International Journal of Fluid Mechanics Research, Vol. 43, No. 1, 2016
Numerical and Experimental Investigation of Fluidic Microdrops Manipulation by Fluidic Mono-Stable Oscillator
†T. Chekifi∗, B. Dennai, R. Khelfaoui,andA. Maazouzi Laboratory ENERGARID, University of Bechar B. P. 417, route de Kenadsa, 08000 Bechar, Algeria
∗E-mail: chekifi.tawfiq@gmail.com
A numerical and experimental study of passive microdrops manipulation has been presented. This paper focuses on the modeling of micro-oscillators systems which are composed by passive amplifier without moving part. The characteristic size of the channels is generally about35µmof depth. The numerical results indi- cate that the production and manipulation of microdrops are possible with passive device within a typical oscillators chamber of2.25 mmdiameter and0.20 mm length when the Reynolds number isRe = 490. The novel microdrops method that is presented in this study provides a simple solution about the production of microdrops problems in micro system. We undertake an experimental step. The first part is based on realization of sample oscillator; the second part is consisted of visualization of the microdrops production and its manipulation.
* * * Nomenclature f frequency [Hz];
ts switching time [s];
tt transmission time [s];
lb loop length [m];
LO outlet length [m];
γ constant of gas 1.4 of air;
T temperature [K];
q mass flow [kg/(s·m)];
∆t time steep [s];
Re Reynolds number;
Ca Capillary number;
We Weber number.
†Received 14.04.2015
Introduction
In the biochemical areas, the reactions are performed in bio-MEMS require production of microdrops. There has been an increasing interest among both biologists and researchers at the medicinal laboratories in the study of mixtures on a metric and micro scale [1]. In the context of the MEMS, a numerical study on static micro oscillators and the possible prospects for technical adapted solution of micro systems have been presented. Micro device can be classified under two categories, passive and active. Where external perturbations are introduced in active microdrops to enhance geometrical form, the process in passive oscillators completely relies on multiphase. The behavioural study of the micro flow oscillators enables the prediction of the state of the drops and the efficiency of device.
The characteristic size of the channels is generally about a few tens of microns. This minia- turization involves series of fundamental problems related to the mechanical fluid. Indeed, at these scales, the fluidic flows are laminar [2].
The working principle of this device consists of disturbing the flow of jets moving along the principal channel by flow oscillations generated by three pairs of lateral canals. The device is called micro injector.
In these cases, the oscillators use special designed geometric configurations, identified by the absence of moving parts, to create an environment where self-induced, sustained oscillations will occur [3,4], they can be used as flow meters. A novel fluidic oscillator has been developed and tested by V. Tesar, (subject) makes these oscillators attractive as micro reactor injection application. A fast microdrop is essential in many operations that are employed in biochemical analysis, administration of drugs, and also other biological processes involving handling of cells and enzymatic reactions, which occur in pharmaceutical products. When transverse-sectional dimensions of channel are approximately ten micrometers, the molecular diffusion can facilitate mixing of two fluids in few seconds. However, when dimensions are approximately hundred micrometers, a micro-mixer-based molecular diffusion can facilitate mixing in ten seconds [2]. The literature describes significant number of devices that have been designed to improve the microdrops on a nanometric scale [4–7].
In this work, two-dimensional geometrical models were generated by GAMBIT and the sim- ulations were performed with FLUENT 6.3 in CFD software to model microdrops production in the fluidic oscillator configuration. The interface was tracked by using the volume of fluid (VOF) method.
1. Description of the Geometrical Model
The working principle of the fluidic oscillator device consists in disturbing the flow of jets issuing from a nozzle and expanding between two curved walls will attach to the less curved one or to the wall which is closer from the jet axis, which leads it to oscillate and flow into feedback channel. The device is also called micro injector, also they can be used as flowmeters where recent advances in computational fluid dynamics (CFD) methods have made it possible to simulate the effect of active flow control devices on major aircraft components. we reuse our results, presented at the ASME 2010 congress, simulation results of air flow in an oscillator geometry without second feedback Fig. 1, it is a configuration with one injector only with events for every injector, that dimension is(32.24×10.6) mm. The output orifice size is equal to0.50 mm[9].
