Droplet formation in a T-shaped microfluidic junction

Using a phase-field model to describe fluid/fluid interfacial dynamics and a lattice Boltzmann model to address hydrodynamics, two dimensional (2D) numerical simulations have been performed to understand the mechanisms of droplet formation in microfluidic T-juntion. Although 2D simulations may not capture underlying physics quantitatively, our findings will help to clarify controversial experimental observations and identify new physical mechanisms. We have systematically examined the influence of capillary number, flow rate ratio, viscosity ratio, and contact angle in the droplet generation process. We clearly observe that the transition from the squeezing regime to the dripping regime occurs at a critical capillary number of 0.018, which is independent of flow rate ratio, viscosity ratio, and contact angle. In the squeezing regime, the squeezing pressure plays a dominant role in the droplet breakup process, which arises when the emerging interface obstructs the main channel. The droplet size depends on both the capillary number and the flow rate ratio, but is independent of the viscosity ratio under completely hydrophobic wetting conditions. In the dripping regime, the droplet size will be significantly influenced by the viscosity ratio as well as the built-up squeezing pressure. When the capillary number increases, the droplet size becomes less dependent on the flow rate ratio. The contact angle also affects the droplet shape, size, and detachment point, especially at small capillary numbers. More hydrophobic wetting properties are expected to produce smaller droplets. Interestingly, the droplet size is dependent on the viscosity ratio in the squeezing regime for less hydrophobic wetting conditions

Lattice Boltzmann simulation of droplet behaviour in microfluidic devices

We developed a lattice Boltzmann model to investigate the droplet dynamics in microfluidic devices. In our model, a stress-free boundary condition was proposed to conserve the total mass of flow system and improve the numerical stability for flows with low Reynolds number The model was extensively validated by the benchmark cases including the Laplace law, the static contact angles at solid surface, and the droplet deformation and breakup under simple shear flow We applied our model to study the effects of the Pelcect number the Capillary number and wettability on droplet formation. The results showed that the Peclet number has little effect on droplet size though it slightly affects the time of droplet formation. In the creeping flow regime, the Capillary number plays a dominating role in the droplet generation process. Wettability of fluids affects the position of droplet detachment, the droplet shape and size, and its impact becomes more significant when the Capillary number decreases. We also found that the hydrophobic surface generally can produce smaller droplet

Droplet formation in microfluidic cross-junctions

Using a lattice Boltzmann multiphase model, three-dimensional numerical simulations have been performed to understand droplet formation in microfluidic cross-junctions at low capillary numbers. Flow regimes, consequence of interaction between two immiscible fluids, are found to be dependent on the capillary number and flow rates of the continuous and dispersed phases. A regime map is created to describe the transition from droplets formation at a cross-junction (DCJ), downstream of cross-junction to stable parallel flows. The influence of flow rate ratio, capillary number, and channel geometry is then systematically studied in the squeezing-pressure-dominated DCJ regime. The plug length is found to exhibit a linear dependence on the flow rate ratio and obey power-law behavior on the capillary number. The channel geometry plays an important role in droplet breakup process. A scaling model is proposed to predict the plug length in the DCJ regime with the fitting constants depending on the geometrical parameters

Analytical solution for the lattice Boltzmann model beyond Naviers-Stokes

To understand lattice Boltzmann model capability for capturing nonequilibrium effects, the model with first-order expansion of the equilibrium distribution function is analytically investigated. In particular, the velocity profile of Couette flows is exactly obtained for the D2Q9 model, which shows retaining the first order expansion can capture rarefaction effects in the incompressible limit. Meanwhile, it clearly demonstrates that the D2Q9 model is not able to reflect flow characteristics in the Knudsen layer

Microfluidic DNA amplification - a review

The application of microfluidic devices for DNA amplification has recently been extensively studied. Here, we review the important development of microfluidic polymerase chain reaction (PCR) devices and discuss the underlying physical principles for the optimal design and operation of the device. In particular, we focus on continuous-flow microfluidic PCR on-chip, which can be readily implemented as an integrated function of a micro-total-analysis system. To overcome sample carryover contamination and surface adsorption associated with microfluidic PCR, microdroplet technology has recently been utilized to perform PCR in droplets, which can eliminate the synthesis of short chimeric products, shorten thermal-cycling time, and offers great potential for single DNA molecule and single-cell amplification. The work on chip-based PCR in droplets is highlighted

Numerical investigation of the radial quadrupole and scissors modes in trapped gases

The analytical expressions for the frequency and damping of the radial quadrupole and scissors modes, as obtained from the method of moments, are limited to the harmonic potential. In addition, the analytical results may not be suciently accurate as an average relaxation time is used and the high-order moments are ignored. Here, we propose to numerically solve the Boltzmann model equation in the hydrodynamic, transition, and collisionless regimes to study mode frequency and damping. When the gas is trapped by the harmonic potential, we nd that the analytical expressions underestimate the damping in the transition regime. In addition, we demonstrate that the numerical simulations are able to provide reasonable predictions for the collective oscillations in the Gaussian potentials

