Breakup of microdroplets in asymmetric $\mathsf{T}$ junctions

Symmetric $\mathsf{T}$ junctions have been used widely in microfluidics to generate equal-sized microdroplets, which are applicable in drug delivery systems. A newly proposed method for generating unequal-sized microdroplets at a $\mathsf{T}$ junction is investigated theoretically and experimentally. Asymmetric $\mathsf{T}$ junctions with branches of identical lengths and different cross sections are utilized for this aim. An equation for the critical breakup of droplets at asymmetric $\mathsf{T}$ junctions and one for determining the breakup point of droplets are developed. A good agreement was observed between the theories (present and previous) and the experiments.

Figure 1

(a) Microchannel cross section. (b) Droplet before breakup at the $\mathsf{T}$ junction.

Figure 2

Critical capillary number as a function of the dimensionless droplet's initial length corresponding to Eqs. (11) and (12) for λ $=$ 0.5 and α $=$ 1. Equation (13) represents a symmetric breakup, while one of the Eqs. (11) or (12) should represent an asymmetric breakup. Equation (11) is valid since for a specific capillary number the critical breakup for asymmetric breakup should occur in a larger initial length than for a symmetric breakup.

Figure 3

A schematic of $\mathsf{T}$ junction geometry used in this study.

Figure 4

Different regimes for a droplet at the asymmetric $\mathsf{T}$ junction [44]. (a) $w_1$/$w_2=0.7$, (b) $w_1$/$w_2=0.75$, (c) $w_1$/$w_2=0.95$, and (d) $w_1$/$w_2=0.75$.

Figure 5

Phase diagram for different geometries. ——, theory [Eq. (11) with α $=$ 0.13 for $w_1$/$w_2=0.7$ and $w_1$/$w_2=0.75$, α $=$ 0.15 for $w_1$/$w_2=0.875$, and α $=$ 0.2 for $w_1$/$w_2=0.95$]; — —, theory from Ref. [24] [Eq. (14) with χ $=$ 1.06 for $w_1$/$w_2=0.7$, χ $=$ 0.97 for $w_1$/$w_2=0.75$, χ $=$ 0.82 for $w_1$/$w_2=0.875$, and χ $=$ 0.75 for $w_1$/$w_2=0.95$]; ✦, experimental points for breakup with obstruction; ▲, experimental points for unstable breakup; ■, experimental points for no breakup.

Figure 6

Phase diagram for different $\mathsf{T}$ junction width ratios. As the width ratio decreases the boundary moves towards the right.

Figure 7

Volume ratio of daughter droplets generated in different geometries. —, theory [Eq. (3)]; ✦, experimental points for breakup with obstruction; ▲, experimental points for unstable breakup.

Figure 8

Dimensionless distance of the breakup point from the center of the $\mathsf{T}$ junction versus the width ratio of the branches $w_1$/$w_2$. —, theory [Eq. (6)]; ■, experiment.

Figure 9

Dimensionless breakup length versus capillary number for different branch width ratios. ■, $l_b$${}_2$/$l_0$; ✦, $l_b$${}_1$/$l_0$; ▲, ($l_b$${}_1+l_b$${}_2$)/2$l_0$; ——, linear curve fit for experimental data. $l_b$${}_1$ is the small part breakup length and $l_b$${}_2$ is the large part breakup length of the droplet at the $\mathsf{T}$ junction.