Abstract—Among different droplet manipulations, controlled droplet-splitting is of great significance due to its ability to increase throughput and operational capability. Furthermore, unequal droplet- splitting can provide greater flexibility and a wider range of dilution factors. In this study, we developed two-dimensional, time-dependent complex fluid dynamics simulations to model droplet formation in a flow focusing device, followed by splitting in a Y-shaped junction with sub-channels of unequal widths. From the results obtained from the numerical study, we correlated the diameters of the droplets in the sub- channels to the Weber number, thereby demarcating the droplet splitting and non-splitting regimes. Keywords—Microfluidics, unequal droplet splitting, two phase flow, flow focusing device. I. INTRODUCTION HE past two decades has seen a phenomenal growth in the field of microfluidics, ranging from particle separation, mixing of biological reagents and cell encapsulation by droplet- based microfluidics devices [1], [2]. Precise droplet manipulation after their generation is crucial in enhancing their utility, especially in microfluidic chips. The ability to divide droplets into smaller daughter droplets of desired volumes plays an important role in diluting, concentrating or separating particles in a droplet and can therefore be extremely beneficial in various droplet-based microfluidic platforms. Furthermore, droplet fission can scale-up the experimental capacity of each droplet since each mother droplet is essentially a reaction or storage vessel. Various studies have been reported for active droplet splitting that make use of electric fields [3], pneumatic valves [4] and acoustic forces [5]. While these methods are effective, the application of external fields is complicated and limits their practical application. Passive schemes, mediated by microchannel geometries and resulting hydraulic resistances that make use of microchannel bifurcation have been employed for droplet splitting with great success [6]. Moreover, most experiments reported till date focus on equal droplet splitting. There are only few studies that discuss unequal splitting of droplets, that is, splitting in 1:x ratio. Unequal droplet splitting can accelerate sample dilution process and expand the range of achievable dilution factors. II. MATERIAL AND METHODS Governing Equations The governing equations consist of those for the conservation Bahram Talebjedi is with the University of British Columbia, Canada (e- mail: bahram.talebjedi@ubc.ca). of mass and momentum:  ∙ ሺሻ ൌ 0 (1)  డ௨ డ௧ ൅ ሺ ∙ ሻ ൌ  ∙ ሾെ ൅ ሿ ൅  ௦௧ (2) where;  ൌ ሺ ൅ ሺሻ  ሻ (3) in which ρ, μ, u, p, indicate density, dynamic viscosity, velocity, and pressure, respectively. F st is the surface tension force acting at the interface of immiscible fluids. The interface location is traced by solving an additional transport equation of the phase- field method. The dimensionless phase field function, φ, is defined to describe the multiphase flow. The phase field variable range is between -1 and 1, where the lower bond defines the phase 1 and upper bond refers to second phase. The transport of the fluid interface, separating the two phases, is provided by the Cahn-Hilliard equation [6]: డథ డ௧ ൅  ∙  ൌ  ∙ ఊఒ ఢ మ  (4) where ψ is referred to the phase field help variable,  ൌ െ ∙  ଶ  ൅ ሺ ଶ െ 1ሻ (5) and u is the velocity (m/s), γ is the mobility parameter (m 3 ꞏs/kg), λ is the mixing energy density (N), and  (m) denotes the interface thickness parameter. The mixing energy density can be computed using (6) relating λ to  and the surface tension coefficient, σ: ൌ ଷఢఙ √ (6) The interface thickness parameter is set to ൌℎ ௖ /2, where hc is the characteristic mesh size in the region swept by the interface. The mobility parameter, γ, which designates the time scale of the Cahn-Hilliard diffusion, is equal to the square of the interface thickness parameter, ൌ ଶ (7) In the phase-field model, volume fractions of phases are measured using phase filed variable, Geometrical Based Unequal Droplet Splitting Using Microfluidic Y-Junction Bahram Talebjedi, Amirmohammad Sattari, Ahmed Zoher Sihorwala, Mina Hoorfar T World Academy of Science, Engineering and Technology International Journal of Biomedical and Biological Engineering Vol:15, No:5, 2021 177 International Scholarly and Scientific Research & Innovation 15(5) 2021 ISNI:0000000091950263 Open Science Index, Biomedical and Biological Engineering Vol:15, No:5, 2021 publications.waset.org/10012038/pdf