Fundamentals and Applications of Electrowetting

Electrowetting (EW) effect is defined as changing in the interfacial energy of solid–liquid interface which causes to change in solid–liquid contact angle. In EW on dielectric (EWOD) actuations, the microliter drops are usually placed between two substrates which have some advantages. By modifying the voltages applied to the electrodes, it is possible to manipulate the droplets by setting up surface tension gradients along the plate. In this paper, the free energy based lattice Boltzmann method which has been recently extended by the authors for modeling and simulation of EW phenomenon has been applied to simulate EWOD. Also here we report the results of simulation of EW on superhydrophobic surfaces and pinning problem. The results have been compared with experimental data and show good accuracy of the numerical simulation.

Tempered fractional calculus, as an extension of fractional calculus, has been successfully applied in numerous scientific and engineering fields. Although several traditional numerical methods have been improved for solving a variety of tempered fractional partial differential equations, solving these equations by the lattice Boltzmann (LB) method is an unresolved issue. This paper is dedicated to presenting a novel LB method for the tempered time-fractional diffusion equation. The tempered time-fractional diffusion equation is first transformed into an integer-order partial differential equation by approximating the tempered fractional derivative term. Then the LB method is proposed to solve the transformed objective equation. The Chapman-Enskog procedure is conducted to confirm that the present LB method can accurately recover the objective equation. Some numerical examples with an analytical solution are employed to validate the present LB method, and a strong consistency is observed between the numerical and analytical solutions. The numerical simulations indicate that the LB method is a second-order accurate scheme. The proposed LB method presents a new approach to solving the tempered time-fractional diffusion equation, which is beneficial for the widespread application of the tempered time-fractional diffusion equation in addressing complex transport problems.

This paper describes effect of characteristics of dielectric layer on performances of droplet transport in EWOD (Electro wetting on dielectric) microfluidic devices. EWOD is a technology for manipulating droplets discretely by controlling the surface wettability electrically. Films of Parylene C, PDMS, and SU-8 were prepared for the dielectric layer and effects of deposition method, thickness and permittivity of these films were investigated experimentally. The results show that water droplets can be easily transported at low voltage when the dielectric film with high permittivity is deposited thinly and uniformly.

One of the fundamental problems in simulating the motion of sharp interfaces between immiscible fluids is a description of the transition that occurs when the interfaces merge and reconnect. It is well known that classical methods involving sharp interfaces fail to describe this type of phenomena. Following some previous work in this area, we suggest a physically motivated regularization of the Euler equations which allows topological transitions to occur smoothly. In this model, the sharp interface is replaced by a narrow transition layer across which the fluids may mix. The model describes a flow of a binary mixture, and the internal structure of the interface is determined by both diffusion and motion. An advantage of our regularization is that it automatically yields a continuous description of surface tension, which can play an important role in topological transitions. An additional scalar field is introduced to describe the concentration of one of the fluid components and the resulting system of equations couples the Euler (or Navier–Stokes) and the Cahn–Hilliard equations. The model takes into account weak non–locality (dispersion) associated with an internal length scale and localized dissipation due to mixing. The non–locality introduces a dimensional surface energy; dissipation is added to handle the loss of regularity of solutions to the sharp interface equations and to provide a mechanism for topological changes. In particular, we study a non–trivial limit when both components are incompressible, the pressure is kinematic but the velocity field is non–solenoidal (quasi–incompressibility). To demonstrate the effects of quasi–incompressibility, we analyse the linear stage of spinodal decomposition in one dimension. We show that when the densities of the fluids are not perfectly matched, the evolution of the concentration field causes fluid motion even if the fluids are inviscid. In the limit of infinitely thin and well–separated interfacial layers, an appropriately scaled quasi–incompressible Euler–Cahn–Hilliard system converges to the classical sharp interface model. In order to investigate the behaviour of the model outside the range of parameters where the sharp interface approximation is sufficient, we consider a simple example of a change of topology and show that the model permits the transition to occur without an associated singularity.

