Abstract
Researchers usually simplify their simulations by considering the Newtonian fluid assumption in microfluidic devices. However, it is essential to study the behavior of real non-Newtonian fluids in such systems. Moreover, using the external electric or magnetic fields in these systems can be very beneficial for manipulating the droplet size. This study considers the simulation of the process of non-Newtonian droplets’ formation under the influence of an external electric field. The novelty of this study is the use of a shear-thinning fluid as the droplet phase in this process, which has been less studied despite its numerous applications. The effects of an external electric field on this process are also investigated. Aqueous carboxymethyl cellulose (CMC) solution with different mass concentrations is selected as the non-Newtonian fluid of the droplet phase. The level set numerical method is used to analyze the formation of droplets in a T-junction. First, the effects of changing the key parameters such as the inlet velocities of phases, the concentration of the droplet phase, and the contact angle and the time of first droplet formation are investigated. The results indicate that as the concentration of the droplet phase increases, the diameter of the droplet decreases. Next, by applying a voltage difference to the system, an electric field is created inside the system. It is found that the stronger the electric field, the larger the droplet size due to the direction of electric forces applied to the interface of the droplet.
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Li, X., Chen, X.: Effect of interface wettability on the flow characteristics of liquid in smooth microchannels. Acta Mech. 230, 2111–2123 (2019). https://doi.org/10.1007/s00707-019-2371-z
Chatterjee, K., Staples, A.: Slip flow in a microchannel driven by rhythmic wall contractions. Acta Mech. 229, 4113–4129 (2018). https://doi.org/10.1007/s00707-018-2210-7
Whitesides, G.M.: The origins and the future of microfluidics. Nature 442, 368–373 (2006). https://doi.org/10.1038/nature05058
Ebadi, A., Toutouni, R., Farshchi Heydari, M.J., Fathipour, M., Soltani, M.: A novel numerical modeling paradigm for bio particle tracing in non-inertial microfluidics devices. Microsyst. Technol. (2019). https://doi.org/10.1007/s00542-018-4275-6
Pan, Z., Zhang, R., Yuan, C., Wu, H.: Direct measurement of microscale flow structures induced by inertial focusing of single particle and particle trains in a confined microchannel. Phys. Fluids. (2018). https://doi.org/10.1063/1.5048478
Huang, N.T., Hwong, Y.J., Lai, R.L.: A microfluidic microwell device for immunomagnetic single-cell trapping. Microfluid. Nanofluidics (2018). https://doi.org/10.1007/s10404-018-2040-x
Shen, F., Xue, S., Xu, M., Pang, Y., Liu, Z.M.: Experimental study of single-particle trapping mechanisms into microcavities using microfluidics. Phys. Fluids. (2019). https://doi.org/10.1063/1.5081918
Ichikawa, Y., Yamamoto, K., Yamamoto, M., Motosuke, M.: Near-hydrophobic-surface flow measurement by micro-3D PTV for evaluation of drag reduction. Phys. Fluids. (2017). https://doi.org/10.1063/1.5001345
Ageev, A.I., Osiptsov, A.N.: Slow viscous flow in a microchannel with similar and different superhydrophobic walls. J. Phys. Conf. Ser. (2018). https://doi.org/10.1088/1742-6596/1141/1/012134
Mohammadi, A., Floryan, J.M.: Mechanism of drag generation by surface corrugation. Phys. Fluids (2012). https://doi.org/10.1063/1.3675557
