Modification of Surface Tension in Aqueous Solutions of Sodium Oleate According to Temperature and pH in the Flotation Bath

The Influence of pH and Temperature on the Equilibrium and Dynamic Surface Tension of Aqueous Solutions of Sodium Oleate

“…Over a longer time period, the subsurface concentration will begin to approach bulk concentration and c s can be factored outside the back diffusion integral in Eq. [3]. Within this modified expression, as t approaches infinity, the integral approaches unity.…”

“…In this model, the surface is considered as a two-dimensional monolayer; boundary conditions for the derivation of Eq. [3] are c 0 = 0 at t = 0 and c s is constant at t → ∞.…”

“…At the very beginning of the diffusion process, there is little desorption from the surface to subsurface; the last term in Eq. [3] can be neglected. As a result, an approximate value of the surface concentration can be calculated from the equation…”

“…Owing to the convolution integral in the Ward and Tordai equation [3], which accounts for back diffusion, the equation cannot be solved. However, an asymptotic solution to this equation was recently derived, which is useful to describe the DST decay curves (23).…”

“…The influence of such complexes on the surface activity of the solution/vapor interface has been studied. Most important, the oleate solution shows a pronounced minimum in the equilibrium surface tension at a specific pH at constant bulk concentration (3). This minimum occurs in the neutral pH range but shifts significantly toward alkaline pH with an increase in bulk oleate concentration.…”