In this article, we construct a novel 1D-model of microfluidic laminar flows in tapered circular and rectangular channels assuming the flow in channels fully developed. In the model, we take into account the inertance and dynamic pressure terms. The model can be used for a wide range of flows: from the pure capillary flow regime, where the capillary forces are the main driver of the liquid in the channel, to the external pressure flow regime where the external pressure applied to the liquid at the entrance to the channel is much larger than the capillary pressure in the channel, so that the capillary force can be ignored. We apply the model to rectangular Y-shape junctions, where the base channel is connected to a reservoir and the end channels are exposed to atmospheric air. We show that, in asymmetric Y-shape junctions, there can be a time of meniscus arrest, where only one of the two channels with a smaller radius fills, and, the other one, with a larger radius, is arrested. The time of meniscus arrest decreases with an increase in the applied external pressure; when this pressure becomes large enough, the meniscus arrest disappears. However, if the ratio of the radii of the end channels is large, the meniscus arrest does not appear because the flow resistance in the channel with the smaller radius is much large than in the channel with the larger radius so that the initial flow in the wider channel cannot be stopped by the differences in the surface tension pressures in these channels. In this article, we also investigate the applicability of the fully developed flow approximation assumed in the model.
[First paragraph] In a recent paper Yamada et al. propose the novel concept of "pinched flow fractionation" (PFF) for the continuous size separation and analysis of particles in microfabricated lab-on-a-chip devices. In their description of the basic principle they claim that especially the width of the pinched and broadened segments will affect theseparation performance. In the following we comment on the physics behind this statement.
The Rouse number is commonly used to estimate the mode of the sediment transports in turbulent flows with large Reynolds number. However, in microchannels such as in modern inkjet systems, the liquid flows are usually laminar. In this paper, I modify the Rouse number by expanding it to the case of weakly turbulent and laminar flows and construct a calculator to estimate the modes of sediment transport in microchannels. To illustrate the applicability of the modified Rouse number, I apply it to the transport of sediments in an inkjet system and compare theoretical results with experimental obse…
In this paper we numerically investigate the breakup dynamics of droplets in an emulsion flowing in a tapered microchannel with a narrow constriction. The mesoscale approach for multicomponent fluids with near contact interactions is shown to capture the deformation and breakup dynamics of droplets interacting within the constriction, in agreement with experimental evidences. In addition, it permits to investigate in detail the hydrodynamic phenomena occurring during the breakup stages. Finally, a suitable deformation parameter is introduced and analyzed to characterize the state of deformatio…
The liquid flow and conjugated heat transfer performance of single-phase laminar flow in rectangular microchannels equipped with longitudinal vortex generators (LVGs) are numerically investigated. Deionized-water with temperature-dependent thermo-physical properties is employed to conduct the simulations. Three-dimensional simulations are performed using an open-source flow solver based on finite volume approach and SIMPLEC algorithm. Five different configurations of the microchannel with different angles of attack of the LVGs are considered. Simulation results are compared with available expe…
At finite Reynolds numbers, Re, particles migrate across laminar flow streamlines to their equilibrium positions in microchannels. This migration is attributed to a lift force, and the balance between this lift and gravity determines the location of particles in channels. Here we demonstrate that velocity of finite-size particles located near a channel wall differs significantly from that of an undisturbed flow, and that their equilibrium position depends on this, referred to as slip velocity, difference. We then present theoretical arguments, which allow us to generalize expressions for a lif…
A computational fluid dynamics model is used to predict the oscillatory flow through tapered cylindrical tube sections (jet pumps). The asymmetric shape of jet pumps results in a time-averaged pressure drop that can be used to suppress Gedeon streaming in closed-loop thermoacoustic devices. However, previous work has shown that flow separation in the diverging flow direction counteracts the time-averaged pressure drop. In this work, the characteristics of flow separation in jet pumps are identified and coupled with the observed jet pump performance. Furthermore, it is shown that the onset of f…
Electrokinetic flow can be generated as a highly coupled phenomenon among velocity field, electric conductivity field and electric field. It can exhibit different responses to AC electric fields in different frequency regimes, according to different instability/receptivity mechanisms. In this investigation, by both flow visualization and single-point laser-induced fluorescence (LIF) method, the response of AC electrokinetic flow and the transition routes towards chaos and turbulence have been experimentally investigated. It is found, when the AC frequency $f_f<30$ Hz, the interface responds at…
Liquid-infused surfaces (LIS) can reduce friction drag in both laminar and turbulent flows. However, the heat transfer properties of such multi-phase surfaces have still not been investigated to a large extent. We use numerical simulations to study conjugate heat transfer of liquid-filled grooves. It is shown that heat transfer can increase for both laminar and turbulent liquid flows due to recirculation in the surface texture. For the increase to be substantial, the thermal conductivity of the solid must be similar to the thermal conductivity of the fluids, and the recirculation in the groove…
We employ micro-particle image velocimetry ($μ$-PIV) to investigate laminar micro-flows in hydrophobic microstructured channels, in particular the slip length. These microchannels consist of longitudinal micro-grooves, which can trap air and prompt a shear-free boundary condition and thus slippage enhancement. Our measurements reveal an increase of the slip length when the width of the micro-grooves is enlarged. The result of the slip length is smaller than the analytical prediction by Philip et al. [1] for an infinitely large and textured channel comprised of alternating shear-free and no-sli…
Precise measurement of flow velocity in microfluidic channels is of importance in microfluidic applications, such as quantitative chemical analysis, sample preparation and drug synthesis. However, simple approaches for quickly and precisely measuring the flow velocity in microchannels are still lacking. Herein, we propose a deep neural networks assisted scalar image velocimetry (DNN-SIV) for quick and precise extraction of fluid velocity in a shallow microfluidic channel with a high aspect ratio, which is a basic geometry for cell culture, from a dye concentration field with spatiotemporal gra…
We consider laminar, fully-developed, Poiseuille flows of liquid in the Cassie state through diabatic, parallel-plate microchannels symmetrically textured with isoflux ridges. Through the use of matched asymptotic expansions we analytically develop expressions for (apparent hydrodynamic) slip lengths and variously-defined Nusselt numbers. Our small parameter ($ε$) is the pitch of the ridges divided by the height of the microchannel. When the ridges are oriented parallel to the flow, we quantify the error in the Nusselt number expressions in the literature and provide a new closed-form result. …
We consider laminar flow in channels constrained geometrically to remain between two parallel planes; this geometry is typical of microchannels obtained with a single step by current microfabrication techniques. For pressure-driven Stokes flow in this geometry and assuming that the channel dimensions change slowly in the streamwise direction, we show that the velocity component perpendicular to the constraint plane cannot be zero unless the channel has both constant curvature and constant cross-sectional width. This result implies that it is, in principle, possible to design "planar mixers", i…
Laminar flow in devices fabricated from soft materials causes deformation of the passage geometry, which affects the flow rate--pressure drop relation. For a given pressure drop, in channels with narrow rectangular cross-section, the flow rate varies as the cube of the channel height, so deformation can produce significant quantitative effects, including nonlinear dependence on the pressure drop [{Gervais, T., El-Ali, J., Günther, A. \& Jensen, K.\ F.}\ 2006 Flow-induced deformation of shallow microfluidic channels.\ \textit{Lab Chip} \textbf{6}, 500--507]. Gervais et. al. proposed a successfu…