Javaherchian, J., Moosavi, A.: Pressure drop reduction of power-law fluids in hydrophobic microgrooved channels. Phys. Fluids. 31, 073106 (2019). https://doi.org/10.1063/1.5115820
Lin, X., Bao, F., Tu, C., Yin, Z., Gao, X., Lin, J.: Dynamics of bubble formation in highly viscous liquid in co-flowing microfluidic device. Microfluid. Nanofluidics (2019). https://doi.org/10.1007/s10404-019-2221-2
Hin, S., Paust, N., Keller, M., Rombach, M., Strohmeier, O., Zengerle, R., Mitsakakis, K.: Temperature change rate actuated bubble mixing for homogeneous rehydration of dry pre-stored reagents in centrifugal microfluidics. Lab Chip. 18, 362–370 (2018). https://doi.org/10.1039/c7lc01249g
Tan, H.: Numerical study of a bubble driven micromixer based on thermal inkjet technology. Phys. Fluids. (2019). https://doi.org/10.1063/1.5098449
Sakurai, R., Yamamoto, K., Motosuke, M.: Concentration-adjustable micromixers using droplet injection into a microchannel. Analyst. 144, 2780–2787 (2019). https://doi.org/10.1039/c8an02310g
Shamloo, A., Hassani-Gangaraj, M.: Investigating the effect of reagent parameters on the efficiency of cell lysis within droplets. Phys. Fluids 32, 62002 (2020). https://doi.org/10.1063/5.0009840
Bijarchi, M.A., Dizani, M., Honarmand, M., Shafii, M.B.: Splitting dynamics of ferrofluid droplet inside a microfluidic T-junction using a Pulse-Width Modulated magnetic field in Micro-magnetofluidics. Soft Matter (2020). https://doi.org/10.1039/D0SM01764G
Favakeh, A., Bijarchi, M.A., Shafii, M.B.: Ferrofluid droplet formation from a nozzle using alternating magnetic field with different magnetic coil positions. J. Magn. Magn. Mater. (2020). https://doi.org/10.1016/j.jmmm.2019.166134
Bijarchi, M.A., Shafii, M.B.: Experimental investigation on the dynamics of on-demand ferrofluid drop formation under a pulse-width-modulated nonuniform magnetic field. Langmuir 36, 7724–7740 (2020). https://doi.org/10.1021/acs.langmuir.0c00097
Shojaeian, M., Lehr, F.X., Göringer, H.U., Hardt, S.: On-demand production of femtoliter drops in microchannels and their use as biological reaction compartments. Anal. Chem. 91, 3484–3491 (2019). https://doi.org/10.1021/acs.analchem.8b05063
Nasiri, R., Shamloo, A., Akbari, J., Tebon, P., Dokmeci, M.R., Ahadian, S.: Design and simulation of an integrated centrifugal microfluidic device for CTCs separation and cell lysis. Micromachines (2020). https://doi.org/10.3390/mi11070699
Mai, T.D., Ferraro, D., Aboud, N., Renault, R., Serra, M., Tran, N.T., Viovy, J.L., Smadja, C., Descroix, S., Taverna, M.: Single-step immunoassays and microfluidic droplet operation: towards a versatile approach for detection of amyloid-β peptide-based biomarkers of Alzheimer’s disease. Sens. Actuators B Chem. 255, 2126–2135 (2018). https://doi.org/10.1016/j.snb.2017.09.003
Naghdloo, A., Ghazimirsaeed, E., Shamloo, A.: Numerical simulation of mixing and heat transfer in an integrated centrifugal microfluidic system for nested-PCR amplification and gene detection. Sens. Actuators B Chem. 283, 831–841 (2019). https://doi.org/10.1016/j.snb.2018.12.084
Sun, D., Cao, F., Cong, L., Xu, W., Chen, Q., Shi, W., Xu, S.: Cellular heterogeneity identified by single-cell alkaline phosphatase (ALP) via a SERRS-microfluidic droplet platform. Lab Chip. 19, 335–342 (2019). https://doi.org/10.1039/C8LC01006D
Amadeh, A., Ghazimirsaeed, E., Shamloo, A., Dizani, M.: Improving the performance of a photonic PCR system using TiO2 nanoparticles. J. Ind. Eng. Chem. (2020). https://doi.org/10.1016/j.jiec.2020.10.036
