Abstract

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. Furthermore, this work demonstrates that the dynamics of bubble formation along with the bubble waiting time are very sensitive to small perturbation in the physical properties of the liquid, and this sensitivity has a significant effect on the observed chaotic behaviour.

Highlights

  • 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

  • The results show that the influence of surface tension on bubble departure frequency is insignificant

  • Experiments to determine the influence of small changes to water hardness on the nonlinear behaviour of liquid penetration into a capillary and air pressure fluctuations during subsequent bubble departures were conducted, and the results compared favourably to model predictions

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Summary

Introduction

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. From the many investigations into the chaotic nature of bubble ­departure[5,6,11,12,13,14,15,16], it can be concluded that two groups of phenomena are responsible for the occurrence of chaotic bubble departures: the particular dynamics of the bubble flow in the liquid as well as the hydrodynamics of liquid flow around the c­ apillary[5,6,11,14,15,16,17,18] and the erratic changes of pressure in the gas supply system that accompany this ­flow[5,11,12,19,20,21]; these phenomena are associated with the nonlinear dynamics of the capillary filling process These dynamics are sensitive to the physical and chemical properties of the two-phase system, notably the viscosity and surface tension, as well as to the container geometry, and have been previously ­investigated[21]. The bubble growth time depends on the forces acting on the growing bubble; these forces include the drag f­orce[22], the buoyancy f­orce[23], the surface tension

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