BREAKUP OF MULTIPLE JETS IN IMMISCIBLE LIQUID-LIQUID SYSTEMS: A COMPUTATIONAL FLUID DYNAMICS STUDY

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1 BREAKUP OF MULTIPLE JETS IN IMMISCIBLE LIQUID-LIQUID SYSTEMS: A COMPUTATIONAL FLUID DYNAMICS STUDY Vishnu Pareek 1, Harisinh Parmar 1,Chi M. Phan 1, Geoffrey Evans 2, 1 Centre for Process Systems Computations, Curtin University, Perth, WA 6845, AUSTRALIA 2 Department of Chemical Engineering, University of Newcastle, University Drive Callaghan NSW 2308 Corresponding author s V.Pareek@exchange.curtin.edu.au ABSTRACT Hydrodynamic behavior of immiscible liquid-liquid systems has great importance in many industrial operations such as mining, food, cosmetics and pharmaceuticals industries. This behavior governs jet formation and breakup, droplet formation and coalescence in emulsification. For successful emulsion applications, it is very important to generate small and uniform droplets to ensure product stability. In addition, the breakup of the jet increases the interfacial area and hence enhances efficiency of processes such as heat transfer, mass transfer and sometimes chemical reactions. In this study, the formation of droplets from multiple circular nozzles into an immiscible liquid was studied using computational fluid dynamics (CFD). The unsteady motion of the interface separating two immiscible fluids is followed by solving the Navier Stokes equations for incompressible and Newtonian fluids with a volume of fluid (VOF) method. Most significantly, the interaction between neighboring jets was modelled for micro-jet condition. INTRODUCTION An emulsion is a mixture of two immiscible liquids where one liquid is dispersed in the form of small drops in another liquid that forms a continuous phase (Becher, 1965, Leal- Calderon et al., 2007). Emulsions are exceedingly important for a variety of applications such as macromolecular delivery (Degim and Çelebi, 2007, Okochi and Nakano, 2000, Vasiljevic et al., 2006), oil recovery (Huang and Varadaraj, 1996, Taylor and Hawkins, 1992), food processing (Muschiolik, 2007), hazardous material handling (Ouyang et al., 1995), mining explosives (Oxley, 1998), and cosmetics (Schramm, 2005). The presence of a surfactant is necessary for the long-term stability of emulsions: the surfactant molecules migrate to the liquid-liquid interface, inhibit droplet coalescence (Becher, 1965) and provide a better platform for some of the mentioned applications. Conventionally, emulsions are produced by mixers, in which droplets are formed by shear force. Recently, micro devices have been applied to produce emulsions with greater control and less energy consumption (Hessel et al., 2005). In an ideal emulsification process, smaller droplet size, higher flow-rate and multiple injections are desired to improve emulsion stability and production rate. Subsequently, the relationship of both droplet size and higher flow rate is critical for successful industrial application and hence creates an optimization possibility for micro-emulsification processes (Phan and Evans, 2008). Computational fluid

