热泡式喷墨的建模与分析

喷墨过程的数值建模是建立在一维热传导公式,温度—压强关系式和能量、物质转换关系的平衡的基础上的。一维热传导公式用来考虑气泡和它周围液体之间的能量交换以及气—液交界层的温度分布。温度—压强关系式和能量转换关系用来考虑气泡的增长和破裂过程。气泡产生的初始温度、初始压强以及控制电压等参数都在本模型中进行分析,分析的结果为设计喷墨打印机提供了最基础的资料。     

热泡式喷墨的建模与分析

喷墨过程的数值建模是建立在一维热传导公式，温度-压强关系式和能量、物质转换关系的平衡的基础上的。一维热传导公式用来考虑气泡和它周围液体之间的能量交换以及气-液交界层的温度分布。温度-压强关系式和能量转换关系用来考虑气泡的增长和破裂过程。气泡产生的初始温度、初始压强以及控制电压等参数都在本模型中进行分析，分析的结果为设计喷墨打印机提供了最基础的资料。     

Numerical Simulation of the Evolution of a Gas Bubble in a Liquid Near a Wall

A numerical technique based on the application of the boundary element method is proposed for studying the axially symmetric dynamics of a bubble in a liquid near a solid wall. It is assumed that the liquid is ideally incompressible and its flow is potential. The process of expansion and contraction of a spheroidal bubble is considered, including the toroidal phase of its movement. The velocity and pressure fields in the liquid surrounding the bubble are evaluated along with the shape of the bubble surface and the velocity of its displacement. The numerical convergence of the algorithm with an increase in the number of boundary elements and a refinement of the time step is shown, and comparison with the experimental and numerical results of other authors is performed. The capabilities of the technique are illustrated by solving a problem of collapse of a spheroidal bubble in water. The bublle is located a short distance from the wall.     

Computations of Explosive Boiling in Microgravity

Dynamics of the explosive growth of a vapor bubble in microgravity is investigated by direct numerical simulation. A front tracking/finite difference technique is used to solve for the velocity and the temperature field in both phases and to account for inertia, viscosity, and surface deformation. The method is validated by comparison of the numerical results with the available analytical formulations such as the evaporation of a one-dimensional liquid/vapor interface, frequency of oscillations of capillary waves, and other numerical results. Evolution of a three-dimensional vapor nucleus during explosive boiling is followed and a fine scale structure similar to experimental results is observed. Two-dimensional simulations yield a similar qualitative instability growth.     

Numerical simulation of growth of a vapor bubble during flow boiling of water in a microchannel

The present study is performed to numerically analyze the growth of a vapor bubble during flow of water through a microchannel. The complete Navier–Stokes equations, along with continuity and energy equations, are solved using the SIMPLER (semi-implicit method for pressure-linked equations revised) method. The liquid–vapor interface is captured using the level set technique. The microchannel is 200-m square in cross-section and the bubble is placed at the center of the channel with superheated liquid around it. The results show steady initial bubble growth followed by a rapid axial expansion after the bubble fills the channel cross-section. A trapped liquid layer is observed between the bubble and the channel as it elongates. The bubble growth rate increased with the incoming liquid superheat, but decreased with Reynolds number. The formation of a vapor patch at the walls is found to be dependent on the time the bubble takes to fill up the channel. The upstream interface of the bubble is found to exhibit both forward and reverse movement during bubble growth. The results show little effect of gravity on the bubble growth rate under the specified conditions. The bubble growth features obtained from the numerical results are found to be qualitatively similar to experimental observations.     

