Scaling variation in the pinch-off of colloid-polymer mixtures

The scaling laws of drop pinch-off are known to be affected by drop compositions including dissolved polymers and non-Brownian particles. When the size of the particles is comparable to the characteristic length scale of the polymer network, these particles may interact strongly with the polymer environment, leading to new types of scaling behaviors not reported before.

Using high-speed imaging, we experimentally studied the time evolution of the neck diameter h_min of drops composed of silica nanoparticles dispersed in PEO solution when extruded from a nozzle.

After initial Newtonian necking with h_min ∼ t^2/3, the subsequent stage may exhibit scaling variation, characterized by either exponential or power-law decay, depending on the nanoparticle volume fraction ϕ. The exponential decay h_min ∼ e^-t/τ signifies the coil-stretch transition in typical viscoelastic suspensions. We conducted an analysis of the power-law scenario h_min ∼ t^α at high ϕ, categorizing the entire process into three distinct regimes based on the exponents α. The dependences of critical thicknesses at transition points and exponents on polymer concentration offer initial insights into the potential transition from heterogeneous to homogeneous thinning in the mixture. This novel scaling variation bears implications for accurately predicting and controlling droplet fragmentation in industrial applications.