Depletion forces in thin liquid films due to nonionic and ionic surfactant micelles

• Depletion force is a special case of oscillatory structural force at short distances.
• Analytical expressions for depletion force are available for hard-sphere particles.
• The osmotic effect of charged micelles is dominated by the dissociated counterions.
• We are dealing with electrostatic repulsion influenced by the depletion interaction.
• The theory agrees well with data for the thickness and contact angles of foam films.

The depletion force can be considered as a special (limiting) case of the oscillatory structural force at short distances between two surfaces. Here, we consider analytical expressions for the structural force in the depletion zone and compare their predictions with experimental data. In the case of particles that interact as hard spheres, an expression for the depth of the depletion minimum as a function of the particle volume fraction ϕ is available. This expression has been used to predict the rise of the contact angle α of plane-parallel foam films from nonionic surfactant solutions with the increase of surfactant concentration — a depletion effect due to the nonionic micelles, which can be treated as hard spheres. Further, knowing the theoretical α-vs.-ϕ dependence, from the experimental values of α the micelle aggregation number has been calculated, and the results agree well with data obtained by other methods. In the case of electrically charged particles, the depletion effect is strongly affected by the soft and long-range electrostatic repulsion. This interplay of electrostatic and depletion effects can be quantified by upgrading the Poisson–Boltzmann theory of electric double layer to take into account the presence of charged particles (macroions). The resulting theoretical model predicts the equilibrium thickness, h0, of plane-parallel films formed from micellar solutions of ionic surfactants in excellent agreement with the experiment.

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