Numerical simulation of radially converging shock waves in a bubble cavity

This paper presents a numerical technique investigating the final stage of focusing a radially converging nonspherical shock wave in the neighborhood of center of the axially symmetric cavitation bubble subjected to strong compression. Hydrodynamic model used includes liquid compressibility, heat conductivity of vapor and liquid, as well as evaporation and condensation on the interphase surface; the realistic wide-range equations of state are used. The calculation is performed on moving grids with explicit accentuation of the bubble surface. This technique is based on the TVD modification of the Godunov second order accuracy scheme in space and time. Its efficiency is due to an allowance for the special features of the problem in the final stage of focusing of nonspherical shock wave in the central part of the bubble. After the value of deformation of the shock exceeds the threshold (i.e., when the shock wave becomes largely nonspherical) in the central field of the bubble the curvilinear radially diverging grid is changed by the rectilinear oblique-angled grid close to Cartesian. At the same moment, the spherical immovable system of the reference frame is changed to a cylindrical system. The recalculation of the cell parameters from grid to grid is made by the method of conservative interpolation. The efficiency of the proposed approach is shown by the test problem’s calculation results and an illustrative example.     

Fabrication and testing of bubble powered micropumps using embedded microheater

A bubble-powered micropump which consists of a pair of nozzle-diffuser flow controller and a pumping chamber was fabricated and tested in this study. The two-parallel micro line heaters were fabricated to be embedded in the silicon dioxide layer above a silicon wafer which serves as a base plate for the micropump. A pumping chamber, a pair of nozzle-diffuser unit and microchannels including the liquid inlet and outlet port were fabricated by etching through another silicon wafer. A glass wafer having two holes of inlet and outlet ports of liquid serve as upper plate of the pump. Sequential photographs of bubble nucleation, growth and collapse were visualized by CCD camera. The liquid flow through the nozzle during the period of bubble growth and slight back flow of liquid at the collapse period can be clearly seen. The volume flow rate was found to be dependent on the duty ratio and the operation frequency. The volume flow rate decreases as the duty ratio increases in the micropump with either circular or square pumping chamber.     

Evolution of a small sphericity distortion of a vapor bubble during its supercompression

The possibility of using two models to study the evolution and maximum increase in amplitude of small distortions of sphericity of a bubble during its strong compression in a liquid is investigated. The investigation is performed in the conditions of experiments on acoustic cavitation of deuterated acetone. The first (fully hydrodynamic) model is based on the two-dimensional equations of gas dynamics. It is valid in every stage of the bubble compression. But its use takes up a lot of computational time. The second (simplified) model is derived by splitting the liquid and vapor motion into a spherical part and its small nonspherical perturbation. To describe the spherical component, a onedimensional version of the two-dimensional model is used in this model. The advantage of the simplified model over the full one is its much lower consumption of computational time. At the same time, the evolution of the nonspherical perturbation in this model is described by utilizing a number of assumptions, validity of which is justified only at the initial stage of the bubble compression. It is therefore logical to apply the simplified model at the initial low-speed stage of the bubble compression, while the full hydrodynamic one is applied at its final high-speed stage. It has been shown that such a combination allows one to significantly reduce the computational time. It has been found that the simplified model alone can be used to evaluate the maximum increase of the amplitude of small sphericity distortions of a bubble during its compression.     

Application of a one-fluid model for large scale homogeneous unsteady cavitation: The modified Schmidt model

It is found that the one-fluid cavitation model developed by Schmidt et al. [Schmidt DP, Rutland CJ, Corradini ML. A fully compressible, two-dimensional model of small, high speed, cavitating nozzles. Atomiz Sprays 1999;9:255–76] (Schmidt Model) does not work consistently when applied to simulate the unsteady transient cavitating flows with a large vapor to liquid density ratio or under the condition of a low surrounding pressure. In this work, the apparent difficulties of the Schmidt model are analyzed and a modified Schmidt model is proposed for greater robustness and consistency. The modified Schmidt model is then applied to study the creation, evolution and collapse of transient cavitation commonly observed in underwater explosions and industrial pipe flow. The model is firstly verified by simulating several cavitating flows where analytical, experimental or numerical results are available for comparison, and then applied to multi-dimensional transient cavitating flows generated by underwater explosions. The numerical results show that the modified Schmidt model can overcome the difficulties associated with the (original) Schmidt model and be applied to both small and large scale transient cavitating flows to predict the pressure surge caused by cavitation collapse regardless of the surrounding pressure.     

