Numerical study of a liquid/liquid slug flow in a micro-reactor

The great advantages of micro–reactors are associated with an extremely high surface–to–volume ratio. Hence, micro–reactors permit promising operating conditions, such as almost perfect heat or mass transfer. The hydrodynamics of a liquid/liquid slug flow in a micro–channel is characterized by complex vortex structures in both the disperse and the continuous phase. The disperse phase, in our investigations, is not wetting the walls and, thus, a thin film of the continuous phase persists between the disperse phase and the wall. Due to this phenomenon, a relative movement between disperse and continuous phase is possible and, indeed, observed. Understanding of these complex phenomena allows for a control of the hydrodynamics, and thus, to tailor the heat and mass transport in a desired manner. To study the physics of this complex liquid/liquid system, a modified level–set method in conjunction with an immersed–boundary formulation is engaged. The mesh resolution represents a challenge, as the spatial resolution has to resolve the thin film between the disperse phase and the wall adequately. All simulations are implemented within the software OpenFOAM. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of mass transfer in liquid/liquid slug flow

The mass transport for a liquid/liquid extraction system is examined using a numerical concept following the idea of the interface-tracking method. Separate, body-fitted, static computational domains are arranged around an imported steady-state interface topology. The domains are coupled at the free interface to capture the behaviour of the conjugated system. The steady-state hydrodynamics are the basis for the simulation of the transient mass transport, which is calculated as a passive scalar concentration or one-way coupling. The investigation is restricted to the extraction from the disperse to the continuous phase. Simulation results for an extraction from the disperse to the continuous phase show that most of the mass is transferred through the wall-film region into the continuous phase. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of van der Waals force with smoothed particle hydrodynamics: Application to the rupture of thin liquid films

The rupture of thin liquid films driven by the van der Waals force is of significance in many engineering processes, and most previous studies have relied on the lubrication approximation. In this paper, we develop a smoothed particle hydrodynamics (SPH) representation for the van der Waals force and simulate the rupture of thin liquid films without resort to lubrication theory. The van der Waals force in SPH is only imposed on one layer, i.e., the outermost layer of fluid particles, where a weighting function is deployed to evaluate the contributions of particles on or near the interface. However, to obtain an accurate hydrostatic pressure in reaction to the van der Waals force, a smaller smoothing length is used for the calculation of the weighting function than that used for SPH discretizations of the bulk fluid. The same surface particles are also used to model the surface tension. To deal with the rupture of a thin liquid film with a very small aspect ratio ε (ε = thickness/length), a coordinate transformation is introduced to shrink the length of the liquid film to achieve accurate numerical resolution with a manageable number of particles. As verifications of our physical model and numerical algorithm, we simulate the hydrostatic pressure in a stationary film and the relaxation of an initially square droplet and compare the SPH results with the analytical solutions. The method is then applied to simulate the rupture of thin liquid films with moderate and small aspect ratios (ε = 0.5 and 0.005). The convergence of the method is verified by refining particle spacing to four different levels. The effect of the capillary number on the rupture process is analyzed.     

Marangoni-driven liquid films rising out of a meniscus onto a nearly-horizontal substrate

We revisit the situation of a thin liquid film driven up an inclined substrate by a thermally induced Marangoni shear stress against the opposing parallel component of gravity. In contrast to previous studies, we focus here on the meniscus region, in a case where the substrate is nearly horizontal. Our numerical simulations show that the time-dependent lubrication model for the film profile can reach a steady state in the meniscus region that is unlike the monotonic solutions investigated earlier. A systematic investigation of the steady states of the lubrication model is carried out by studying the phase space of the corresponding third-order ODE system. We find a rich structure of the phase space including multiple non-monotonic solutions with the same far-field film thickness. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite-amplitude long-wave instability of Bingham liquid films

The long-wave perturbation method is employed to investigate the weakly nonlinear hydrodynamic stability of a thin Bingham liquid film flowing down a vertical wall. The normal mode approach is first used to compute the linear stability solution for the film flow. The method of multiple scales is then used to obtain the weak nonlinear dynamics of the film flow for stability analysis. It is shown that the necessary condition for the existence of such a solution is governed by the Ginzburg–Landau equation. The modeling results indicate that both the subcritical instability and supercritical stability conditions can possibly occur in a Bingham liquid film flow system. For the film flow in stable states, the larger the value of the yield stress, the higher the stability of the liquid film. However, the flow becomes somewhat unstable in unstable states as the value of the yield stress increases.     