The phenomenon of boiling is visible all around us from cooking to power generation, but despite such all around usages many aspects of boiling are still not very well understood as it is a very complex process and occurs over a wide range of system scales. We often rely on empirical correlations when we want to evaluate different parameters connected with boiling phenomena. Along with the development of empirical correlations for engineering applications, considerable advances are there in understanding the fundamentals of the boiling process. Since the process is very complex and multiple thermal and fluid variables are involved, a complete theoretical model for predicting the boiling heat transfer is yet to be developed. Boiling phenomenon is still being intensively studied and is the focus of research activities in numerous institutions across the world. A better understanding of the physics of boiling can be achieved by either detailed measurements or high-resolution numerical simulation. These two approaches are now complementing each other in understanding the physics of boiling more completely. In recent years, numerical modeling has improved considerably thanks to ever-increasing computational power. With advancing computing capabilities and advent of new numerical techniques for two-phase flow, simulations of boiling heat transfer have become feasible. The main two approaches in numerical simulation of boiling are (i) interpenetrating media approach and (ii) single-fluid approach. In addition to this, some newer techniques like the phase field method and the lattice Boltzmann method have to some extent been used for simulating boiling flows. In this review, we look at the different approaches of numerical simulation of boiling currently being used.

This work focuses on the development of efficient computational tools for the simulation of turbulent multiphase polydispersed flows. In terms of methodologies we focus here on the use of Large Eddy Simulation (LES) and Quadrature-Based Methods of Moments (QBMM). In terms of applications the work is finalised, in order to be applied in the future, to particle production processes (precipitation and crystallisation in particular). An important part of the work concerns the study of the flow field in a Confined Impinging Jets Reactor (CIJR), frequently used in particle production processes. The first part is limited to the comparison and analysis of micro Particle Image Velocimetry (μPIV) experiments, carried out in a previous work, and Direct Numerical Simulation (DNS), carried out in this thesis. In particular the effects of boundary and operating conditions are studied and the numerical simulations are used to understand the experimental predictions and demonstrate the importance of unavoidable fluctuations in the experimental inlets. This represents a preparatory work for the LES modelling of the CIJR. Before investigating the accuracy of LES predictions for this particular application, the model and the implementation are studied in a more general context, represented by a well-known test case such as the periodic turbulent channel flow: the LES model implementation in TransAT, the code used in this work, is compared with DNS data and with predictions of other codes. LES simulations for the CIJR, provided with the proper boundary conditions obtained by the previous DNS/μPIV study, are then performed and compared with experiments, validating the model in a more realistic test case. Since particle precipitation and crystallization often result in complex interactions between particles and the continuous phase, in the second part of the work particular attention has been paid in the modelling of the momentum transfer and the resulting velocity of the particles (relative to the fluid). In particular the possibility of describing poly-disperse fluid-solid systems with QBMM together with LES and Equilibrium Eulerian Model (EEM) is assessed. The study is performed by comparing our predictions with DNS Lagrangian data in the turbulent channel flow previously described, seeded with particles corresponding to a realistic Particle Size Distribution (PSD). The last part of the work deals with particle collisions, extending QBMM to the investigation of non-equilibrium flows governed by the Boltzmann Equation with a hard-sphere collision kernel. The evolution of the particle velocity distribution is predicted and compared with other methods for kinetic equations such as Lattice Boltzmann Method (LBM), Discrete Velocity Method (DVM) and Grad's Moment Method (GM). The overall results of this thesis can be extended to a broad range of other applications of single-phase, dispersed multiphase and non-equilibrium flows

