I think the only useful quantity you can calculate from accurate radius measurement in a jammed channel is droplet volume. If you consult the old colloid literature where all those early colloid chemists, engineers, and physicists solved the Laplace curvature equations for pendant drops, AND you can also measure the curvature of the jammed droplets from the contact line on one side of the channel to the other, then you can probably determine the interfacial tension between the liquid and the water

If you can make such diameter measurements in the case of two plates compressing the liquid AND be able to measure the force needed to separate the plates, you might be able to access the interfacial tension. I only am sure of the case where a liquid in air is compressed between parallel plates, but cases corresponding to your situation may be in the literature. Here the Laplace equation has two radii of curvature, the large radius you measure and a much smaller one approximated by half the plate separation distance.

The geometry of squeezed bubbles (or droplets), including the apparent radius of curvature of the (apparent, 2D) vertices in terms of the surface tension and of the gap between both plates is discussed incidentally in this publication of mine, hope you find what you need: https://www.researchgate.net/publication/49773321_Rapid_Plateau_border_size_variations_expected_in_three_simple_experiments_on_2D_liquid_foams

Article Rapid Plateau border size variations expected in three simpl...