2 dynamics have been employed recently (Soleymani et al., 2008, Hua et al., 2007, Homma et al., 2006) for predicting hydrodynamic characteristics of liquid jet and resulting droplets in immiscible liquid-liquid systems. The breakup process of a viscous jet in another viscous liquid is an important phenomenon in fluid mechanics. Taylor (Taylor, 1934) observed that the jet of viscous fluid surrounded by another viscous fluid could be stable in a shear flow initially and become unstable and finally break up into a line of equally spaced small droplets. Tomotika (Tomotika, 1935, Tomotika, 1936) analyzed this phenomenon theoretically. He calculated the velocity field, considering linear theory, viscosity and interfacial tension of the both fluids, for the case of an infinitely long cylindrical jet in the presence of a small spatially periodic disturbance along the jet. His prediction of the droplet size, related to the viscosity ratio of the two fluids, was in good agreement with Taylor's (Taylor, 1934) experiments. Tomotika's linear theory was extended for the cases of a single jet in recent years. (Goldin et al., 1969, Stone et al., 1986, Bousfield et al., 1986, Stone and Leal, 1989). However, there is very little understanding of the influence of separating distance on the interaction between neighboring jets for micro-emulsification optimization. It this work, we have quantified the influence of the interaction between neighboring jets for two and three jets injected at the same time. BACKGROUND For a liquid jet (dispersed phase) moving within another liquid (continuous phase), the disturbance on the liquid/liquid surface can be described by following form: nt + iky δ t, y = δ e (1) ( ) i Where δ and δ i are the dynamic and initial magnitude of the disturbances, respectively; n is the growth rate of disturbance; and k is the wave number which is related to the wavelength, λ, by : k = 2 π / λ (2) The infinitesimal disturbances can either grow or decay depending on the system properties, including viscosities and densities of both liquids, interfacial tension, and jet radius, a. If there is a maximum value of n, then the corresponding disturbance would grow fastest and dominate jet breakup. This maximum value of n, which is denoted as n*, can be found by linear instability analysis. Consequently, the resultant droplet size can be calculated from the corresponding wave number. The linear analysis includes 3 steps: (i) determining the fluid motions caused the interfacial disturbances in both phases; (ii) matching the motions at the interface (stresses and velocities in both normal and tangent directions) to find the characteristic equation; and (iii) solving the characteristic equation to find n* (Phan and Evans, 2008). More recently, the interaction between interfacial waves of neighboring jets has been experimentally observed (Elemans et al., 1997) to follow either on-phase or out-of-phase 2

3 effects (Figure 1). Subsequently, a qualitative analysis (Knops et al., 2001) was carried out to describe dissipation between two interfacial disturbances and consequently predict the critical distance between jets. For engineering processes, the stationary jets are almost impractical. Instead, most industrial processes, such as micro reactors, employ moving jets (Hessel et al., 2005). In these cases, jet moving velocity is much higher than rotational and axial component of the thread velocity created by interfacial disturbance (v jet >> v r, v z ). Therefore, the approximation approach is no longer applicable. Most likely moving jets are broken up in the out-of-phase arrangement (Pennemann et al., 2005). It should be noted that the CFD simulation (Pennemann et al., 2005) was done for a single jet only and then mirroring for multiple jets. As the results, the jets are inherently in-phase and the jet-jet interaction was not included. In this work, computational fluid dynamics was employed to study moving multiple jets with higher velocity and interaction between these jets. Axial Velocity component (1) (2) (3) Radial Velocity components Out-of-phase phenomena Figure 1 Interaction between three jets on the basis of velocity field, showing off-phase relationship. COMPUTATIONAL MODEL Various methods are available for the dynamic characterization of free surfaces such as front tracking, level set, marker particles, shock capturing, smooth particle hydrodynamics, lattice Boltzmann and volume of fluid (VOF) (Gopala and van Wachem, 2008). The CFD software package Fluent (Fluent Inc., 2010) and VOF formulation was used to simulate the 3