With a plane oscillator of constant depth made with a square tube. Such plane oscillators are simulated by a fully CFD approach.
Fig. 1.Fluidic oscillator injection mixer system, initial configuration of first case [9].
2. VOF Method for Microdrops Production
Modeling and simulation offer an important complimentary means to understand droplet dy- namics and optimize device design and operation.
The interface tracking method is a sharp interface approach, in which the interfaces are assumed to be infinitely thin, i. e., zero thickness. A set of governing equation are applied to each phase or component, and the interfacial conditions are used as boundary. Through iteration; the velocity of the interface is defined, and the interface then moves to a new location ready for the next time step.
By this manner, the computation continues, and the interface is exactly tracked. This approach can provide very accurate results for cases without sever topological changes, and it forms the foun- dation of the front tracking methods. However, such an approach encounters singularity problems when significant topological changes (e. g., breakup and coalescence of droplets) occur. In these situations, artificial treatments or ad hoc criteria are required.
The VOF (volume of fluid) method uses the volume fraction of one fluid phase or component (denoted asC) to characterize the interface (here, we refer to two immiscible fluids). In the bulk phase (i. e., a pure fluid),Cis equal to zero or unity; in multi-fluid computational cells,0< C <1.
In general, the VOF model uses phase averaging to define the amount of continuous and dispersed phase in each cell. A variable,α, was defined as [10]:
• α= 1when the cell is100 %filled with continuous phase
• α= 0when the cell is100 %filled with dispersed phase
• 0< α <1when the cell contains an interface between the two phases.
The density ρ, and viscosityµ, for both phases (water and gasoil) can be calculated using a lin- ear dependence: The subscript “1” is chosen for the continuous liquid (primary) phase, while the subscript “2” for the discrete phase (microdrops)
ρ=ρ1α+ρ2(1−α), (1)
µ=µ1α+µ2(1−α). (2)
There are several different VOF algorithms with different accuracies and complexities in CFD.
The geometric reconstruction scheme used in this study is based on the work of Youngs [11] and further described by [12]. This scheme permits a piecewise-linear approach, which assumes that the interface has a linear slope within each cell, and the position of the interface is calculated from the volume fraction and its derivatives in the cell. The solutions of the velocity field and pressure are calculated using a body-force-weighted discretization scheme for the pressure and the Pressure- Implicit with Splitting of Operators (PISO) scheme for the pressure velocity.
The body-force-weighted scheme is used since it works well with the VOF model, and the PISO scheme is chosen to improve the efficiency of the calculation of the momentum balance after the pressure correction equation is solved.
The CFD software was used to simulate the flow of oil microdrops into a fluidic oscillator. it uses a control-volume-based technique to convert the governing equations into algebraic equations that can then be solved numerically. The governing equations are the mass conservation equation for each phase and the momentum equation:
∂C
∂t +u∇C= 0, (3)
where the velocity is given byu. In addition, a single momentum equation is used for the mixture of two-phase-fluid. The momentum equation hence is described by:
∂
∂t(ρu) +∇ ·(ρuu) +∇u· ∇[µ] =−∇P+F, (4) whereF =σκ(x)nis the surface tension force,κis the curvature of the interface,nis a unit vector normal to the interface,σis the surface tension coefficient
The main corresponding dimensionless number is the Capillary number which compares sur- face tension forces with viscous forces.
Ca = νu
σ , (5)
where the viscosity of continuum phase is usually used, generating uniform droplets is an important step of achieving microdroplet functionalities. Using pressure as driving force to generate droplet is one of the fastest and commonly used methods.