Cheow, L.F., Yobas, L., Kwong, D.L.: Digital microfluidics: droplet based logic gates. Appl. Phys. Lett. 90, 1–4 (2007). https://doi.org/10.1063/1.2435607
Zhang, Q., Zhang, M., Djeghlaf, L., Bataille, J., Gamby, J., Haghiri-Gosnet, A.M., Pallandre, A.: Logic digital fluidic in miniaturized functional devices: perspective to the next generation of microfluidic lab-on-chips. Electrophoresis 38, 953–976 (2017). https://doi.org/10.1002/elps.201600429
Teh, S.Y., Lin, R., Hung, L.H., Lee, A.P.: Droplet microfluidics. Lab Chip. 8, 198–220 (2008). https://doi.org/10.1039/b715524g
Cedillo-Alcantar, D.F., Han, Y.D., Choi, J., Garcia-Cordero, J.L., Revzin, A.: Automated droplet-based microfluidic platform for multiplexed analysis of biochemical markers in small volumes. Anal. Chem. 91, 5133–5141 (2019). https://doi.org/10.1021/acs.analchem.8b05689
Geng, H., Feng, J., Stabryla, L.M., Cho, S.K.: Dielectrowetting manipulation for digital microfluidics: creating, transporting, splitting, and merging of droplets. Lab Chip. 17, 1060–1068 (2017). https://doi.org/10.1039/c7lc00006e
Teo, A.J.T., Li, K.H.H., Nguyen, N.T., Guo, W., Heere, N., Xi, H.D., Tsao, C.W., Li, W., Tan, S.H.: Negative pressure induced droplet generation in a microfluidic flow-focusing device. Anal. Chem. 89, 4387–4391 (2017). https://doi.org/10.1021/acs.analchem.6b05053
Xu, J.H., Li, S.W., Tan, J., Luo, G.S.: Correlations of droplet formation in T-junction microfluidic devices: from squeezing to dripping. Microfluid. Nanofluidics 5, 711–717 (2008). https://doi.org/10.1007/s10404-008-0306-4
De Menech, M., Garstecki, P., Jousse, F., Stone, H.A.: Transition from squeezing to dripping in a microfluidic T-shaped junction. J. Fluid Mech. 595, 141–161 (2008)
Liu, H., Zhang, Y.: Droplet formation in a T-shaped microfluidic junction. J. Appl. Phys. 106, 34906 (2009). https://doi.org/10.1063/1.3187831
Christopher, G.F., Noharuddin, N.N., Taylor, J.A., Anna, S.L.: Experimental observations of the squeezing-to-dripping transition in T-shaped microfluidic junctions. Phys. Rev. E. 78, 36317 (2008). https://doi.org/10.1103/PhysRevE.78.036317
Jullien, M.C., Tsang Mui Ching, M.J., Cohen, C., Menetrier, L., Tabeling, P.: Droplet breakup in microfluidic T-junctions at small capillary numbers. Phys. Fluids. 21, 1–7 (2009). https://doi.org/10.1063/1.3170983
Sivasamy, J., Wong, T.N., Nguyen, N.T., Kao, L.T.H.: An investigation on the mechanism of droplet formation in a microfluidic T-junction. Microfluid. Nanofluidics 11, 1–10 (2011). https://doi.org/10.1007/s10404-011-0767-8
Nekouei, M., Vanapalli, S.A.: Volume-of-fluid simulations in microfluidic T-junction devices: influence of viscosity ratio on droplet size. Phys. Fluids (2017). https://doi.org/10.1063/1.4978801
Zeng, W., Li, S., Fu, H.: Modeling of the pressure fluctuations induced by the process of droplet formation in a T-junction microdroplet generator. Sens. Actuators A Phys. 272, 11–17 (2018). https://doi.org/10.1016/j.sna.2018.01.013
Bashir, S., Rees, J.M., Zimmerman, W.B.: Simulations of microfluidic droplet formation using the two-phase level set method. Chem. Eng. Sci. 66, 4733–4741 (2011). https://doi.org/10.1016/j.ces.2011.06.034
Soh, G.Y., Yeoh, G.H., Timchenko, V.: Numerical investigation on the velocity fields during droplet formation in a microfluidic T-junction. Chem. Eng. Sci. 139, 99–108 (2016). https://doi.org/10.1016/j.ces.2015.09.025
Gu, Z., Liow, J.L.: Micro-droplet formation with non-Newtonian solutions in microfluidic T-junctions with different inlet angles. In: 2012 7th IEEE International Conference on Nano/Micro Engineering Molecular System. NEMS 2012. pp 423–428 (2012). https://doi.org/10.1109/NEMS.2012.6196809