4 formation and detachment of a glucose solution drop into a stationary continuous phase of canola oil. VOF has advantages in interface tracking over other approaches. It is also relatively simple and accurate to apply to the boundary fitted grids and accommodates breaking and forming of interfaces. Model Design The three-dimensional geometries of the column with two and three nozzles, and the meshes of the fluid volumes were generated using Gambit (Fluent Inc.). All circular nozzles have an inner diameter, D, of 1.6 mm and length of 10 mm. Half of the length (5 mm) is submerged into the continuous phase, which is connected to a rectangular column with a length (X), height (Z) and width (Y) of mm respectively (Figure 2 (a)). The physical properties of liquid/liquid system are tabulated in Table 1. The simulation conditions are described below: The entrances of three nozzles was defined as a velocity inlet The outflow from the column was defined as pressure outlet with gauge pressure equal to zero (in equilibrium with atmosphere) The side walls of the channels were defined as symmetry since the real channel used in the experimental study had a width of 300 mm All the other walls are assumed to be stationary with a no-slip boundary condition Distance between nozzles is 3.2 mm or 2D. (distance between 2 nozzle axes is 3D) Two systems are investigated: two and three jets (equally distanced) Numerical methods Transient simulations were carried out using Fluent (Fluent Inc.) to track the interface between the glucose solution drop and the continuous phase. The VOF model is a surfacetracking technique that is useful when studying the position of the interface between two immiscible fluids. A single set of momentum equations is shared by the fluids, and the volume fraction of each of the fluids in each computational cell is tracked throughout the domain. The flow was assumed to be incompressible laminar, dominated by the surface tension and viscous forces. The VOF model uses phase averaging to define the amount of continuous and dispersed phase in each cell. The PRESTO (pressure staggering option) scheme was used for pressure interpolation. The pressure-velocity coupling was done using the SIMPLE scheme. A second order upwind discretization was applied for the momentum equation. For interpolating the gas-liquid interface the geometric reconstruction scheme was used. An adequate time step (usually 1x 10-5 Seconds) was used to limit global Courant number to The results were considered to attain steady state and converged when global mass fluxes were balanced and all the residuals were maintained below QUICK scheme was used for volume fraction equation. A double precision solver was used to minimize truncation errors. The same flow rate (6 ml/min per channel) was used for all the simulations. 4

5 Velocity Inlet Dispersed phase 5mm 5 mm Z=100 mm Pressure (a) Fig. 2 Geometry and boundary setting of the model (b) Final Grid configuration which was used in simulation (b) 5

ρ d (kg/m 3 ) GRID SIZE SELECTION Tab. 1 Properties of Water-Canola oil system ρ c (kg/m 3 ) Grid size is critical in properly resolving distinct interfaces involving small dimensions.

6 ρ d (kg/m 3 ) GRID SIZE SELECTION Tab. 1 Properties of Water-Canola oil system ρ c (kg/m 3 ) Grid size is critical in properly resolving distinct interfaces involving small dimensions. In the VOF model at any given instance, a cell in the computational domain has either of three conditions; completely filled, completely empty or interface. Hence an initial estimate of the expected minimum bubble size or jet diameter must be made to decide the grid size. In order to study the effect of grid size three different grid configurations was compared and the final grid is shown in Figure 2 (b). Namely, a uniform grid of 1mm using map scheme was developed, thereafter a refinement was performed near the inlet regions of the three channels respectively. A rectangular cube of dimensions 2.4 mm wide, 2.4 mm deep and 100 mm height was meshed with uniform grid of 0.1 mm and aspect ratio with the largest grid size of 1mm was used in the remaining cross-section. The hexahedral mash type and Cooper type scheme was used in fine mesh areas. 1.8 million cells taken into simulation. The physics of the system do suggest the later refined grids would produce near to physical results. It was observed that the finest grid of the three configurations used, provided the smoothest interface tracking as expected. Thus, this configuration was chosen to carry out further investigations. RESULT AND DISCUSSION µ d (Pas) µ c (Pas) γ (N/m) (a) (b) Fig. 3 Velocity pattern of continuous and dispersed phase at nozzle exit (a) two jets (b) three jets 6

Jet interaction at nozzle opening For the two channels simulation, the simultaneous jets are moving slightly closer and remain on the same axis throughout the path of the jet.