Many micro fluidic devices have been designed to apply pressure to generate uniform droplet, including geometry dominated device [13,14], flow focusing devices; T-junctions [1] and co-flowing devices [15]. For device design optimization and operation, it is important to understand the under- lying mechanism of droplet generation processes in micro channels.
T-junction is one of the most frequently used micro fluidic geometries to produce immiscible fluid segment (plugs) and droplet. Although this approach has been widely used, the currently available information is still fragmented due to differences in channel dimensions, flow rate, fluid proprieties and surface materials.
3. Simulation Results
We simulate the dynamics of microdroplets flowing into oscillator consisting of complex geo- metrical form as shown in Fig. 1.
The simulation of the micro-injection systems is obtained with several hypotheses:
• liquid and laminar regime;
• incompressible;
• inlet pressure2·105Pa, outlet pressure105Pa;
• results are presented for theRe = 300at the nozzle.
3,1 3,2 3,3 3,4 3,5 3,6 3,7
0,155 0,16 0,165 0,17
m a ss e fl o w ra te k g /m 3
Times (s)
Fig. 2.Mass flow rate in the output for surface tension the coefficient equal to0.028 N/m.
0 0,2 0,4 0,6 0,8 1
0,15 0,155 0,16 0,165 0,17 0,175
Massfractionphase
Times(s) mass…
Fig. 3.Mass fraction of oil phase in the output for surface tension the coefficient is equal to0.028 N/m.
0 0,2 0,4 0,6 0,8 1
0,181 0,184 0,187 0,19
massfractionphase
Times(s) pha…
Fig. 4.Mass fraction of oil phase in the output for surface tension coefficient equal to0.9 N/m.
y=169,0ln(x)+1137,6
0 200 400 600 800 1000 1200
Ͳ0,1 0,1 0,7 0,9
Frequency(Hz)
0͕3 0͕ϱ
sƵƌĨaceƚĞnsŝŽŶ;E/m)
Oilphase(microdrops)frequency
Fig. 5.Frequency of mass fraction oil phase.
Table 1.
The Capillary, Weber and Reynolds numbers variation σ[N/m] 0.9 0.4 0.2 0.1 0.028 2.10−3 Ca·10−4 19 32 88 176 1051 8835
Re325 319 321 334 332 322
We·10−3 1063 1406 2836 5878 34919 284480
We choose generating drops with the oscillator. In this step, the principal channel supplies water while the control input supplies oil with surface tension coefficient equal to0.02888 N/mof 20◦C(Surface Science Instruments from Data Physics Instruments).
The PISO (pressure-implicit with splitting of operators) scheme is applied for pressure-velocity coupling. We used a second order Euler scheme for the transient terms. The numerical stability is ensured by setting the maximum Courant number to0.25.
First results of mass flow rate and mass faction phase of oil are presented below respectively to Fig. 2 – 5.
Mass flow rate present a harmonic signal without stable maximal and minimal amplitude. It should be noted that if the components are liquid, the signal frequency is really difficult for estima- tion in comparison with gaseous flow. However, the Fourier transform fitting allows calculation of frequency values for mass fraction of the oil phase.
The non-dimensional numbers characterize flow phenomenon through the oscillator; Capillary, Reynolds and Weber numbers are reported in Table 1.
Frequency variation depending on the surface tension is shown in Fig. 5
In following, the effect of pressure of frequency mass fraction oil phase is presented in Fig. 6:
we reduce principal supply pressure and undertake secondary alimentation constant pressure.
The following figure refers to the critical Capillary number in which the droplets get detached from the holes.
The presented results are obtained with several hypotheses, similar to the first case with gaseous flow. However all supposition required laminar flow. In literature all results concerning microdrops simulation allow increasing pressure estimate at millibar. The Reynolds number for all cases is equal to320.
