Polymer stabilized emulsions are commonplace in industries ranging from cosmetics and foods to pharmaceuticals. Understanding the physical properties of emulsions is of critical importance to the rapid advancement of industrial applications. In this work, we use a sessile drop geometry to examine the effects of viscosity changes of the surrounding glycerine/water solution on polystyrene-b-polyethylene oxide (PS-PEO) covered toluene droplets. In the experiment, emulsion drops are driven by the buoyant force into a smooth mica surface. The drops buckle as they approach the mica, trapping some of the outer fluid which slowly drains out over time. The characteristic time of the drainage process as well as the surface tension was measured as a function of glycerine/water concentration. The surface tension is found to have a minimum at a glycerine concentration of approximately 50% (by weight to water) and the drainage rate is shown to be well described by a recent model. The simple experiment not only shows how critical features of emulsion stability can be easily and reliably measured, but also identifies important new features of the drainage process.