7 Jet interaction at nozzle opening For the two channels simulation, the simultaneous jets are moving slightly closer and remain on the same axis throughout the path of the jet. The distance between jets before breakup was observed at 1.8 mm. "In-phase" mode observed initially but "out-of-phase" was observed after steady state (Fig 3 (a)) was reached. In case of three channels, the simultaneous velocity field in the cross section of the nozzle exit (inset) and volume fraction of dispersed and continuous phase and velocity pattern nozzle exit is shown in Fig 3 (b). Strong interactions between outer and middle jets cause outer jets to bend inward initially and then three jets remain parallel until breakup. The distance between these parallel jets is approximately 1.6 mm, i.e. ~ D. Breakup process of jets Breakup processes of two and three simultaneous jets were studied using 3 Dimensional VOF simulations and shown in Figure 4. An out-of-phase phenomenon is observed between two parallel jets. In case of three simultaneous jets, out-of-phase mode observed between middle and outer jets but in-phase mode observed for two outer jets. Adjacent jets observed radial component dominance and hence jet breakup experienced out-of-phase mode. As shown in Figure 5, velocity pattern at the time of droplet breakup suggest the radial component and axial component effect. Initially, axial velocity component is much higher than radial component due to moving jet velocity. However, near the breakup region (approximately 25 mm below nozzle exit), the radial component gets stronger and dominates jet breakup process. Such a high value of radial velocity demonstrated the linear instability analysis (Knops et al., 2001), which was based on small velocities, is not appropriate for this system. Fig. 4 Instantaneous volume fraction of dispersed phase (Water-glucose) in continuous phase (Canola oil) after: 3 s, 4.1 s and 5.6 s respectively. (All three images were taken as 25 mm below from nozzle exit) 7

8 Fig. 5. Velocity pattern of continuous and dispersed phase at drop formation process CONCLUSION AND SCOPE OF FURTHER STUDY Computational fluid dynamics simulations, solving the Navier Stokes equations with a volume of fluid and continuum surface methods were conducted to study the hydrodynamics of a liquid jet in another immiscible liquid and jet interaction in 2 jet and 3 jet system. For 2 jets, the simulations showed that jets move slightly closer initially and remains parallel until breaking up. For the 3 jets arrangement, stronger interaction was observed: the two outer jets moved further inward, with a smaller critical distance between jets. Jet breakup and droplet formation clearly observed in "out-of-phase" modes for both 2 and 3 jets simulations. The simulations also demonstrated a high variation between axial and radial components during breakup, which make the linear instability analysis inappropriate for these systems. The study highlights the jet interaction before and during jet breakup. Further studies are planned to quantify the influence of jet velocity and channel distance on the interaction, which are critical to for micro-devices design. These include (i) more realistic simulation domain to study pressure distribution at the channel inlets due to jet interaction at the other end and (ii) five and more jets to quantify the influence of outer jets. More significantly, experimental work will be employed to validate the phenomena predicted by the model. 8

