Interfacial rheology of viscoelastic gel-like layers
Theodor D. Gurkov,1,* Boryana Nenova,1 Elena K. Kostova,1 and Wolfgang Gaschler2
1
Department of Chemical Engineering, Faculty of Chemistry, University of Sofia
James Bourchier Avenue 1, Sofia 1164, Bulgaria
2
BASF SE, Ludwigshafen am Rhein 67065, Germany
*e-mail: [email protected]
Partially entangled layers on fluid interfaces (containing proteins, polymer mixtures,
particles, etc.) often exhibit rheological behavior which resembles that of a solid or gel-like
material. It can manifest itself as visco-elasticity [1]. Here we take into account the presence
of irreversibly adsorbed molecules (insoluble in the bulk phase, or engaged in a network-type
structure on the surface). Such molecules contribute to the stress via mechanical elasticity.
We investigate air/ water interfaces covered by a mixture of an anionic surfactant and a
polymer (starch) with cationic groups. Periodic deformations of expansion/ compression are
applied by means of a Langmuir trough, with approximately constant rate of strain.
The time dependence of the strain during the oscillatory deformation is represented by an
explicit function, using expansion in Fourier series. This strain function is inserted into the
constitutive equation that pertains to a particular rheological model. The stress response, as
predicted by the theoretical model, is calculated and compared with the experimentally
measured stress – strain curve. The best fit (Fig. 1) gives values for the material parameters of
the layer. Such are, e.g., the Gibbs elasticity (due to the presence of adsorbed surfactant
molecules that can be exchanged with the adjacent bulk solution, or can escape out of the
planar layer), the mechanical elasticity (due to irreversibly adsorbed molecules), the
“apparent” viscosity (related to the mass exchange, depending on the deformation rate).
1.5
τ = σ(γ)−σ(0)
1.0
experiment
model fit
0.5
0.0
-0.5
-1.0
-1.5
-0.10
-0.05
0.00
0.05
0.10
γ = ln(A / A 0 )
Figure 1. Fit of stress response to oscillations, using a rheological model with two elasticities
and one viscosity.
We discuss the applicability of different variants of rheological models; the layer properties
are explored at different density (surface pressure). The rheological parameters of the material
are interpreted in terms of the molecular processes of exchange between the interface and the
contiguous sub-surface.
[1] Gurkov, T.; Petkov, J.; Campbell, B.; Borwankar, R. Dilational and shear rheology of protein
layers at the water-air interface, in: Food Colloids, Fundamentals of Formulation (E. Dickinson, R.
Miller, Eds.), Royal Soc. Chem., Cambridge, UK, 2001, 181-190.