Nooranidoost, M., Izbassarov, D., Muradoglu, M.: Droplet formation in a flow focusing configuration: effects of viscoelasticity. Phys. Fluids. (2016). https://doi.org/10.1063/1.4971841
Chiarello, E., Gupta, A., Mistura, G., Sbragaglia, M., Pierno, M.: Droplet breakup driven by shear thinning solutions in a microfluidic T-junction. Phys. Rev. Fluids. 2, 1–13 (2017). https://doi.org/10.1103/PhysRevFluids.2.123602
Liang, D., Ma, R., Fu, T., Zhu, C., Wang, K., Ma, Y., Luo, G.: Dynamics and formation of alternating droplets under magnetic field at a T-junction. Chem. Eng. Sci. 200, 248–256 (2019). https://doi.org/10.1016/j.ces.2019.01.053
Sahore, V., Doonan, S.R., Bailey, R.C.: Droplet microfluidics in thermoplastics: device fabrication, droplet generation, and content manipulation using integrated electric and magnetic fields. Anal. Methods. 10, 4264–4274 (2018). https://doi.org/10.1039/c8ay01474d
Chen, I.M., Tsai, H.H., Chang, C.W., Zheng, G., Su, Y.C.: Electric-field triggered, on-demand formation of sub-femtoliter droplets. Sens. Actuators B Chem. 260, 541–553 (2018). https://doi.org/10.1016/j.snb.2017.12.152
Nhu, C.N., Thu, H.N., Le Van, L., Duc, T.C., Dau, V.T., Bui, T.T.: Study on flow-focusing microfluidic device with external electric field for droplet generation. In: Fujita, H., Nguyen, D.C., Vu, N.P., Banh, T.L., Puta, H.H. (eds.) Advances in Engineering Research and Application, pp. 553–559. Springer International Publishing, Cham (2019)
Li, Y., Jain, M., Ma, Y., Nandakumar, K.: Control of the breakup process of viscous droplets by an external electric field inside a microfluidic device. Soft Matter 11, 3884–3899 (2015). https://doi.org/10.1039/c5sm00252d
Yang, C., Qiao, R., Mu, K., Zhu, Z., Xu, R.X., Si, T.: Manipulation of jet breakup length and droplet size in axisymmetric flow focusing upon actuation. Phys. Fluids 31, 091702 (2019). https://doi.org/10.1063/1.5122761
Josephides, D.N., Sajjadi, S.: Increased drop formation frequency via reduction of surfactant interactions in flow-focusing microfluidic devices. Langmuir 31, 1218–1224 (2015). https://doi.org/10.1021/la504299r
Van Nguyen, H., Nguyen, H.Q., Nguyen, V.D., Seo, T.S.: A 3D printed screw-and-nut based droplet generator with facile and precise droplet size controllability. Sens. Actuators B Chem. 296, 126676 (2019). https://doi.org/10.1016/j.snb.2019.126676
Tóth, A.B., Holczer, E., Hakkel, O., Tóth, E.L., Iván, K., Fürjes, P.: Modelling and characterisation of droplet generation and trapping in cell analytical two-phase microfluidic system. Proceedings. 1, 526 (2017). https://doi.org/10.3390/proceedings1040526
Yan, Q., Xuan, S., Ruan, X., Wu, J., Gong, X.: Magnetically controllable generation of ferrofluid droplets. Microfluid. Nanofluidics. 19, 1377–1384 (2015). https://doi.org/10.1007/s10404-015-1652-7
Zhang, S., Guivier-Curien, C., Veesler, S., Candoni, N.: Prediction of sizes and frequencies of nanoliter-sized droplets in cylindrical T-junction microfluidics. Chem. Eng. Sci. 138, 128–139 (2015). https://doi.org/10.1016/j.ces.2015.07.046
Chen, H., Man, J., Li, Z., Li, J.: Microfluidic generation of high-viscosity droplets by surface-controlled breakup of segment flow. ACS Appl. Mater. Interfaces. 9(21059), 21064 (2017). https://doi.org/10.1021/acsami.7b03438
Prileszky, T.A., Ogunnaike, B.A., Furst, E.M.: Statistics of droplet sizes generated by a microfluidic device. AIChE J. 62, 2923–2928 (2016). https://doi.org/10.1002/aic.15246