On the peculiar bubble formation,growth, and collapse behaviors in catalytic micro-motor systems

Bubbles often play a critical role in micro-systems involving Janus catalytic micro-motors (JCMs). Here, we examine some peculiar behaviors of the formation, growth, and collapse of the bubbles observed in recent experiments, in which JCM-laden droplets were dispensed on solid substrates and mixed with droplets of hydrogen peroxide solution. First, no oxygen bubble is visible near isolated JCMs when their size is smaller than a certain threshold, but bubbles can form and grow between a circular ring of small JCMs without touching any JCMs. Using analytical modeling and numerical simulations, we show that the lack of bubble formation near small, isolated JCMs originates from the low supersaturation of oxygen near their surface, which is caused by the efficient dissipation of oxygen molecules generated on their surface toward the bulk solution. In contrast, a cluster of small JCMs can collectively produce high enough oxygen supersaturation near the cluster to nucleate a bubble. Second, the radius of these bubbles grows following a power law of \(R \sim t^{0.7}\), rather than the typical \(R \sim t^{1/2}\) or \(R \sim t^{1/3}\) laws for the growth of bubbles driven by simple diffusion or direct gas injection into the bubble. Our numerical simulations showed that this anomalous growth law is a result of the cooperative action of the oxygen supersaturation-driven bubble growth and the mutual motion between the JCMs and the growing bubble. Finally, once a bubble grows to its maximal size, it collapses far more rapidly than the time scale expected for bubbles that contain non-condensable gas and exist in bulk liquids. Our scale analysis and numerical simulations show that this rapid collapse can be explained by the coalescence of the bubble with the air–liquid interface of the liquid film.     

Lattice Boltzmann modeling of dendritic growth in forced and natural convection

A two-dimensional (2D) coupled model is developed for the simulation of dendritic growth during alloy solidification in the presence of forced and natural convection. Instead of conventional continuum-based Navier–Stokes (NS) solvers, the present model adopts a kinetic-based lattice Boltzmann method (LBM), which describes flow dynamics by the evolution of distribution functions of moving pseudo-particles, for the numerical computations of flow dynamics as well as thermal and solutal transport. The dendritic growth is modeled using a solutal equilibrium approach previously proposed by Zhu and Stefanescu (ZS), in which the evolution of the solid/liquid interface is driven by the difference between the local equilibrium composition and the local actual liquid composition. The local equilibrium composition is calculated from the local temperature and curvature. The local temperature and actual liquid composition, controlled by both diffusion and convection, are obtained by solving the LB equations using the lattice Bhatnagar–Gross–Krook (LBGK) scheme. Detailed model validation is performed by comparing the simulations with analytical predictions, which demonstrates the quantitative capability of the proposed model. Furthermore, the convective dendritic growth features predicted by the present model are compared with those obtained from the Zhu–Stefanescu and Navier–Stokes (ZS–NS) model, in which the fluid flow is calculated using an NS solver. It is found that the evolution of the solid fraction of dendritic growth calculated by both models coincides well. However, the present model has the significant advantages of numerical stability and computational efficiency for the simulation of dendritic growth with melt convection.     

Simulation of bubbles

We present a novel framework based on a continuous fluid simulator for general simulation of realistic bubbles, with which we can handle as many significant dynamic bubble effects as possible. To capture a very thin liquid film of bubbles, we have developed a regional level set method allowing multi-manifold interface tracking. Based on the definitions of regional distance and its five operators, the implementation of the regional level set method is very easy. An implicit surface of liquid film with arbitrary thickness can be reconstructed from the regional level set function. To overcome the numerical instability problem, we exploit a new semi-implicit surface tension model which is unconditionally stable and makes the simulation of surface tension dominated phenomena much more efficient. An approximated film thickness evolution model is proposed to control the bubble’s lifecycle. All these new techniques combine into a general framework that can produce various realistic dynamic effects of bubbles.     

