Computational Study of Transition of Oil-water Flow Morphology due to Sudden Contraction in Microfluidic Channel

Transcription

1 Computatonal Study of Transton of Ol-water Flow Morphology due to Sudden Contracton n Mcrofludc Channel J. Chaudhur 1, S. Tmung 1, T. K. Mandal 1,2, and D. Bandyopadhyay *1,2 1 Department of Chemcal Engneerng, Indan Insttute of Technology Guwahat, Inda. 2 Centre for Nanotechnology, Indan Insttute of Technology Guwahat, Inda. *Correspondng Author: Department of Chemcal Engneerng, Indan Insttute of Technology Guwahat, Inda, Pn , Emal: dpban@tg.ernet.n Abstract: The present study shows a strategy to transform larger two-phase flow structures nto the smaller ones by ncorporatng smple tunng of mcrochannel geometry. The two-phase flow s modelled employng the n-bult phase-feld model whch s commercally avalable wth COMSOL Multphyscs software. Wth the help of a seres of numercal smulatons, we show that larger plug flow can be transformed nto smaller droplets by ntroducng an orfce at the T-juncton of the mcrofludc channel. The sze of the droplets can be tuned by varyng the dameter of the orfce. In addton, the frequency of droplets can also be vared by changng the dameter and poston of the orfce along the length of the mcrofludc channel. The results shown n ths study can be helpful n the desgn of mcro-emulsfers and mcroreactors whch demands a collecton of mnaturzed droplets dspersed nsde a contnuous medum. Keywords: multphase flow; mcrofludc channel; computatonal flud dynamcs; mxng. 1. Introducton The control over the flow morphologes of two-phase flow nsde mcrofludc devces have been a subject of nterest for the past few decades because they can be appled to a wde range of applcatons n varous felds of scence and technology [1-4]. The mcroscopc technologes offer several advantages over the conventonal macroscopc ones because of the avalablty of hgher surface to volume rato, ablty to handle small volume of fluds, easer process control and reducton n operatng cost [5]. Whle the effect of gravty and nertal forces become weaker wth reducton n channel dameter, the nfluence of surface and vscous forces becomes stronger. However, very often the flow structures such as slug and plug flow are encountered [6,7], whch are not that desrable for the processes where hgher surface to volume rato s n demand. Thus, t s of mportance to dentfy the condtons for developng smaller sze flow structures where hgher surface to volume rato can be easly acheved. In ths drecton, varous strateges have been explored to control the two-phase flow morphologes and ther transtons from slug to plug to droplet, wth the varaton n the dfferent process parameters. Prevous studes reveal that the flow morphologes can be controlled by varyng the velocty of fluds [8], flud propertes such as nterfacal tenson [9] and vscosty [10], and wettablty of the flud on the wall.

2 For example, flow transton from droplet to slug to annular flow can be acheved by ncreasng the flow rate of dsperse phase whereas larger slugs are transformed nto smaller droplets by ncreasng the vscosty of the contnuous phase. A very recent study [9] shows that water-n-ol and ol-n-water emulson can also be prepared n a sngle mcrofludc channel by ntroducng surfactants at specfc concentratons n the ol and water phases. Further, another study [7] show the transformaton of the flow morphologes from steady to unsteady when the dameter of the mcrochannel s less than 250 µm. In the present work, we study the transton of flow patterns due to margnal change n channel geometry. Ths s accomplshed by placng an orfce at the T- juncton, whch creates an abrupt contracton and expanson nsde the mcrofludc channel. Wth the help of seres of 2D smulatons, we show that by ntroducng an orfce near the mcrochannel T- juncton, the larger flow structures can easly be transformed nto smaller droplets, whch can be employed to develop droplet drven flows. 2. Use of COMSOL Multphyscs In order to model the ol-water flow nsde the mcrochannel, we use the lamnar and ncompressble two-phase flow setup wth the phase-feld model to track the nterface n the commercally avalable COMSOL Multphyscs software. 2.1 Problem Formulaton Fgure 1. Geometry of the mcrochannel. Fgure 1 schematcally shows the geometry under consderaton. Here the channel dameter, d = 500 μm, and dameter of constrcton, d o = 500, 200, 150 and 100 μm. Ol (water) flows n the mcrochannel through horzontal (vertcal nlets) and flows out through the outlet as shown by the drecton of arrows. The flow of a par of ncompressble, mmscble and Newtonan fluds nsde a T-shaped mcrochannel are governed by the followng contnuty and equatons of moton, u 0, (1) u u u p τ f g (2) st In the Eqs. (1) and (2) the subscrpt corresponds to ol ( = 1) and water ( = 2) phases. The notatons, denotes the velocty vector, u s dynamc vscosty, s densty, p s the pressure of the th flud. The over dot denotes the tme dervatve and the vector g s the acceleraton due to gravty actng on the negatve y drecton for the geometry shown n the Fgure 1. The consttutve relaton for the th Newtonan flud s consdered as, τ u u. T We employed phase feld computatonal method to track the nterface. The transport equaton for ths phase feld parameter ( ) s, u G (3) The parameter s 1 for water and 1 for ol. The varable represent the moblty of the nterface and the chemcal potental s defned as, GF 1/ N. The chemcal potental s evaluated as,

