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Register a new userDroplet traffic in microfluidic networks: A simple model for understanding and designing
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We propose a simple model to analyze the traffic of droplets in microfluidic ``dual networks. Such functional networks which consist of two types of channels, namely those accessible or forbidden to droplets, often display a complex behavior characteristic of dynamical systems. By focusing on three recently proposed configurations, we offer an explanation for their remarkable behavior. Additionally, the model allows us to predict the behavior in different parameter regimes. A verification will clarify fundamental issues, such as the network symmetry, the role of the driving conditions, and of the occurrence of reversible behavior. The model lends itself to a fast numerical implementation, thus can help designing devices, identifying parameter windows where the behavior is sufficiently robust for a devices to be practically useful, and exploring new functionalities.
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We investigate the role of intense vortical structures, similar to those in a turbulent flow, in enhancing collisions (and coalescences) which lead to the formation of large aggregates in particle-laden flows. By using a Burgers vortex model, we show, in particular, that vortex stretching significantly enhances sharp inhomogeneities in spatial particle densities, related to the rapid ejection of particles from intense vortices. Furthermore our work shows how such spatial clustering leads to an enhancement of collision rates and extreme statistics of collisional velocities. We also study the role of poly-disperse suspensions in this enhancement. Our work uncovers an important principle which, {if valid for realistic turbulent flows, may be a factor in} how small nuclei water droplets in warm clouds can aggregate to sizes large enough to trigger rain.
The effects of viscoelasticity on the dynamics and break-up of fluid threads in microfluidic T-junctions are investigated using numerical simulations of dilute polymer solutions at changing the Capillary number ($mbox {Ca}$), i.e. at changing the balance between the viscous forces and the surface tension at the interface, up to $mbox{Ca} approx 3 times 10^{-2}$. A Navier-Stokes (NS) description of the solvent based on the lattice Boltzmann models (LBM) is here coupled to constitutive equations for finite extensible non-linear elastic dumbbells with the closure proposed by Peterlin (FENE-P model). We present the results of three-dimensional simulations in a range of $mbox{Ca}$ which is broad enough to characterize all the three characteristic mechanisms of breakup in the confined T-junction, i.e. ${it squeezing}$, ${it dripping}$ and ${it jetting}$ regimes. The various model parameters of the FENE-P constitutive equations, including the polymer relaxation time $tau_P$ and the finite extensibility parameter $L^2$, are changed to provide quantitative details on how the dynamics and break-up properties are affected by viscoelasticity. We will analyze cases with ${it Droplet ~Viscoelasticity}$ (DV), where viscoelastic properties are confined in the dispersed (d) phase, as well as cases with ${it Matrix ~Viscoelasticity}$ (MV), where viscoelastic properties are confined in the continuous (c) phase. Moderate flow-rate ratios $Q approx {cal O}(1)$ of the two phases are considered in the present study. Overall, we find that the effects are more pronounced in the case with MV, as the flow driving the break-up process upstream of the emerging thread can be sensibly perturbed by the polymer stresses.
Microfluidic systems are now being designed with precision to execute increasingly complex tasks. However, their operation often requires numerous external control devices due to the typically linear nature of microscale flows, which has hampered the development of integrated control mechanisms. We address this difficulty by designing microfluidic networks that exhibit a nonlinear relation between applied pressure and flow rate, which can be harnessed to switch the direction of internal flows solely by manipulating input and/or output pressures. We show that these networks exhibit an experimentally-supported fluid analog of Braesss paradox, in which closing an intermediate channel results in a higher, rather than lower, total flow rate. The harnessed behavior is scalable and can be used to implement flow routing with multiple switches. These findings have the potential to advance development of built-in control mechanisms in microfluidic networks, thereby facilitating the creation of portable systems that may one day be as controllable as microelectronic circuits.
Based on mesoscale lattice Boltzmann (LB) numerical simulations, we investigate the effects of viscoelasticity on the break-up of liquid threads in microfluidic cross-junctions, where droplets are formed by focusing a liquid thread of a dispersed (d) phase into another co-flowing continuous (c) immiscible phase. Working at small Capillary numbers, we investigate the effects of non-Newtonian phases in the transition from droplet formation at the cross-junction (DCJ) to droplet formation downstream of the cross-junction (DC) (Liu $&$ Zhang, ${it Phys. ~Fluids.}$ ${bf 23}$, 082101 (2011)). We will analyze cases with ${it Droplet ~Viscoelasticity}$ (DV), where viscoelastic properties are confined in the dispersed phase, as well as cases with ${it Matrix ~Viscoelasticity}$ (MV), where viscoelastic properties are confined in the continuous phase. Moderate flow-rate ratios $Q approx {cal O}(1)$ of the two phases are considered in the present study. Overall, we find that the effects are more pronounced in the case with MV, where viscoelasticity is found to influence the break-up point of the threads, which moves closer to the cross-junction and stabilizes. This is attributed to an increase of the polymer feedback stress forming in the corner flows, where the side channels of the device meet the main channel. Quantitative predictions on the break-up point of the threads are provided as a function of the Deborah number, i.e. the dimensionless number measuring the importance of viscoelasticity with respect to Capillary forces.
The tendency for flows in microfluidic systems to behave linearly poses a challenge for designing integrated flow control schemes to carry out complex fluid processing tasks. This hindrance has led to the use of numerous external control devices to manipulate flows, thereby thwarting the potential scalability and portability of lab-on-a-chip technology. Here, we devise a microfluidic network exhibiting nonlinear flow dynamics that enable new mechanisms for on-chip flow control. This network is shown to exhibit oscillatory output patterns, bistable flow states, hysteresis, signal amplification, and negative-conductance transitions, all without reliance on dedicated external control hardware, movable parts, flexible components, or oscillatory inputs. These dynamics arise from nonlinear fluid inertia effects in laminar flows that we amplify and harness through the design of the network geometry. We suggest that these results, which are supported by fluid dynamical simulations and theoretical modeling, have the potential to inspire development of new built-in control capabilities, such as on-chip timing and synchronized flow patterns.
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