Simulating fluid flows in micro and nano devices : the challenge of non-equilibrium behaviour

We review some recent developments in the modelling of non-equilibrium (rarefied) gas flows at the micro- and nano-scale, concentrating on two different but promising approaches: extended hydrodynamic models, and lattice Boltzmann methods. Following a brief exposition of the challenges that non-equilibrium poses in micro- and nano-scale gas flows, we turn first to extended hydrodynamics, outlining the effective abandonment of Burnett-type models in favour of high-order regularised moment equations. We show that the latter models, with properly-constituted boundary conditions, can capture critical non-equilibrium flow phenomena quite well. We then review the boundary conditions required if the conventional Navier-Stokes-Fourier (NSF) fluid dynamic model is applied at the micro scale, describing how 2nd-order Maxwell-type conditions can be used to compensate for some of the non-equilibrium flow behaviour near solid surfaces. While extended hydrodynamics is not yet widely-used for real flow problems because of its inherent complexity, we finish this section with an outline of recent 'phenomenological extended hydrodynamics' (PEH) techniques-essentially the NSF equations scaled to incorporate non-equilibrium behaviour close to solid surfaces-which offer promise as engineering models. Understanding non-equilibrium within lattice Boltzmann (LB) framework is not as advanced as in the hydrodynamic framework, although LB can borrow some of the techniques which are being developed in the latter-in particular, the near-wall scaling of certain fluid properties that has proven effective in PEH. We describe how, with this modification, the standard 2nd-order LB method is showing promise in predicting some rarefaction phenomena, indicating that instead of developing higher-order off-lattice LB methods with a large number of discrete velocities, a simplified high-order LB method with near-wall scaling may prove to be just as effective as a simulation tool

Accuracy analysis of high-order lattice Boltzmann models for rarefied gas flows

In this work, we have theoretically analyzed and numerically evaluated the accuracy of high-order lattice Boltzmann (LB) models for capturing non-equilibrium effects in rarefied gas flows. In the incompressible limit, the LB equation is shown to be able to reduce to the linearized Bhatnagar–Gross–Krook (BGK) equation. Therefore, when the same Gauss–Hermite quadrature is used, LB method closely resembles the discrete velocity method (DVM). In addition, the order of Hermite expansion for the equilibrium distribution function is found not to be directly correlated with the approximation order in terms of the Knudsen number to the BGK equation for incompressible flows. Meanwhile, we have numerically evaluated the LB models for a standing-shear-wave problem, which is designed specifically for assessing model accuracy by excluding the influence of gas molecule/surface interactions at wall boundaries. The numerical simulation results confirm that the high-order terms in the discrete equilibrium distribution function play a negligible role in capturing non-equilibrium effect for low-speed flows. By contrast, appropriate Gauss–Hermite quadrature has the most significant effect on whether LB models can describe the essential flow physics of rarefied gas accurately. Our simulation results, where the effect of wall/gas interactions is excluded, can lead to conclusion on the LB modeling capability that the models with higher-order quadratures provide more accurate results. For the same order Gauss–Hermite quadrature, the exact abscissae will also modestly influence numerical accuracy. Using the same Gauss–Hermite quadrature, the numerical results of both LB and DVM methods are in excellent agreement for flows across a broad range of the Knudsen numbers, which confirms that the LB simulation is similar to the DVM process. Therefore, LB method can offer flexible models suitable for simulating continuum flows at the Navier–Stokes level and rarefied gas flows at the linearized Boltzmann model equation level

Gauss-Hermite quadratures and accuracy of lattice Boltzmann models for non-equilibrium gas flows

Recently, kinetic theory-based lattice Boltzmann (LB) models have been developed to model nonequilibrium gas flows. Depending on the order of quadratures, a hierarchy of LB models can be constructed which we have previously shown to capture rarefaction effects in the standing-shearwave problems. Here, we further examine the capability of high-order LB models in modeling nonequilibrium flows considering gas and surface interactions and their effect on the bulk flow. The Maxwellian gas and surface interaction model, which has been commonly used in other kinetic methods including the direct simulation Monte Carlo method, is used in the LB simulations. In general, the LB models with high-order Gauss-Hermite quadratures can capture flow characteristics in the Knudsen layer and higher order quadratures give more accurate prediction. However, for the Gauss-Hermite quadratures, the present simulation results show that the LB models with the quadratures obtained from the even-order Hermite polynomials perform significantly better than those from the odd-order polynomials. This may be attributed to the zero-velocity component in the odd-order discrete set, which does not participate in wall and gas collisions, and thus underestimates the wall effect