Gas bubbles in micro capillaries – hydrodynamics and mass transfer

Process design of multi-phase unit operations on the micro-scale relies on the detailed knowledge of the hydrodynamics and mass transfer behavior of discrete disperse fluid particles. The present work examines the hydrodynamics and mass transfer of gas bubbles in vertical capillaries. The hydrodynamic behavior of a single bubble in a capillary including is examined numerically using a modified level-set method [1]. Additionally, the influence of surface-active contaminations (‘surfactants’) and the resulting Marangoni effects are taken into account [2]. This enables the differentiation between bubbles with a mobile, i.e. clean, interface and those with a immobile, i.e. contaminated, interface. Based on the hydrodynamics, the mass transfer is examined. In the present work, mass transfer is from the bubble into the bulk fluid. By using a very high mesh resolution, the local concentration field in and around the gas bubble can be resolved, which gives access to the local mass transfer. Results are in good agreement available correlations from literature. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

New asymptotic heat transfer model in thin liquid films

In this article, we present a model of heat transfer occurring through a liquid film flowing down a vertical wall. This new model is formally derived using the method of asymptotic expansions by introducing appropriately chosen dimensionless variables. In our study the small parameter, known as the film parameter, is chosen as the ratio of the flow depth to the characteristic wavelength. A new Nusselt solution is obtained, taking into account the hydrodynamic free surface variations and the contributions of the higher order terms coming from temperature variation effects. Comparisons are made with numerical solutions of the full Fourier equations in a steady state frame. The flow and heat transfer are coupled through Marangoni and temperature dependent viscosity effects. Even if these effects have been considered separately before, here a fully coupled model is proposed. Another novelty consists in the asymptotic approach in contrast to the weighted residual approach which have been formerly applied to these problems.     

Computational modelling of slug flow in a capillary microreactor

The benefits of slug flow capillary microreactor exhibit the ability to adjust two individual transport mechanisms, i.e., convection inside the slug and diffusion between two consecutive slugs. The mass transfer rate is enhanced by internal circulation, which arises due to the shear between slug axis and continuous phase or capillary wall. The knowledge of circulation patterns within the slug plays an important role in the design of a capillary microreactor. Apart from this, well defined slug flow generation is a key activity in the development of methodology to study hydrodynamics and mass transfer. In the present paper we discuss computational fluid dynamics (CFD) modelling aspects of internal circulations (single phase) and slug flow generation (two-phase).     

Rheological effect on thermocapillary flow of a liquid film jet painted on a moving boundary

In the present paper, a liquid (or melt) film of relatively high temperature ejected from a vessel and painted on the moving solid film is analyzed by using the second-order fluid model of the non-Newtonian fluid. The thermocapillary flow driven by the temperature gradient on the free surface of a Newtonian liquid film was discussed before. The effect of rheological fluid on thermocapillary flow is considered in the present paper. The analysis is based on the approximations of lubrication theory and perturbation theory. The equation of liquid height and the process of thermal hydrodynamics of the non-Newtonian liquid film are obtained, and the case of weak effect of the rheological fluid is solved in detail.     

Stability of liquid films adjacent to compressible streams

An analysis is presented for the linear stability of a liquid film, adjacent to a compressible viscous gas stream. The analysis is valid for all wavelengths and liquid Reynolds numbers. The pressure and shear perturbations exerted by the gas on the liquid are calculated, using a gas model which takes into account the gas viscosity, velocity profile, and heat transfer. The results show that an inviscid, uniform stream model for the gas is inadequate unless the disturbed boundary layer is very thin. Although the present linear analysis is in fairly good agreement with the experimental observations for subsonic flow, it does not predict the observed wavelengths and wave speeds for supersonic flow.     

Numerical simulation of ice formation in a reservoir

The one-dimensional formulation is considered of a two-phase Stefan problem of heat flow with an unknown phase transition temperature that depends on the concentration of impurity. A numerical method is described for implementing the constraints that the heat and mass conservation are given on the unknown nonstationary boundary between the liquid and solid phases. Some examples are included of simulations for the sodium chloride solutions of different concentrations.     

Dynamic simulation on the preparation process of thin films by pulsed laser

An ablation model of targets irradiated by pulsed laser is established. By using the simple energy balance conditions, the relationship between ablation surface location and time is derived. By an adiabatic approximation, the continuous-temperature condition, energy conservation and all boundary conditions can be established. By applying the analytical method and integral-approximation method, the solid and liquid phase temperature distributions are obtained and found to be a function of time and location. The interface of solid and liquid phase is also derived. The results are compared with the other published data. In addition, the dynamics process of pulsed laser deposition of KTN (Kta_0.65Nb_0.35O₃) thin film is simulated in detail by using fluid dynamics theory. By combining the expression of the target ablation ratio and the dynamic equation and by using the experimental data, the effects of laser action parameters on the thickness distribution of thin film and on the thin film component characteristics are discussed. The results are in good agreement with the experimental data.     

Mathematical Modeling and Simulation of Antibubble Dynamics

In this study, we propose a mathematical model and perform numerical simulations for the antibubble dynamics. An antibubble is a droplet of liquid surrounded by a thin film of a lighter liquid, which is also in a heavier surrounding fluid. The model is based on a phase-field method using a conservative Allen-Cahn equation with a space-time dependent Lagrange multiplier and a modified Navier-Stokes equation. In this model, the inner fluid, middle fluid and outer fluid locate in specific diffusive layer regions according to specific phase filed (order parameter) values. If we represent the antibubble with conventional binary or ternary phase-field models, then it is difficult to have stable thin film. However, the proposed approach can prevent nonphysical breakup of fluid film during the simulation. Various numerical tests are performed to verify the efficiency of the proposed model.     