Unsteady development of a deformable bubble rising in a quiescent liquid

An accurate finite-volume based numerical method for the simulation of an isothermal two-phase flow, consisting of a rising deformable bubble translating in a quiescent, unbounded liquid, is presented. This direct simulation method is built on a sharp interface concept and developed on an Eulerian, Cartesian fixed-grid with a cut-cell scheme and marker points to track the moving interface. The unsteady Navier–Stokes equations in both liquid and gas phases are solved separately. The mass continuity and momentum flux conditions are explicitly matched at the true surface phase boundary to determine the evolving interface shape and movement of the bubble. The highlights of this method are that it utilizes a combined Eulerian–Lagrangian approach, and is capable of treating the interface as a sharp discontinuity. A fixed underlying grid is used to represent the control volume. The interface, however, is denoted by a separate set of marker particles which move along with the interface. A quadratic curve fitting algorithm with marker points is used to yield smooth and accurate information of the interface curvatures. This numerical scheme can handle a wide range of density and viscosity ratios. The bubble is assumed to be spherical and at rest initially, but deforms as it rises through the liquid pool due to buoyancy. Additionally, the flow is assumed to be axisymmetric and incompressible. The bubble deformation and dynamic motion are characterized by the Reynolds number, the Weber number, the density ratio and the viscosity ratio. The effects of these parameters on the translational bubble dynamics and shape are given and the physical mechanisms are explained and discussed. Results for the shape, velocity profile and various forces acting on the bubble are presented here as a function of time until the bubble reaches terminal velocity. The range of Reynolds numbers investigated is 1 < Re < 100, and that of Weber number is 1 < We < 10.     

Modeling strong compression of a gas bubble in fluid

A technique for calculating strong adiabatic compression of a gas bubble in fluid is proposed. The compression results from the pressure applied to the outer surface of the fluid. The motion of the fluid and gas is described by two-dimensional dynamic equations of compressed fluid and gas with realistic equations of its state. The effects of viscosity and thermal conductivity are not allowed for. The bubble surface is defined as a contact interface where there is a surface tension. Coupled Euler-Lagrange coordinates are used, with the bubble surface serving as a coordinate system. A spherical system of coordinates is used as a fixed reference. Equations of gas and fluid dynamics are solved by Godunov’s equations with second-order accuracy in space and time. The economic feasibility of the technique is illustrated by some model problems. The proposed method has been proven to be much more efficient than the classic first-order-approximation Godunov’s schemes traditionally used in solving problems of a highly compressed bubble. One of the scenarios is used to show the influence of slight spherical-shape distortions of the bubble on the evolution of the radially converged shock wave resulting from the strong compression.     

A multiphase compressible model for the simulation of multiphase flows

A compressible model able to manage incompressible two-phase flows as well as compressible motions is proposed. After a presentation of the multiphase compressible concept, the new model and related numerical methods are detailed on fixed structured grids. The presented model is a 1-fluid model with a reformulated mass conservation equation which takes into account the effects of compressibility. The coupling between pressure and flow velocity is ensured by introducing mass conservation terms in the momentum and energy equations. The numerical model is then validated with four test cases involving the compression of an air bubble by water, the liquid injection in a closed cavity filled with air, a bubble subjected to an ultrasound field and finally the oscillations of a deformed air bubble in melted steel. The numerical results are compared with analytical results and convergence orders in space are provided.     

Nonlinear radial oscillations and spatial translations of a nonspherical gas bubble in a liquid

A mathematical model of dynamics of a gas bubble in a liquid with non-small distortions of its spherical shape has been developed, with allowing for the spatial translations of the bubble, as well as the influence of the gravitational force and the liquid velocity. The liquid viscosity and compressibility are taken into account approximately. It has been shown that in some particular cases the derived equations are coincident with those obtained by the other authors. Some results of solving the problem of oscillations of a moving nonspherical bubble under periodic variation of liquid pressure are presented.     