Wong, V.L., Loizou, K., Lau, P.L., Graham, R.S., Hewakandamby, B.N.: Numerical simulation of the effect of rheological parameters on shear-thinning droplet formation. Am. Soc. Mech. Eng. Fluids Eng. Div. FEDSM (2014). https://doi.org/10.1115/FEDSM2014-21363
Allgén, L.-G., Roswall, S.: A dielectric study of a carboxymethylcellulose in aqueous solution. J. Polym. Sci. 12, 229–236 (1954). https://doi.org/10.1002/pol.1954.120120119
Nabizadeh, A., Hassanzadeh, H., Sharifi, M., Keshavarz Moraveji, M.: Effects of dynamic contact angle on immiscible two-phase flow displacement in angular pores: a computational fluid dynamics approach. J. Mol. Liq. (2019). https://doi.org/10.1016/j.molliq.2019.111457
Wang, X.D., Lee, D.J., Peng, X.F., Lai, J.Y.: Spreading dynamics and dynamic contact angle of non-Newtonian fluids. Langmuir 23, 8042–8047 (2007). https://doi.org/10.1021/la0701125
Šikalo, Š, Wilhelm, H.D., Roisman, I.V., Jakirlić, S., Tropea, C.: Dynamic contact angle of spreading droplets: experiments and simulations. Phys. Fluids. 17, 1–13 (2005). https://doi.org/10.1063/1.1928828
Jangir, P., Jana, A.K.: CFD simulation of droplet splitting at microfluidic T-junctions in oil–water two-phase flow using conservative level set method. J. Braz. Soc. Mech. Sci. Eng. 41, 1–16 (2019). https://doi.org/10.1007/s40430-019-1569-2
Li, L., Zhang, C.: Electro-hydrodynamics of droplet generation in a co-flowing microfluidic device under electric control. Colloids Surf. A Physicochem. Eng. Asp. 586, 124258 (2020). https://doi.org/10.1016/j.colsurfa.2019.124258
Sheng, P., Qian, T., Wang, X.: Hydrodynamic boundary condition at the fluid-solid interface. Int. J. Mod. Phys. B. 21, 4131–4143 (2007). https://doi.org/10.1142/S0217979207045311
Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79, 12–49 (1988). https://doi.org/10.1016/0021-9991(88)90002-2
Wong, V.L., Loizou, K., Lau, P.L., Graham, R.S., Hewakandamby, B.N.: Numerical studies of shear-thinning droplet formation in a microfluidic T-junction using two-phase level-SET method. Chem. Eng. Sci. 174, 157–173 (2017). https://doi.org/10.1016/j.ces.2017.08.027
Lan, W., Li, S., Wang, Y., Luo, G.: CFD simulation of droplet formation in microchannels by a modified level set method. Ind. Eng. Chem. Res. 53, 4913–4921 (2014). https://doi.org/10.1021/ie403060w
Olsson, E., Kreiss, G.: A conservative level set method for two phase flow. J. Comput. Phys. 210, 225–246 (2005). https://doi.org/10.1016/j.jcp.2005.04.007
Harten, A.: The artificial compression method for computation of shocks and contact discontinuities. I. Single conservation laws. Commun. Pure Appl. Math. 30, 611–638 (1977). https://doi.org/10.1002/cpa.3160300506
Zare, Y., Park, S.P., Rhee, K.Y.: Analysis of complex viscosity and shear thinning behavior in poly (lactic acid)/poly (ethylene oxide)/carbon nanotubes biosensor based on Carreau-Yasuda model. Results Phys. 13, 102245 (2019). https://doi.org/10.1016/j.rinp.2019.102245
Van Der Graaf, S., Nisisako, T., Schroën, C.G.P.H., Van Der Sman, R.G.M., Boom, R.M.: Lattice Boltzmann simulations of droplet formation in a T-shaped microchannel. Langmuir 22, 4144–4152 (2006). https://doi.org/10.1021/la052682f
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Amiri, N., Honarmand, M., Dizani, M. et al. Shear-thinning droplet formation inside a microfluidic T-junction under an electric field. Acta Mech 232, 2535–2554 (2021). https://doi.org/10.1007/s00707-021-02965-y
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DOI: https://doi.org/10.1007/s00707-021-02965-y