Experimental study of forces between quasi-two-dimensional emulsion droplets near jamming

We experimentally study the jamming of quasi-two-dimensional emulsions. Our experiments consist of oil-in-water emulsion droplets confined between two parallel plates. From the droplet outlines, we can determine the forces between every droplet pair to within 8% over a wide range of area fractions $ϕ$. We study three bidisperse samples that jam at area fractions $ϕ_c \approx 0.86$. Our data show that for $ϕ> ϕ_c$, the contact numbers and pressure have power-law dependence on $ϕ-ϕ_c$ in agreement with the critical scaling found in numerical simulations. Furthermore, we see a link between the interparticle force law and the exponent for the pressure scaling, supporting prior computational observations. We also observe linear-like force chains (chains of large inter-droplet forces) that extend over 10 particle lengths, and examine the origin of their linearity. We find that the relative orientation of large force segments are random and that the tendency for force chains to be linear is not due to correlations in the direction of neighboring large forces, but instead occurs because the directions are biased towards being linear to balance the forces on each droplet.

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