9 REFERENCES (2010) Fluent User Manual, ANSYS BECHER, P Emulsions: theory and practice, Reinhold Pub. Corp. New York. BOUSFIELD, D., KEUNINGS, R., MARRUCCI, G. & DENN, M Nonlinear analysis of the surface tension driven breakup of viscoelastic filaments. Journal of Non-Newtonian Fluid Mechanics, 21, DEGIM, T. & ÇELEBI, N Controlled delivery of peptides and proteins. Current pharmaceutical design, 13, ELEMANS, P., VAN WUNNIK, J. & VAN DAM, R Development of morphology in blends of immiscible polymers. AIChE Journal, 43, GOLDIN, M., YERUSHALMI, J., PFEFFER, R. & SHINNAR, R Breakup of a laminar capillary jet of a viscoelastic fluid. Journal of Fluid Mechanics, 38, GOPALA, V. R. & VAN WACHEM, B. G. M Volume of fluid methods for immiscible-fluid and free-surface flows. Chemical Engineering Journal, 141, HESSEL, V., LÖWE, H. & SCHÖNFELD, F Micromixers - a review on passive and active mixing principles. Chemical Engineering Science, 60, HOMMA, S., KOGA, J., MATSUMOTO, S., SONG, M. & TRYGGVASON, G Breakup mode of an axisymmetric liquid jet injected into another immiscible liquid. Chemical Engineering Science, 61, HUA, J., ZHANG, B. & LOU, J Numerical simulation of microdroplet formation in coflowing immiscible liquids. AIChE Journal, 53, HUANG, J. S. & VARADARAJ, R Colloid and interface science in the oil industry. Current Opinion in Colloid & Interface Science, 1, KNOPS, Y. M. M., SLOT, J. J. M., ELEMANS, P. H. M. & BULTERS, M. J. H Simultaneous breakup of multiple viscous threads surrounded by viscous liquid. Aiche Journal, 47, LEAL-CALDERON, F., SCHMITT, V. & BIBETTE, J Emulsion science: basic principles, Springer Verlag. Berlin Germany. MUSCHIOLIK, G Multiple emulsions for food use. Current Opinion in Colloid & Interface Science, 12, OKOCHI, H. & NAKANO, M Preparation and evaluation of w/o/w type emulsions containing vancomycin. Advanced drug delivery reviews, 45, OUYANG, Y., MANSELL, R. & RHUE, R Emulsion-mediated transport of nonaqueous-phase liquid in porous media: a review. Critical reviews in environmental science and technology, 25, OXLEY, J. C The chemistry of explosives. Explosive Effects Appl, PENNEMANN, H., HARDT, S., HESSEL, V., LOEB, P. & WEISE, F Micromixer based liquid/liquid dispersion. Chemical Engineering & Technology, 28, PHAN, C. & EVANS, G Influence of Jet Velocity on Jet Breakup in Immiscible Liquid-Liquid Systems. Chemeca 2008: Towards a Sustainable Australasia,

10 SCHRAMM, L. L Emulsions, foams, and suspensions: fundamentals and applications, Vch Verlagsgesellschaft Mbh.Weinheim. SOLEYMANI, A., LAARI, A. & TURUNEN, I Simulation of drop formation in a single hole in solvent extraction using the volume-of-fluid method. Chemical Engineering Research and Design, 86, STONE, H., BENTLEY, B. & LEAL, L An experimental study of transient effects in the breakup of viscous drops. Journal of Fluid Mechanics, 173, STONE, H. & LEAL, L Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid. Journal of Fluid Mechanics, 198, TAYLOR, G The formation of emulsions in definable fields of flow. Proceedings of the Royal Society of London. Series A, 146, 501. TAYLOR, K. C. & HAWKINS, B. F Emulsions in enhanced oil recovery. Emulsions: Fundamentals and Applications in the Petroleum Industry, Schramm, LL (Ed.), American Chemical Society, Washington, DC, TOMOTIKA, S On the instability of a cylindrical thread of a viscous liquid surrounded by another viscous fluid. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 150, TOMOTIKA, S Breaking up of a Drop of Viscous Liquid Immersed in Another Viscous Fluid Which is Extending at a Uniform Rate. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 153, VASILJEVIC, D., PAROJCIC, J., PRIMORAC, M. & VULETA, G An investigation into the characteristics and drug release properties of multiple W/O/W emulsion systems containing low concentration of lipophilic polymeric emulsifier. International journal of pharmaceutics, 309, BRIEF BIOGRAPHY OF PRESENTER Mr. Harisinh Parmar is currently doing PhD project on jet emulsification in Curtin University. He finished his Masters by research in polymer rheology by research from RMIT, Melbourne. He published two journal and two conference paper during his masters by research and presented one paper in a conference. His PhD study includes experimental and CFD study of multiple jets in another immiscible liquid. Phase interaction and drop formation study is the main focus in this project. 10

CHAPTER 7 NUMERICAL MODELLING OF A SPIRAL HEAT EXCHANGER USING CFD TECHNIQUE

CHAPTER 7 NUMERICAL MODELLING OF A SPIRAL HEAT EXCHANGER USING CFD TECHNIQUE In this chapter, the governing equations for the proposed numerical model with discretisation methods are presented. Spiral