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The accurate description of the growth or dissolution dynamics of a soluble gas bubble in a super- or undersaturated solution requires taking into account a number of physical effects that contribute to the instantaneous mass transfer rate. One of these effects is the so-called history effect. It refers to the contribution of the local concentration boundary layer around the bubble that has developed from past mass transfer events between the bubble and liquid surroundings. In Part 1 of this work \citep{penas2016}, a theoretical treatment of this effect was given for a spherical, isolated bubble. Here, Part 2 provides an experimental and numerical study of the history effect regarding a spherical bubble attached to a horizontal flat plate and in the presence of gravity. The simulation technique developed in this paper is based on a streamfunction--vorticity formulation that may be applied to other flows where bubbles or drops exchange mass in the presence of a gravity field. Using this numerical tool, simulations are performed for the same conditions used in the experiments, in which the bubble is exposed to subsequent growth and dissolution stages, using step-wise variations in the ambient pressure. Besides proving the relevance of the history effect, the simulations highlight the importance that boundary-induced advection has to accurately describe bubble growth and shrinkage, i.e. the bubble radius evolution. In addition, natural convection has a significant influence that shows up in the velocity field even at short times, though, given the supersaturation conditions studied here, the bubble evolution is expected to be mainly diffusive.