More specially, we simulate low Reynolds number flows (Re = 320) with0.002<Ca<0.9, where we describe the Capillary number evolution based on the viscosity and the average velocity in the main channel, which is the ratio of viscous stress over the restorative Laplace pressure [1].
0 50 100 150 200 250 300 350 400 450
0 0,1 0,2 0,3 0,4 0,5 0,6
F re q u e n cy H z
pressure bar
Fig. 6.Mass fraction frequency of oil phase for surface tension equal to0.028 N/m.
1 201 401 601 801 1001 1201
0 0,2 0,4 0,6 0,8 1
Ca*10Ͳ4
Fig. 7.The Capilary number.
0 5000 10000 15000 20000 25000 30000 35000 40000
0 200 400 600 800 1000 1200
We*10Ͳ3
Ca*10Ͳ4
Fig. 8.The Weber number.
a) b)
Fig. 9.The first sample oscillator without glass covers (a), nozzle size (b), realized by ISC team, ENERGARID laboratory.
The frequency of mass flow signal was linear for surface tension equal to0.0028 N/m (see Fig. 6). The frequency of oil discrete phase evolution versus of surface tension coefficient is shown in the same figure, which presents important results. The frequency becomes stable when surface tension coefficient is upper than0.2 N/m. Figs. 7 and 8 represent the evolution of, respectively, the Capillary and Weber numbers.
4. First Experimental Steps
Experimentally, we present the first results obtained for the same model, the latter is fabricated using Etching method to provide uniform surface properties on all walls of the channel. The first samples which were produced in our laboratory are based on geometrical size from our first work published in ASME 2010 congress [9]. The simple method consists of chemical development pro- cess and photosensitive plate exposition in ultraviolet rays. The geometrical form of the sample is reported between model and plaque. After that we can plunge the plaque in a solution of the ferric chloride. The sample is consisted of plaque and glass, as showed in Fig. 9.
Fig. 10.Experimental setup.a)
b)
Fig. 11.Oil on water microdrops production step in the mixing region with 0.85 ml/s for both inlets (water and oil) .The following pictures present an experimental process, in which it describes the visualization system, Figs. 11 – 13. We have used two peristaltic pumps (Masterflex L/S Drive HV-77521-47) to supply variable inlet liquid flow. In addition, the microscope XTD-2A (stereo microscope) is used to film and visualize the process development. No miscible liquid (water and oil) are administrated in the oscillator device. The mass flow rates variation is between0.36and0.9 ml/s.
00-44 s 00-68 s
00-14 s 00-24 s
00-06 s 00-14 s
Fig. 12.Visualization of microdrops, the frequency apparition of microdrops is equal to10 Hz for maximal mass flow0.85 ml/s, where microdrops are flowing toward the outlet of the oscillator
(microdrops are indicated by arrows).
00-85 s 02-29 s
Fig. 13.Experimental visualization of microdrops the frequency apparition in the left branch of microdrops is equal to69 Hzfor minimal mass flow0.36 ml/s, where microdrops are flowing toward the feedback.
The results of the first experimental visualization of microdrops production are showed in men- tioned three picture sets.
The initial contact of two miscible liquids is presented in the Fig. 11a, we observe the detach- ment of the first microdrop. In the Second steps the microdrop is oriented in large zone of oscillator.
Conclusions
The development of this micro fluidic oscillator system was mainly focused on the production simulation of microdrops. In the past decade, droplet micro fluidics have been steadily attracted the attention of diverse groups of researchers in many multidisciplinary engineering applications (medicine, biology, biochemistry, etc.) the oscillator model that is proposed to produce microdrops without moving part is an important step. The frequency of discrete phase frequency depends sen- sitively on micro flow frequency. We can adjust this parameter if we manipulate pressure supply parameter. For surface tension the coefficient is equal to0.02888 N/m, the Capillary number and Weber number estimate respectively,0.1051and34919, The discrete phase frequency depends also on surface tension. In the second phase of this work we must undertake experimentation of oscil- lators sample to validate our results. This work presents an opportunity especially for the chemical engineering.
