fed with alternating streams of segregated solutes. We show the occurence of convection-enhanced mixing regimes downsteram the channel: i) an early-mixing regime, δ(ξ)~ξ1/3 resembling the classical Leveque scaling of the thermal boundary layer, ii) an intermediate anomalous regime δ(ξ)~ξ3/5, where most of mixing occurs, and iii) an asymptotic scaling where the dynamics of mixing depends on the spanwise velocity profile and can be predicted by localization theory (Giona M. et al., EPL, 83 (2008) 34001). We develop a complete theoretical derivation for each of these regimes and discuss the implications of the results presented for real-world microflow devices.

Rapid and effective enrichment of mononuclear cells from blood using acoustophoresis

Effective separation methods for fractionating blood components are needed for numerous diagnostic and research applications. This paper presents the use of acoustophoresis, an ultrasound based microfluidic separation technology, for label-free, gentle and continuous separation of mononuclear cells (MNCs) from diluted whole blood. Red blood cells (RBCs) and MNCs behave similar in an acoustic standing wave field, compromising acoustic separation of MNC from RBC in standard buffer systems. However, by optimizing the buffer conditions and thereby changing the acoustophoretic mobility of the cells, we were able to enrich MNCs relative to RBCs by a factor of 2,800 with MNC recoveries up to 88%. The acoustophoretic microchip can perform cell separation at a processing rate of more than 1 × 105 cells/s, corresponding to 5 µl/min undiluted whole blood equivalent. Thus, acoustophoresis can be easily integrated with further down-stream applications such as flow cytometry, making it a superior alternative to existing MNC isolation techniques.

Complex spectral properties of non-Hermitian operators: An application to open-flow mixing systems

We study the spectral properties of the advection-diffusion operator associated with a non-chaotic 3d Stokes flow defined in the annular region between counter-rotating cylinders of finite length. The focus is on the dependence of the eigenvalue-eigenfunction spectrum on the Peclet number Pe. Several convection-enhanced mixing regimes are identified, each characterized by a power law scaling, -μd~Pe-γ (γ<1) of the real part of the dominant eigenvalue, -μd, vs.Pe. Among these regimes, a Pe-independent scaling -μd=const (i.e., γ=0), qualitatively similar to the asymptotic regime of globally chaotic flows, is observed. This regime arises as the consequence of different eigenvalues branches interchanging dominance at increasing Pe. A combination of perturbation analysis and functional-theoretical arguments is used to explain the occurrence and the range of existence of each regime.

Ultrasound Characterization of Microbead and Cell Suspensions by Speed of Sound Measurements of Neutrally Buoyant Samples

We present an experimental method including error analysis for the measurement of the density and compressibility of cells and microbeads; these being the two central material properties in ultrasound-based acoustophoretic applications such as particle separation, trapping, and up-concentration. The density of the microparticles is determined by using a neutrally buoyant selection process that involves centrifuging of microparticles suspended in different density solutions, CsCl for microbeads and Percoll for cells. The speed of sound at 3 MHz in the neutrally buoyant suspensions is measured as a function of the microparticle volume fraction, and from this the compressibility of the microparticles is inferred. Finally, from the obtained compressibility and density, the acoustic scattering coefficients and contrast factor of the microparticles are determined, and in a sensitivity analysis, the impact of the measurement errors on the computed acoustic properties is reported. The determination of these parameters and their uncertainties allow for accurate predictions of the acoustophoretic response of the microparticles. The method is validated by determining the density (0.1-1% relative uncertainty) and compressibility (1-3% relative uncertainty) of previously well-characterized polymer microbeads and subsequently applied to determine the density (0.1-1% relative uncertainty), compressibility (1% relative uncertainty), scattering coefficients, and acoustic contrast factors for nonfixed and fixed cells, such as red blood cells, white blood cells, DU-145 prostate cancer cells, MCF-7 breast cancer cells, and LU-HNSCC-25 head and neck squamous carcinoma cells in phosphate buffered saline. The results show agreement with published data obtained by other methods.

Dispersion of overdamped diffusing particles in channel flows coupled to transverse acoustophoretic potentials: transport regimes and scaling anomalies.

We address the dispersion properties of overdamped Brownian particles migrating in a two-dimensional acoustophoretic microchannel, where a pressure-driven axial Stokes flow coexists with a transverse acoustophoretic potential. Depending on the number and symmetries of the stable nodal points of the acoustophoretic force with respect to the axial velocity profile, different convection-enhanced dispersion regimes can be observed. Among these regimes, an anomalous scaling, for which the axial dispersion increases exponentially with the particle Peclét number, is observed whenever two or more stable acoustophoretic nodes are associated with different axial velocities. A theoretical explanation of this regime is derived, based on exact moment homogenization. Attention is also focused on transient dispersion, which can exhibit superballistic behavior 〈(x-〈x〉)^{2}〉∼t^{3},x being the axial coordinate.