Droplet breakup driven by shear thinning solutions in a microfluidic T-junction

Droplet-based microfluidics turned out to be an efficient and adjustable platform for digital analysis, encapsulation of cells, drug formulation, and polymerase chain reaction. Typically, for most biomedical applications, the handling of complex, non-Newtonian fluids is involved, e.g., synovial and salivary fluids, collagen, and gel scaffolds. In this study, we investigate the problem of droplet formation occurring in a microfluidic T-shaped junction, when the continuous phase is made of shear thinning liquids. At first, we review in detail the breakup process, providing extensive, side-by-side comparisons between Newtonian and non-Newtonian liquids over unexplored ranges of flow conditions and viscous responses. The non-Newtonian liquid carrying the droplets is made of Xanthan solutions, a stiff, rodlike polysaccharide displaying a marked shear thinning rheology. By defining an effective Capillary number, a simple yet effective methodology is used to account for the shear-dependent viscous response occurring at the breakup. The droplet size can be predicted over a wide range of flow conditions simply by knowing the rheology of the bulk continuous phase. Experimental results are complemented with numerical simulations of purely shear thinning fluids using lattice Boltzmann models. The good agreement between the experimental and numerical data confirm the validity of the proposed rescaling with the effective Capillary number.

Figure 1

Images of droplet breakup at the microfluidic T-junction in the Newtonian (left, liquid N3 of Table 1 is shown) and shear thinning (right, X400 of Table 2 is shown) continuous phase. The inlets of the junction have the same width $W$ and the same height; the dispersed phase enters in the junction from the top with flow rate $Q_d$, the continuous phase comes from the left side with flow rate $Q_c$. The length $L$ of the droplets is measured by real-time image processing while they cross a rectangular window (the dashed contour) positioned downstream of the junction. Droplets are formed in squeezing [see snapshots (a) and (f)], dripping [(c) and (h)], or jetting [(e) and (j)] regimes. Snapshots [(b) and (g)] and [(d) and (i)] outline the emergent dripping and jetting regimes respectively.

Figure 2

Normalized, dimensionless length $L/W$ of the droplets formed at the microfluidic T-junction as a function of either the flow rate of the continuous phase $Q_c$ [top axis of panels (a)–(e), bottom axis of panels (g)–(i)] or the corresponding Capillary number $\mathrm{Ca}$ [bottom axis in panels (a)–(e)] for different values of the flow-rate ratio $\phi$, indicated by different symbols according to the legend reported in panel (f). Panels (a)–(e) refer to the Newtonian fluids listed in Table 1, while panels (g)–(i) correspond to the polymers listed in Table 2. Open circles mark the flow rate $Q_c^{*}$ corresponding to the onset of the jetting regime, accordingly to the maps shown in Fig. S1 of the SM [34].

Figure 3

Experimental (top, white panels) and numerical (bottom, orange panels) normalized droplet length $L/W$ as a function of the flow rate of the continuous phase $Q_c$ (left column) and the effective Capillary number $\overline{\text{Ca}}$ defined in Eq. (4) (right column), for different values of the flow-rate ratio $\phi$, which is increasing from top to bottom. All the graphs are in log-log scale. Open symbols refer to Newtonian fluids, filled symbols of the experimental graphs to shear thinning Xanthan solutions at different concentrations, filled symbols of the numerical graphs to power-law fluids with different flow behavior indexes $n$. The line is a power-law fit to the experimental data, with fitting parameters reported in Table 3.

Figure 4

Snapshots of the droplet formation process in numerical simulations with LBM, reporting two representative situations before (left column) and after (right column) the breakup process has occurred. 3D snapshots are overlaid on the velocity vector field evaluated on a slice located at half of the channel height. The flow-rate ratio is kept fixed to $\phi =0.5$ and the flow rate in the continuous phase to $Q_c=1.23$ lbu. Different power-law exponents are used: Newtonian fluid $[n=1$, panels (a) and (b)], thinning fluid with thinning exponent $n=0.9$ [panels (c) and (d)], and $n=0.75$ [panels (e) and (f)]. The corresponding stress is reported in Fig. 5. Time is made dimensionless using the shear time ${\tau }_{\mathrm{shear}}=W/U_{av}$.

Figure 5

Viscous stress evaluated from the velocity profiles shown in Fig. 4. Further information is provided in the movies of the SM.