Session T34: Micro/Nano Flows: Mixing/Separation

Generalized Taylor dispersion theory for particle transport in wide channels with different surface topographies

In both microfluidic and natural applications, solid boundaries may have rough surface topographies. Hydrodynamic interactions between the rough surface and the flow influence the motion of particles in these environments. Here we generalize the classical Taylor dispersion theory (Taylor, 1953) to include surface roughness, deriving an asymptotic long-time convective diffusion equation for a solute suspended in a wide, structured channel and subject to a steady low-Reynolds-number shear flow. Our theory captures dispersion over general surface shapes of small amplitude expressible as a Fourier series. We demonstrate that the leading-order correction to the diffusion tensor is a superposition of the contributions of each surface mode. Surface corrugations can result in anisotropic diffusion with an increase in dispersion along the main flow direction and potential enhancement or reduction in dispersion perpendicular to the flow direction depending on surface characteristics. We also investigate the effects of symmetric bumpy surfaces and random surfaces, finding enhancement of 30% relative to standard Taylor dispersion for some flow conditions. Overall, these effects demonstrate that it is possible to influence dispersion and steer particles through surface topography.   

Detection of Opiates using Droplet Microfluidics and Surface-Enhanced Raman Spectroscopy

Droplet microfluidics is combined with surface-enhanced Raman spectroscopy to detect chemicals that result from illicit opiate manufacturing. The opiate epidemic causes approximately 60,000 overdose deaths in the US annually. There is a fundamental need for remote detection of chemical byproducts that emanate from illicit manufacturing.  

To this end, we have developed an extremely sensitive detector that can identify these byproducts autonomously in remote settings. Droplet microfluidics allows for long term continuous operation of a single microfluidic chip for more than one week at a time, without significant surface fouling. In addition, the discrete reaction chambers of each droplet limits the aggregated of nominally 40nm diameter silver particles. This prevent clogging of the microchannels that can result from over aggregation of the nanoparticles.   

Flow regimes, mixing degree and reaction yield in microreactors

Experimental flow visualizations, PIV, and simulations are carried out jointly to investigate how the flow regimes affect the reaction yield in T- and X-microreactors. The microreactors are fed with an aqueous solution of ascorbic acid into one of the inlet channels and an aqueous solution of methylene blue and hydrochloric acid into the other which, upon reacting, produce a colorless reaction product that can be directly measured in experiments. Different kinetic constants are considered. The interaction between chemical reactions, flow topology, and mixing is not trivial. At low Reynolds number, Re, the two reactant streams remain stratified in the mixing channels due to their different densities, and mixing is promoted only by diffusion. By increasing the Reynolds number, the engulfment regime occurs, which is characterized by the presence of vortical structures (different in T- and X-microreactors) in the confluence region and in the outlet channels, enhancing mixing thanks to convection. In the stratified regime, the reaction yield decreases with the Reynolds number due to a decrease in residence time. Instead, with the onset of the engulfment regimes, the reaction yield starts to increase with Re because the enhancement in the mixing degree between the streams overcomes the reduction of the residence time. The reaction yield also depends on the Damköhler number (Da), which represents the ratio between the characteristic time of chemical reaction and that of convection, and on the reaction kinetic constant. In the stratified regime, the reaction yield follows a Da^0.3 dependence, independently of the kinetic constant. In the engulfment regime, on the other hand, there is a strong dependence also on kinetic constant for both T- and Xmicroreactors.

    

Microfluidic assisted synthesis of silver nanoparticles: coupled PBM-CFD simulations and experimental study

The implementation of microfluidic approaches alongside a computational "digital twin" can be used to extend the knowledge of the formation of silver nanoparticles (AgNPs) and decrease the cost and ecological impact, by minimising trials and waste. In this work, the synthesis of AgNPs is investigated via a coupled population balance model and computational fluid dynamics (PBM-CFD) approach which aims to predict the final mean particle size and particle size distribution (PSD) for different operating conditions in a microfluidic T-mixer. Three synthesis steps are considered: the reduction of silver ions to silver atoms, nucleation, and growth of AgNPs. The nucleation and growth kinetic constants were calculated from UV-vis measurements through the Finke-Watzky two-step mechanism, generally used to describe metal-nanoparticles synthesis. PBM-CFD results are validated against experiments, in terms of silver ion concentration and PSD at different outlet channel lengths. It is shown that mass diffusivity and reaction kinetics have a significant effect on the species concentrations, as well as PBM parameters such as critical nucleus size and aggregation efficiency.   

Nanoscale fluid dynamics of permeability through surface-functionalized membranes

Numerous experimental and computational studies have shown that the inclusion of 2D materials, such as graphene oxide, can significantly reduce fluid permeability in composite barrier materials. In this talk, we highlight the importance of two critical factors that can play a surprisingly large role in fluid permeability across such composite materials, namely, the fluid initially imbibed within the material and the degree of surface functionalization on the interior surfaces, both of which can affect interlayer spacing within the membrane. We present a model that relates fluid permeability to several properties of the membrane, which is informed by and validated against an extensive set of molecular-dynamics simulations that we perform.   

TEM observation of liquid-gas interfacial instability

Nanofluidics has drawn significant interest over the past decade due to its unique dynamics. So far, there has been little understanding as to how nanoscale interactions affect fluid behavior. Here, we used transmission electron microscopy to observe water behavior inside a one-dimensional graphene nanochannel with high spatial and temporal resolutions. An ultrathin water film, a residue in the channel after the recession of the meniscus caused by the electron beam irradiation, became unstable and consequently formed ripples along the length of the channel. We explained the results by a theoretical analysis considering the effect of the van der Waals interaction between thin water film and graphene layers. It was found that the interactions could considerably reduce the fastest-growing wavelength as the film became thinner than a few nanometers.

