The Influence of Water Hardness Perturbations on Bubble Departure Dynamics

The influence of small changes to water hardness on the nonlinear behaviour of liquid penetration into a capillary and the resulting air pressure fluctuations during air bubble formation are examined in this paper. Experiments were undertaken in which bubbles were generated both in water having a surface tensile force of σ  = 72.2 mN/m and in an aqueous solution of calcium carbonate having a surface tensile force of σ  = 75.4 mN/m, each contained in a glass capillary with an internal diameter of 1 mm. It is shown that both the maximum value of liquid penetration into the capillary and bubble growth time are affected by perturbations to the water hardness. The time it takes for the bubble to depart the capillary was estimated using the following nonlinear data analysis methods: time delay ( τ ), attractor reconstructions, correlation dimension ( D ), and largest Lyapunov exponent ( λ ). All estimates demonstrate that the pressure fluctuations in the c-c aqueous solutions and extent of liquid solution penetration into the capillary during the time between subsequent bubble departures behave chaotically.