3 1 2 F ftotdv f dv 2 (4) V In Eq. (4), V f s the total free energy densty, whch tot s the sum of the bulk energy or double well potental f /4N 1 ] and the surface 2 2 [ 2 nterfacal tenson γ between ol and water phases were vared from N/m. 3. Results and dscussons energy. The mxng energy densty s expressed as, 3 N / 2 2, n whch and N are the nterfacal tenson and thckness of the dffused nterface. The nterfacal densty, vscosty, permttvty, and conductvty, are evaluated n terms of as, and. The surface tenson force n Eq. (2) s defned as a product of the chemcal potental G and the gradent of the phase feld ( ) as, f st G. (5) 2.2 Boundary condtons Fgure 1 schematcally shows the geometry of the problem consdered. At the nlets, normal nflow velocty (v = U) boundary condton and at the outlet, default pressure wth no vscous stress boundary condton are enforced. The walls are wettng, nonslppng, and mpermeable. The equlbrum contact angle (θ) of a water droplet on the wall and embedded nsde ol s set to 140. The "physcscontrolled" meshng scheme was chosen wth "fne" element sze, whch created trangular cells wth almost 7000 cells nsde the control volume. Slcone ol and water were chosen as the test fluds. The denstes of ol and water phase were kept at 1000 kg/m 3. The vscostes of ol and water phase were kept at 0.01 and Pa s, respectvely. The Fgure 2. Full cycle of the formaton of ol-water flow structures n a T-juncton mcrochannel wthout and wth an orfce. Images (a) (e) show the mechansm of plug formaton at dfferent tme (t) nterval n mllsecond (ms). Whle mages (f) (j) show the mechansm of formaton of flow structure n presence of an orfce at dfferent tme nterval. The mages (a) (e) n the Fgure 2 shows the formaton of a water plug (darker blue shade) n contnuous ol phase (lghter red shade), whch s commonly observed n the two-phase flow studes 7, 8. In ths case, the velocty of ol (U o ) and water (U w ) are taken to be 0.1 and 0.01 m/s, respectvely. The subscrpt o and w represents ol and water phases. Fgure 2 (f) (j) shows the pathway of droplet formaton for a smlar flow condton n presence of sudden contracton nsde the mcrofludc channel. Clearly, the fgure suggests that the flow s transformed from plug to droplets wth ncreased droplet frequency, due to the presence of an orfce. The channel contracton at the T-juncton nduces an abrupt velocty dfference n the ol and water phases, whch cause hgher shear at the ol-water nterface at the zone of contracton. In consequence, the water

