Forces between two oil drops in aqueous solution measured by AFM

Modelling drop-drop interactions in an atomic force microscope

“…We also examine in detail: the sensitivity of the force between drops to the boundary condition; the effects of the behaviour at the three-phase contact line during interaction; and the influence of the contact angle at the three-phase contact line. The following parameters were used: identical drops with radius R 0 = 40 µm , initial separation h 0 = 0.7 µm , maximum piezo displacement ∆X max = 0.9 µm , cantilever spring constant K = 0.028 N/m , concentration 9 mM sds, that gives a Debye length κ −1 of 3.2 nm and a surface tension of about 8 mN/m [5]. These values are representative of those in the experiments [5].…”

“…(2σ/R 0 ) is the Lagrange multiplier associated with the constant drop volume constraint and Π is the disjoining pressure. In the experiments of [5], a layer of adsorbed negatively charged surfactant on the drops produces a repulsive double layer disjoining pressure of the form Π(h) = w exp(−κh(r, t)) C810 where w = 64nkT tanh 2 (eψ 0 /4kT ) > 0 depends on the surface potential ψ 0 of the drops and κ = 2ne 2 / kT is the usual Debye-Hückel parameter that depends on salt concentration n.…”

“…Carnie et al [2] modelled the afm force measurement experiment between two drops in the experimental configuration of Dagastine et al [5]. The results demonstrated the combined effects of electrical double layer repulsion between oil drops charged by adsorbed surfactant, hydrodynamic repulsion and attraction arising from drainage of the aqueous film between the drops and drop deformation due to surface forces, hydrodynamic forces and surface tension.…”

“…Dagastine et al [5] measured the force between two approaching droplets of decane (≈ 40 µm radius) in an aqueous solution of sodium dodecyl sulphate (sds) in which one drop is attached X measures the distance between the piezo stage and some fixed platform, ∆s is the cantilever deflection, z(r, t) the drop height and h(r, t) the film thickness.…”

“…A characteristic feature in the measured forces between decane drops [5] is the dependence on the approach velocity V . At low velocities, the force law C808 is reversible, being the same on approach and retract, with an approximately constant compliance region.…”