Yonghao Zhang

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.

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-junction. 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...

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.

Phase-field modeling droplet dynamics with soluble surfactants

Using lattice Boltzmann approach, a phase-field model is proposed for simulating droplet motion with soluble surfactants. The model can recover the Langmuir and Frumkin adsorption isotherms in equilibrium. From the equilibrium equation of state, we can determine the interfacial tension lowering scale according to the interface surfactant concentration. The model is able to capture short-time and long-time adsorption dynamics of surfactants. We apply the model to examine the effect of soluble surfactants on droplet deformation, breakup and coalescence. The increase of surfactant concentration and attractive lateral interaction can enhance droplet deformation, promote droplet breakup, and inhibit droplet coalescence. We also demonstrate that the Marangoni stresses can reduce the interface mobility and slow down the film drainage process, thus acting as an additional repulsive force to prevent the droplet coalescence.

Correlation of polymer particle size with droplet size in suspension polymerisation of methylmethacrylate in a batch oscillatory-baffled reactor

We report our pioneering experimental investigation of polymer particle size and size distribution in suspension polymerisation of methylmethacrylate (MMA) in a batch 50 mm diameter stainless-steel jacketed oscillatory-baffled reactor. In such a reactor, fluid mixing is achieved by eddies that are generated when fluid passes through a set of equally spaced stationary orifice baffles. Those periodically formed vortices can be controlled by a combination of operational and geometrical parameters, such as oscillation frequency, oscillation amplitude, baffle diameter and baffle spacing. Based on a confidential and scaled-down fcormulation of a proprietary dental-grade MMA resin supplied by the Bonar Polymers, polymerisation reactions were performed under a controlled environment and the effects of the operational conditions on transient droplet size, final polymer particle size and their size distributions are studied. The mean particle size of polymer, dv,0.5, is compared with the Sauter mean size of droplet, d32, obtained with no reaction taking place and a correlation between d32 and dv,0.5 is established, which predicts the final particle sizes of polymer being made in such a reactor with a high degree of accuracy. In addition, a comparison of polymer particle size distribution, molecular weight distribution and residual initiator content is also carried out between our reactor and the traditional stirred-tank reactor.

Modeling and simulation of thermocapillary flows using lattice Boltzmann method

To understand how thermocapillary forces manipulate droplet motion in microfluidic channels, we develop a lattice Boltzmann (LB) multiphase model to simulate thermocapillary flows. The complex hydrodynamic interactions are described by an improved color-fluid LB model, in which the interfacial tension forces and the Marangoni stresses are modeled in a consistent manner using the concept of a continuum surface force. An additional convection-diffusion equation is solved in the LB framework to obtain the temperature field, which is coupled to the interfacial tension through an equation of state. A stress-free boundary condition is also introduced to treat outflow boundary, which can conserve the total mass of an incompressible system, thus improving the numerical stability for creeping flows. The model is firstly validated against the analytical solutions for the thermocapillary driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then used to simulate thermocapillary migration of three-dimensional deformable droplet at various Marangoni numbers, and its accuracy is once again verified against the theoretical prediction in the limit of zero Marangoni number. Finally, we numerically investigate how the localized heating from a laser can block the microfluidic droplet motion through the induced thermocapillary forces. The droplet motion can be completely blocked provided that the intensity of laser exceeds a threshold value, below which the droplet motion successively undergoes four stages: constant velocity, deceleration, acceleration, and constant velocity. When the droplet motion is completely blocked, four steady vortices are clearly visible, and the droplet is fully filled by two internal vortices. The external vortices diminish when the intensity of laser increases.