4 phase penetratng nto the ol n ths regon produces smaller droplets Further, the dameter of orfce, d o and the nterfacal tenson (γ) are found to have a strong nfluence on the droplet dameter, d d, whch s depcted n Fgure 3 (a) (d) n whch d o s set to 200, 150 and 100 μm n mages (b), (c) and (d), respectvely. Fgure 3 (e) shows the varaton of dmensonless droplet dameter, h d (= d d /d) wth dmensonless orfce dameter, h o (= d o /d) at dfferent nterfacal tenson γ. These plots suggest that wde range of droplet dameter could be acheved by controllng orfce dameter and γ. Fgure 3. Flow transton from large sze plug to mnute droplets due to presence of orfce at the T juncton. Here, from (a) (d), the dameter of orfce, do decreases from mm such that the value of dmensonless orfce dameter, ho (= do/d) = 1, 0.4, 0.3, and 0.2, respectvely. Image (e) shows the varaton of dmensonless droplet dameter, hd (= dd/d) wth ho at dfferent values of γ. Fgure 4. Flow transton from large sze plug to smaller droplets due to presence of orfce at a dstance d from T-juncton. Here, from (a) (d), the dameter of orfce, do decreases from mm such that the value of dmensonless orfce dameter, ho(= do/d) = 1, 0.4, 0.3, and 0.2, respectvely. Image (e) shows the varaton of dmensonless droplet dameter, hd (= dd/d) wth ho at dfferent values of γ.

5 The poston of the orfce (d) from the T-juncton s also found to have a sgnfcant nfluence on the flow morphology. Plots (a) (d) n Fgure 4 show a transton of flow morphology from plug to droplets n such cases. Further the fgure shows that n these stuatons also d o decreases wth d d, as observed for the prevous fgure. Fgure 4 (e) shows the dependence of dmensonless droplet dameter, h d wth dmensonless orfce dameter, h o at varous values of γ. The plot shows that the flow n smaller orfce dameter could develop smaller sze droplets. 4. Conclusons The present study shows a smple strategy to control the ol-water flow patterns by placng a abrupt contracton near a T-juncton of a mcrochannel. The results revealed that smaller dameter orfce could facltate smaller sze flow structures. Also the frequency and sze of droplet could be well control by the sze of orfces and ther postons. Ths approach can be well utlzed n mcrofludc devces where flow structures wth hgh surface to volume rato are desred. 5. Acknowledgement The authors are thankful to Department of Chemcal Engneerng, Indan Insttute of Technology Guwahat for provdng facltes and support to carry out ths research. 6. References 1. S. W. L, J. H. Xu, J. Tan, Y. J. Wang, G. S. Luo Controllable Preparaton of Monodsperse O/W and W/O Emulsons n the Same Mcrofludc Devce, Langmur, 22, 7943 (2006). 2. C.-X. Zhao, L. He, S. Z. Qao, and A. P. J. Mddelberg, Nanopartcle synthess n mcroreactors, Chemcal Engneerng Scence, 66, 1463 (2011). 3. X. Z. Ln, A. D. Terepka, and H. Yang, Synthess of Slver Nanopartcles n a Contnuous Flow Tubular Mcroreactor, Nano Letters, 4, 2227 (2004). 4. J. Skommer, J. Akag, K. Takeda, Y. Fujmura, K. Khoshmanesh, and D. Wlodkowc, Multparameter lab-on-a-chp flow cytometry of the cell cycle, Bosensors and Boelectroncs, 42, 586 (2013). 5. V. Kumar, M. Paraschvou, and K. D. P. Ngam, Sngle-phase flud flow and mxng n mcrochannels, Chemcal Engneerng Scence, 66, 1329 (2011). 6. A. Kawahara, P. M. Y. Chung, and M. Kawaj, Investgaton of two-phase flow pattern, vod fracton and pressure drop n a mcrochannel, Internatonal Journal of Multphase Flow, 28, 1411 (2002). 7. P. M. Y. Chung and M. Kawaj, The effect of channel dameter on adabatc two-phase flow characterstcs n mcrochannels, Internatonal Journal of Multphase Flow, 30, 735 (2004). 8. H. Forough and M. Kawaj, Vscous ol water flows n a mcrochannel ntally saturated wth ol: flow patterns and pressure drop characterstcs, Internatonal Journal of Multphase Flow, 37, 1147 (2011). 9. J. H. Xu, S. W. L, J. Tan, Y. J. Wang, and G. S. Luo, Controllable Preparaton of Monodsperse O/W and W/O Emulsons n the Same Mcrofludc Devce, Langmur, 22, 7943 (2006). 10. T. Cubaud, B. M. Jose, S. Darvsh, and R. Sun, Droplet breakup and vscosty-stratfed flows n mcrochannels, Internatonal Journal of Multphase Flow, 39, 29 (2012).