Numerical investigation of formation and dissolution of CO<Subscript>2</Subscript> bubbles within silicone oil in a cross-junction microchannel

In this paper, a numerical investigation is conducted to study the formation and dissolution process of CO₂ bubbles within silicone oil in a cross-junction microchannel. A coupled multiphase–multicomponent computational fluid dynamics model based on the volume-of-fluid method is used, which is able to capture the physics of the multiphase bubble formation, dissolution mass transfer, and the tracking of the dissolved CO₂ species. The computational model is firstly validated with experimental results where good agreement is attained. Next, the model is used to investigate the bubble formation process at the cross-junction in the presence of dissolution and also the bubble evolution as it is transported along the downstream channel. It is revealed that during bubble formation, there is a high concentration of CO₂ solute around the cross-junction walls, as silicone oil flow to this region is minimal. As the CO₂ bubble travels downstream, the transport of the CO₂ solute is largely driven by the local flow currents of the silicone oil within the vicinity of the bubble. An extensive parametric study is also conducted, looking at the effects of varying the surface tension, diffusion coefficient and flow rates. The results demonstrate that the initial CO₂ bubble length and period of bubble formation are most affected by the flow rate, while the mass transfer is most strongly governed by the diffusion coefficient.     

Computation of incompressible bubble dynamics with a stabilized finite element level set method

This paper presents a stabilized finite element method for the three dimensional computation of incompressible bubble dynamics using a level set method. The interface between the two phases is resolved using the level set approach developed by Sethian [Level Set Methods and Fast Marching Methods, Cambridge University Press, 1999], Sussman et al. [J. Comput. Phys. 114 (1994) 146], and Sussman et al. [J. Comput. Phys. 148 (1999) 81–124]. In this approach the interface is represented as a zero level set of a smooth function. The streamline-upwind/Petrov–Galerkin method was used to discretize the governing flow and level set equations. The continuum surface force (CSF) model proposed by Brackbill et al. [J. Comput. Phys. 100 (1992) 335–354] was applied in order to account for surface tension effects. To restrict the interface from moving while re-distancing, an improved re-distancing scheme proposed in the finite difference context [J. Comput. Phys. 148 (1999) 81–124] is adapted for finite element discretization. This enables us to accurately compute the flows with large density and viscosity differences, as well as surface tension. The capability of the resultant algorithm is demonstrated with two and three dimensional numerical examples of a single bubble rising through a quiescent liquid, and two bubble coalescence.     

Research on a large power thermal bubble micro-ejector with induction heating

The present study investigates a large power thermal bubble micro-ejector with induction heating device. The traditional thermal-bubble ejectors adopted resistors as the heating resources, it can only work with lower power and convey liquid with lower flow rate. Induction heating devices are adopted to replace the resistor for heating liquid in this paper. With this heating method, there is no physical contact between the heating core and the external power supply circuit. The liquid in the chamber of micro-ejector is heated by the induction heating device and changes from liquid phase to gas phase, generating vapor bubbles in the micro chamber of the micro ejector. The bubble expands rapidly and ejects droplets through the nozzle. The prototype of the micro-ejector is fabricated and experiments are carried out. Continuous droplets are ejected out from the nozzle as the applied AC current is 0.6–0.65 A with the power frequency of 100 kHz. The total volume of the continuous droplets is ranging from 18.84 to 49.87 nL, and the corresponding flow rate is about 0.52–1.36 μL/min. Furthermore, this new micro-ejector can be adopted in conveying of micro-scale liquid, the injection of trace drugs and the 3D printing.     

Simulation of bubble-bubble interaction using a lattice Boltzmann method

This paper presents the results obtained from three-dimensional numerical simulations of multiple bubbles rising under buoyancy in a quiescent viscous incompressible fluid. A lattice Boltzmann method, based on the free-energy model, is developed to simulate the behavior of bubble-bubble interaction while rising in the fluid. A new scheme, which involves eighteen lattice points for the first and second derivative, is proposed to achieve stable computations at high fluid-to-bubble density ratio. The effects of the density ratio and the initial bubble configuration on the flow field induced by rising bubbles and on the evolution of bubble shape during their coalescence are investigated. It is found that for two rising bubbles with the same size, the leading bubble rises like an isolated bubble before coalescence. The trailing bubble is entrained by the leading one, and experiences obvious deformation when it enters the wake region of the leading bubble. The shape evolution of the trailing bubble is different at the high and low density ratios. However, for two rising bubbles with different sizes, the larger bubble always has strong effect on the smaller one in any initial configuration.