    

Positivity-preserving numerical method for thin liquid films on vertical cylindrical fibers

When a thin liquid film flows down on a vertical fiber, one can observe the complex and captivating interfacial dynamics of an unsteady flow. Such dynamics are used in various applications due to their high surface area to volume ratio. Recent experiments indicate that when the flow undergoes regime transitions, the magnitude of the film thickness changes dramatically making it difficult to develop a numerical method accounting for the changes. We present a computationally efficient numerical method that can maintain the positivity of the film thickness as well as conserve the volume of the fluid under the coarse mesh setting.   

Computational study of inertial migration of prolate particles in a straight rectangular channel

Inertial migration of spherical particles has been investigated extensively using experiments, theory, and computational modeling. Yet, a systematic investigation of the effect of particle shape on inertial migration is still lacking. Herein, we numerically mapped the migration dynamics of a prolate particle in a straight rectangular microchannel using smoothed particles hydrodynamics (SPH), at moderate Reynolds number flows. After validations, we applied our model to 2:1 and 3:1 shape aspect ratio particles at multiple confinement ratios. Their effects on the final focusing position, rotational behavior, and transitional dynamics were studied. In addition to the commonly reported tumbling motion, for the first time, we identified a new logrolling behavior of a prolate ellipsoidal particle in the confined channel. This new behavior occurs when the confinement ratio is above a threshold value of K = 0.72. Our microfluidic experiments using cell aggregates with similar shape aspect ratio and confinement ratio confirmed this new predicted logrolling motion. Our findings are especially relevant to the applications where particle shape and alignment are used for sorting and analysis, such as the shape-based enrichment of microalgae, bacteria, and chromosomes.   

Elasto-Inertial Focusing and Separation Mechanisms of Particles in Shear-Thinning Viscoelastic Fluid in Rectangular Microchannels

The focusing and separation of particles in rectangular channel flow of shear-thinning viscoelastic fluid is investigated. Flow parameters are chosen to fix the elasticity number to El = 18 in order to ensure the elasto-inertial regime. Experiments and 3D finite element simulations are performed to study the effects of flowrate, particle size, and the extent of shear-thinning property of the fluid on the focusing position of particles. The Giesekus constitutive equation is used in the simulations to capture the shear-thinning and viscoelastic behaviors of the PEO solution. The general focusing pattern is due to the interplay between the elastic and shear-gradient lift forces, as well as the secondary flow transversal drag force that is caused by the non-zero second normal stress difference (N₂₎. At low flowrate with the Weissenberg number Wi = 3.6, both the elastic force and secondary flow effects push the particles towards the channel center. However, at high flowrate, Wi = 18, the elastic force direction is reversed in the central regions. This remarkable behavior of the elastic force, combined with the enhanced shear-gradient lift at high flowrate, will push the particles away from the channel center. The competition between the aforementioned forces causes the bifurcation of the focusing position into two streams that equilibrate in the intermediate region between the channel center and the walls. Owing to the different scaling of these competing forces with the particle diameter, smaller sized particles focus closer to the channel center, and hence, particle separation can be achieved at the channel outlet. Additionally, precise prediction of the focusing position is found to be strongly related to the correct estimation of the shear-thinning extent of the carrying medium in the simulations. The shear-thinning will also gives rise to the unique behavior of the inertial forces near the channel walls which is linked to the ‘warped’ velocity profile in such fluid.   

Dean number effects on the mixing quality of low aspect ratio microfluidic devices

Flow manipulation in microfluidic devices is critical for their various applications in fields such as lab-on-a-chip, biological research, and medical diagnostics. Recent research found that curved channels with varying aspect ratios shifted the distribution of Dean vortices that form in the vertical plane due to a combination of inertial, centrifugal, and viscous effects. We investigated the effect of low Dean flows (De < 20) on low aspect ratio curved channels of microfluidic devices with bumps on the channel walls. We show that for ideal mixing performance, the position and number of bumps on the microfluidic devices needed to be optimized. We also found that mixing may occur at surprisingly low De and low aspect ratios (<1/5).   

Elastic non-linearity of a filament leads to three-period and chaotic solutions in Stokes flow

The flow of Newtonian fluid at a low Reynolds number is generally regular and time-reversible due to the absence of nonlinear effects.  For example, if the fluid is sheared by its boundary motion that is reversed, all the fluid elements return to their initial positions. Consequently, mixing in microchannels happens solely due to molecular diffusion and is very slow.  Here, we show, numerically,  that the introduction of a single, freely-floating,  flexible filament in a time-periodic linear shear flow can break reversibility and give rise to chaos due to elastic nonlinearities if the bending rigidity of the filament is within a carefully chosen range.  Within this range, not only the shape of the filament is spatiotemporally chaotic, but also the flow is an efficient mixer. 

We model the filament using the bead-rod model. We consider two different models for the viscous forces : (a) they are modeled by the Rotne--Pregor tensor. This incorporates the hydrodynamic interaction between every pair of beads. (b) we consider only the diagonal term of the Rotne--Pregor tensor which makes the viscous forces local.  In both of these cases, we find the same qualitative result: the shape of a stiff filament is time-invariant -- either straight or buckled for large enough bending rigidity;  it undergoes a period-n bifurcation (n = 2,3, 4, etc) as the filament is made softer; becomes spatiotemporally chaotic for even softer filaments. For case (a) but not for (b)  we find that the chaos is suppressed if bending rigidity is decreased further.