The phase transition between liquid and vapor is of vital importance in daily life and industry. Given the importance of the lattice Boltzmann method (LBM), in particular the phase field method, in the simulation of two-phase flows, a robust LBM phase transition model is essential. This study introduces a novel approach by integrating the widely used, Hertz–Knudsen–Schrage (HKS) phase change rate into a conservative phase-field LBM. The phase-field and momentum equations are solved using the Boltzmann distribution function, whereas the energy equation is solved using the finite difference method. Once the necessary parameters for the calculation of the phase change rate are obtained, the corresponding source terms are incorporated into each equation. The model's validation is performed through a series of benchmark problems, including the one-dimensional Stefan problem, Nusselt's film condensation, bubble detachment, centered droplet evaporation, and sessile droplet evaporation. The results demonstrate favorable agreement between the LBM solution and analytical or empirical data. Furthermore, this study highlights the model's ability to approximate steady-state phenomena with minimal reliance on the phase change coefficient of the HKS theory. It also underscores the model's capacity to accurately capture transient phenomena by appropriately selecting values for this coefficient. In addition, parametric studies are conducted to investigate evaporation problems using the HKS theory for recognizing the effect of superheat, contact angle, and droplet size on evaporation. Finally, this model not only can detect trends and behaviors of phenomena but also can adapt empirical and analytical results with good agreement.

An interaction potential based lattice Boltzmann method with adaptive mesh refinement (AMR) for two-phase flow simulation

The lattice Boltzmann method (LBM) is shown to be equivalent to the Navier-Stokes equations by applying the Chapman-Enskog (C-E) expansion, which has been established by pioneer researchers. However, it is still difficult for elementary researchers. There is no clear explanation of the small parameter ε used in the C-E expansion. There are several expressions for the viscosity coefficient; some are unclear on the relationship with ε. There are two expressions on the LBM evolution equation. Elementary researchers are perplexed as to which is correct. The LBM achieves second order accuracy by including the numerical viscosity within the physical viscosity. This is not only difficult for elementary researchers to understand but also sometimes leads senior researchers into making errors. The C-E expansion of the LBM was thoroughly reviewed and is presented as a self-contained form in this paper. It is natural to use the time step Δt as ε. The viscosity coefficient is expressed as μ∝Δxc(τ − 1/2). The viscosity relationship and the second order accuracy were confirmed by numerical simulations. The difference in the two expressions on the LBM evolution is simply one of perspective. They are identical. The difference between the relaxation parameter τD for the discrete Boltzmann equation and τ for the LBM was discussed. While τD is a quantity of time, τ is genuinely nondimensional, which is sometimes overlooked.

Formation evaluation including porosity and directional permeability assessment in complex carbonate formations is challenging due to the anisotropic and heterogeneous nature of the formation. The pore structure can be captured by digital rock technology, which makes the constriction of numerical whole core, and the numerical simulations of chemical enhanced oil recovery on digital rock possible. We introduce a new workflow to construct the digital rock based on micron-CT scanned sequential images of the carbonate sample. Firstly, we apply the modified Otsu's global thresholding method to convert the grey-scale micron-CT scanned images to binary images, and we systematically divide the whole core 3D segmented image into small blocks or representative elementary volume (totally 10143 blocks including inactive blocks). Then we estimate the porosity of each block, and use Lattice Boltzmann Method (LBM) to simulate fluid flow in randomly selected blocks and accurately compute the directional permeability of these blocks by simulating Darcy flow through them. The permeability tensor of other blocks is estimated by applying Kriging method based on the estimated porosity of all the blocks and the accurately calculated permeability tensor of the selected blocks. Then we simulate the polymer flooding on the constructed digital rock and show that the simulation process is computational efficient. We calculate the porosity and permeability of the constructed digital whole core and compare them with laboratory measurements. The image analyzed porosity of whole digital rock is comparable with laboratory measurements by only 1% difference. The simulated permeability value with calibration of the whole digital rock is also in good agreement with experimental result by 3.5% difference. Then we simulate the polymer flooding on the constructed digital rock and show that the simulation process is computational efficient. The proposed digital whole core construction workflow integrates the accuracy of LBM simulation and the efficiency of kriging method. The accurately constructed digital whole core only have 10143 blocks including inactive blocks, which greatly reduces the heavy computation time of chemical enhanced oil recovery simulation on digital rock and makes the proposed method more practical in routine analysis and modeling.