Heat and mass transfer in liquid desiccant air-conditioning process at low flow conditions

This paper investigates the transient heat and mass transfer in liquid desiccant air-conditioning process at low flow conditions. Using local volumetric average approach, one-dimensional non-equilibrium heat and mass transfer models are developed to describe the humid air and liquid desiccant interaction at counter flow configuration. Using triethylene glycol solution as desiccant, some experimental studies are completed. Experimental results are used to justify the numerical models. Numerical results are then obtained to demonstrate process characteristics. The models include a transient desiccant flow model for initial liquid desiccant building-up process, empirical wetted specific surface ratio for mass transfer, and heat and mass transfer coefficients. The objective of this research is to develop a process analytical tool for liquid desiccant air-conditioner design.     

Impact of the regularity of the sediment bed on bed-load transport

The present study analyzes the impact of regularly arranged sediment bed on the particle clustering by introducing an artificial non-uniformity in the particle packing. Two simulations only differing in their sediment bed configuration are reported with the non-uniform roughness created through a random vertical displacement of the fixed particles constituting the rough wall. It is found that the irregular roughness enhances particle clustering as well as bed-load transport compared to the case of uniform roughness. As a result the statistics of disperse and continuous phase are markedly different. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computed oscillations of a confined submerged liquid jet

The jet oscillation observed in thin slab continuous casting is studied numerically by modelling the flow of liquid injected through a submerged entry nozzle and into a cavity. The oscillation relies on the exchange of fluid between recirculation cells on each side of the jet via a cross-flow through the gap between the nozzle shaft and the broad face of the cavity wall. Features of the oscillating jet are investigated by varying the resistance to cross-flow. This resistance occurs naturally since the nozzle obstructs cross-flow. The predicted oscillation can be manipulated by altering the cross-flow (through the use of an effective resistance force in the model) or stopped altogether to form a static asymmetrical flow pattern. Flow calculations are performed using a transient, two-dimensional, turbulent, fluid flow model.     

Features of the behavior of a liquid film heated from above and placed over deep liquid

The features of rupture occurring in a liquid film lying on deep liquid are studied. A thermal load applied to the film free surface leads to its deformation and rupture. The process is studied using a mathematical model describing the motion of a thin viscous nonisothermal liquid layer. The model is based on the two-dimensional Navier-Stokes equations. To solve them, the boundary conditions on the film-gas and film-liquid interfaces are written in explicit form. The effect of the thermal load on the film rupture is analyzed numerically depending on the Marangoni number and the stresses on the film-liquid interface. The results of solving model problems are presented.     

Numerical investigation of impinging gas jets onto deformable liquid layers

Impinging jets over liquid surfaces are a common practice in the metallurgy and chemical industries. This paper presents a numerical study of the fluid dynamics involved in this kind of processes. URANS simulations are performed using the volume of fluid (VOF) method to deal with the multiphase physics. This unsteady approach with the appropriate computational domain allows resolution of the big eddies responsible for the low frequency phenomena. The solver we used is based on the finite volume method and turbulence is modelled with the realisable k-? model. Two different configurations belonging to the dimpling and splashing modes are under consideration. The results are compared with PIV and LeDaR experimental data previously obtained by the authors. Attention is focused on the surroundings of the impingement, where the interaction between jet and liquid film is much stronger. Finally, frequency analysis is carried out to study the flapping motion of the jet and cavity oscillations.     

Transient film profile of thin liquid film flow on a stretching surface

In this paper we have studied a non-planar thin liquid film flow on a planar stretching surface. The stretching surface is assumed to stretch impulsively from rest and the effect of inertia of the liquid is considered. Equations describing the laminar flow on the stretching surface are solved analytically. It is observed that faster stretching causes quicker thinning of the film on the stretching surface. Velocity distribution in the liquid film and the transient film profile as functions of time are obtained.     

Theoretical model for swirling thin film flows inside nozzles with converging-diverging shapes

A quasi-one-dimensional model was developed to describe a swirling, thin, liquid film inside nozzles with different wall profiles. The model quantifies the effects of swirl strength, initial film thickness, and Reynolds and Weber numbers on the film thickness along the nozzle surface. Moreover, the model allows for a rapid (at least, qualitative) evaluation of different effects, e.g. of the swirl strength and nozzle geometry, and can serve as a benchmark case for the subsequent more involved numerical simulations. Steady-state solutions are presented as a function of various parameters. The effect of the nozzle geometry on film thickness is explored. As swirling flow entered the expanding (diverging) section of the nozzle, film thickness decreased to satisfy continuity (to conserve mass). Conversely, film thickness increased upon entering the contracting (converging) region of the nozzle. Geometric effects controlled film thicknesses much more than other flow parameters. This quasi-one-dimensional model for a swirling thin film can be useful for designing a swirl jet used in various industrial applications.