Figure 2: Air bubbles coalescing in silicone oils.

(a) Neck radius versus time measured optically. The outer-fluid viscosity is varied across a wide range; μ_out=0.49–29,000 mPa s, while other parameters are held nearly constant (γ=15.9–21.5 mN m⁻¹, ρ=761–976 kg m⁻³, A=0.94 mm). (b) Data rescaled by the drop radius, A, and a timescale, τ_out. The rescaled data follow r(t)=(t/τ_out)^1/2 (dashed line). The small departure at late times occurs when finite-size effects should become important as the neck radius approaches the size of the drops. (c) Coalescence timescale, τ_out, versus μ_out (error bars are from the fits to the data in b). At high viscosity, τ_out is approximately equal to the viscous timescale of the outer fluid (solid line: τ_out=0.72τ_visc,out corresponding to C₁=1.2 in equation 2). At low viscosity, it is approximately given by the inertial timescale of the outer fluid (dashed line: τ_out=0.51τ_inert,out corresponding to D₁=1.4 in equation 3). The lines intersect at μ_out=99 mPa s (Oh_out=0.77).