Deterministic numerical solutions of the Boltzmann equation using the fast spectral method

The Boltzmann equation describes the dynamics of rarefied gas flows, but the multidimensional nature of its collision operator poses a real challenge for its numerical solution. In this paper, the fast spectral method 36], originally developed by Mouhot and Pareschi for the numerical approximation of the collision operator, is extended to deal with other collision kernels, such as those corresponding to the soft, Lennard-Jones, and rigid attracting potentials. The accuracy of the fast spectral method is checked by comparing our numerical solutions of the space-homogeneous Boltzmann equation with the exact Bobylev-Krook-Wu solutions for a gas of Maxwell molecules. It is found that the accuracy is improved by replacing the trapezoidal rule with Gauss-Legendre quadrature in the calculation of the kernel mode, and the conservation of momentum and energy are ensured by the Lagrangian multiplier method without loss of spectral accuracy. The relax-to-equilibrium processes of different collision kernels with the same value of shear viscosity are then compared; the numerical results indicate that different forms of the collision kernels can be used as long as the shear viscosity (not only the value, but also its temperature dependence) is recovered. An iteration scheme is employed to obtain stationary solutions of the space-inhomogeneous Boltzmann equation, where the numerical errors decay exponentially. Four classical benchmarking problems are investigated: the normal shock wave, and the planar Fourier/Couette/force-driven Poiseuille flows. For normal shock waves, our numerical results are compared with a finite difference solution of the Boltzmann equation for hard sphere molecules, experimental data, and molecular dynamics simulation of argon using the realistic Lennard-Jones potential. For planar Fourier/Couette/force-driven Poiseuille flows, our results are compared with the direct simulation Monte Carlo method. Excellent agreements are observed in all test cases, demonstrating the merit of the fast spectral method as a computationally efficient method for rarefied gas dynamics.

Particle–gas turbulence interactions in a kinetic theory approach to granular flows

We describe a new two-fluid model for gas-solid flows that incorporates the gas turbulence influence on the random motion of the particles via a generalised kinetic theory, as well as a new gas turbulence modulation model. Simulation results for fully developed steady vertical pipe flows are in good quantitative agreement with experimental measurements. Our results show that the influence of gas turbulence on the particle microscopic flow behaviour cannot be ignored for relatively dilute flows, especially with smaller particles. Our new turbulent model captures the essential characteristics of gas turbulence modulation in the presence of particles, and can be solved for a wide range of particle-particle restitution coefficients.

Lattice Boltzmann phase-field modeling of thermocapillary flows in a confined microchannel

To understand how thermocapillary forces manipulate the droplet motion in a confined microchannel, a lattice Boltzmann phase-field model is developed to simulate immiscible thermocapillary flows with consideration of fluid-surface interactions. Based on our recent work of Liu et al., 2013 [54], an interfacial force of potential form is proposed to model the interfacial tension force and the Marangoni stress. As only the first-order derivatives are involved, the proposed interfacial force is easily combined with the wetting boundary condition to account for fluid-surface interactions. The hydrodynamic equations are solved using a multiple-relaxation-time algorithm with the interfacial force treated as a forcing term, while an additional convection-diffusion equation is solved by a passive-scalar approach to obtain the temperature field, which is coupled to the interfacial tension by an equation of state. The model is first validated against analytical solutions for the thermocapillary-driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then demonstrated to produce the correct equilibrium contact angle for a binary fluid with different viscosities when a constant interfacial tension is taken into account. Finally, we numerically simulate the thermocapillary flows for a microfluidic droplet adhering on a solid wall and subject to a simple shear flow when a laser is applied to locally heat the fluids, and investigate the influence of contact angle and fluid viscosity ratio on the droplet dynamical behavior. The droplet motion can be completely blocked provided that the contact angle exceeds a threshold value, below which the droplet motion successively undergoes four stages: constant velocity, deceleration, acceleration, and approximately constant velocity. When the droplet motion is completely blocked, three steady vortices are clearly visible, and the droplet is fully filled by two counter-rotating vortices with the smaller one close to the external vortex. The thermocapillary convection is strengthened with decreasing viscosity ratio of the droplet to the carrier fluid. For low viscosity ratios, the droplet motion is completely blocked and exhibits the similar behavior, but the structure of the internal vortices is more complicated at the lowest viscosity ratio. For high viscosity ratios, the droplet motion is partially blocked and undergoes a series of complex transitions, which can be explained as a result of the dynamically varying Marangoni forces.

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.