We undertake an experimental visualization of microdrops production with oscillator device.
The first results of visualization microdrops production indicate difficulties of realization micro device systems. In the experimental setup we reduce micro flow supply to maintain integrity of oscillators. The microdrops are oriented in the left and the right branch of oscillator. The frequency of microdrop production is low estimated than20 Hz. Our purpose in the future is using an indicated experimental material to undertake experimental measurements.
REFERENCES
1. Day, P., Manz, A., and Zhang, Y.-H.,Microdroplet Technology, Principles and Emerging Ap- plication in Biology and Chemistry, Springer, New York, 2012.
2. Tabeling, P.,Introduction `a la Micro Fluidique, Collection Echelles, Belin, 2003.
3. Foster K. and Parker, C. A.,Fluidic Components and Circuits, John Wiley & Sons, New York, 1970, pp. 265–273.
4. Gebhard, U., Hein, H., and Schmidt, U., Numerical Investigation Of Fluidic Micro-Oscillators, J. Micromech. Microeng., 1996,6, pp. 115–117.
5. Sim`oes, E. W., Furlan, Rogerio, Leminski, R. E. B., Rubio, M. G., Pereira, M. T., Mori- moto, N. I., and Santiago-Aviles, J. J., Microfluidic Oscillator for Gas Flow Control and Mea- surement,Flow Meas. Instrum., 2005,16, pp. 7–12.
6. Tesar, V., Tippetts, J. R., and Low, Y. Y., Oscillator Mixer for Chemical Microreactors, In:9-th Int. Sympos. Flow Visualisation, Edinburgh, UK, 2000, pp. 298(1–7).
7. Chekifi, T., Dennai, B., and Khelfaoui, R., Numerical and Experimental Study of Microdrops Flow-Selection by Fluidic Oscillator,DeviceWorld Appl. Sci. J., 2015,33, No. 3, pp. 416–422.
8. Khelfaoui, R., Colin, S. Caen, R., Orieux, S., and Baldas, L., Numerical and Experimental Analysis of Monostable Mini- and Micro-Oscillators, Heat Transf. Eng., 2009, 30, No. 1-2, pp. 121–129.
9. Dennai, B., Khelfaoui, R., and Benyoucef, B. Theoretical Study: Flow Control Mono and Bi- Stable Fluidic Device for Micro-Injection System, In: ASME 8-th Int. Conf. Nanochannels, Microchannels and Minichannels, Montreal, Canada, 2010.
10. Anna. T., Gun, T., and Christian, T. CFD Modelling of Drop Formation in a Liquid-Liquid System, In:6th Int. Conf. Multiphase Flow, ICMF 2007, Leipzig, Germany, 2007.
11. Youngs, D. L., Time-Dependent Multi-Material Flow with Large Fluid Distortion,Numer. Meth.
Fluid Dyn., 1982,24, No. 2, pp. 273–285.
12. Rudman, M., Volume-Tracking Methods for Interfacial Flow Calculations,Int. J. Numer. Meth.
Fluids, 1997,24, pp. 671–691.
13. Sugiura, S., Nakajima, M., and Seki, M., Prediction Of Droplet Diameter for Microchannel Emulsification: Prediction Model for Complicated Microchannel Geometries,Ind. Eng. Chem.
Res., 2004,43, pp. 8233–8238.
14. Yasuno, M., Sugiura, S., Iwamoto, S., Nakajima, M., Shono, A., and Satoh, K., Monodispersed Microbubble Formation Using Microchannel Technique,AIChE J., 2004,50, pp. 3227–3233.
15. Hua, J, Zhang, B., and Lou, J., Numerical Simulation of Microdroplet Formation in Coflowing Immiscible Liquids,AIChE J., 2007,53, pp. 2534–2548.