Numerical simulations are performed for transport and deposition of particles over a fixed obstacle in a fluid flow. The effect of particle size and Stokes number on the particle capture efficiency is investigated using two methods. The first one is one-way coupling combining Lattice Boltzmann (LB) method with Lagrangian point-like approach. The second one is two-way coupling based on the coupling between Lattice Boltzmann method and discrete element (DE) method, which consider the particle influence on the fluid. Then the single fiber collection efficiency characterized by Stokes number (St ) are simulated by LB-DE methods. Results show that two-way coupling method is more appropriate in our case for particles larger than 8 μm . A good agreement has also been observed between our simulation results and existing correlations for single fiber collection efficiency. The numerical simulations presented in this work are useful to understand the particle transport and deposition and to predict the capture efficiency.

Peng-Robinson (P-R) equation of state (EOS) has been widely used in the petroleum industry for hydrocarbon fluids. In this work, a three-dimensional diffuse interface model with P-R EOS for two-phase fluid system is solved by the lattice Boltzmann (LB) method. In this diffuse interface model, an Allen-Cahn (A-C) type phase equation with strong nonlinear source term is derived. Using the multiscale Chapman-Enskog analysis, the A-C type phase equation can be recovered from the proposed LB method. Besides, a Lagrange multiplier is introduced based on the mesoscopic character of the LB scheme so that total mass of the hydrocarbon system is preserved. Three-dimensional numerical simulations of realistic hydrocarbon components, such as isobutane and propane, are implemented to illustrate the effectiveness of the proposed mass conservative LB scheme. Numerical results reach a better agreement with laboratory data compared to previous results of two-dimensional numerical simulations.

By coupling the phase field model with the continuity equation of incompressible fluid, Navier–Stokes equation, electric field equation, and other governing equations, a multi-field coupling model for multi-bubble coalescence in a viscous fluids is established. The phase field method is used to capture the two-phase interface. The motion and coalescence of a pair of coaxial bubbles under an external uniform electric field and the effects of different electric field strengths on the interaction and coalescence of rising bubbles are studied. The results show that the uniform electric field accelerates the collision and coalescence process of double bubbles in the fluid, and increases the rising velocity of the coalesced bubble. The electric field with an intensity of E = 2 kV/mm is reduced about 2 times compared with that without electric field in coalescence time. When the electric field strength is strong (E ≥ 1 kV/mm), the coalesced bubble will rupture before it rises to the top of the calculation area, and the time of the bubble rupturing also decreases with the increase of the electric field strength. The phase field method is compared with the simulation results of Lattice Boltzmann Method (LBM), and the shape of bubble obtained by the two methods is in good agreement, which verifies the correctness of the calculation model.

Phase-field lattice Boltzmann method for the simulation of gas-liquid mass transfer

The free-energy lattice Boltzmann (LB) method is a multiphase LB approach based on the thermodynamic theory. Compared with traditional free-energy LB models, which employ a nonideal thermodynamic pressure tensor, the chemical-potential-based free-energy LB model has attracted much attention in recent years as it avoids computing the thermodynamic pressure tensor and its divergence. In this paper, we propose an improved wetting boundary condition for the chemical-potential-based free-energy LB model. Different from the original wetting boundary condition in the literature, the improved wetting boundary condition utilizes a surface chemical potential that is compatible with the chemical potential of the fluid domain. Accordingly, the thermodynamic consistency of the chemical-potential-based free-energy LB model can be retained by the improved wetting boundary condition. Numerical simulations are performed for droplets resting on flat and cylindrical surfaces with different contact angles. The numerical results show that the improved wetting boundary condition yields more reasonable results and the maximum spurious velocities are found to be smaller by 2 ∼ 3 orders of magnitude than those produced by the original wetting boundary condition.