Yield stress and elasticity influence on surface tension measurements
We have performed surface tension measurements on carbopol gels of different concentrations and yield stresses. Our setup, based on the force exerted by a capillary bridge on two parallel plates, allows to measure an effective surface tension of the complex fluid and to investigate the influence of flow history. More precisely the effective surface tension measured after stretching the bridge is always higher than after compressing it. The difference between the two values is due to the existence of a yield stress in the fluid. The experimental observations are successfully reproduced with a simple elasto-plastic model. The shape of successive stretching-compression cycles can be described by taking into account the yield stress and the elasticity of the gel. We show that the surface tension of yield stress fluids is the mean of the effective surface tension values only if the elastic modulus is high compared to the yield stress. This work highlights that thermodynamical quantities measurements are challenged by the fluid out-of-equilibrium state implied by jamming, even at small scales where the shape of the bridge is driven by surface energy. Therefore setups allowing deformation in opposite directions are relevant for measurements on yield stress fluids.
Yield stress fluids are widespread materials in everyday life, food industry, cosmetics, building industry, oil industry and many other fields. They are of a great interest because they have the property to flow only when the applied stress is greater than a critical stress called yield stress larson_structure_1999. They include emulsions, suspensions, gels, granular pastes and foams.
Their bulk properties have been studied extensively since the work of Herschel and Bulkley in 1926 herschel_konsistenzmessungen_1926 and are now well characterized coussot_yield_2014. Besides, capillarity and wetting are well known for simple fluids. Recently a lot of work has also been done on surface tension and wetting of soft solids mora_capillarity_2010; salez_adhesion_2013; weijs_capillarity_2014 and on the competition between capillary forces and elasticity of the substrate jerison_deformation_2011; marchand_capillary_2012. But until now few studies have focused specifically on the surface tension of yield stress fluids boujlel_measuring_2013.
However surface tension and wetting properties of yield stress fluids are of a great importance for capillary imbibition, coating, surface instabilities and adhesion, among other applications.
Here we explore the competition between surface tension, which is an equilibrium property to be measured, and yield stress effects that often keep the system out of thermodynamical equilibrium due to a dynamical arrest of flow. This situation can be compared to contact angle hysteresis: the contact angle is always smaller or greater than the equilibrium (Young) value, depending on the history of the contact line de_gennes_capillarity_2003.
Géraud et al. studied this competition in capillary rise experiments geraud_capillary_2014; this method allowed to measure the surface tension and the yield stress of the fluid at the same time. Yet, with their setup, a large amount of liquid is needed, the contact angle must be measured in another experiment, the results are extremely sentitive to the least defect on the inner surface of the capillaries and only fluids of low yield stress ( Pa) can be characterized this way.
The method presented here allows to get rid of these difficulties. Moreover both extension and compression of the system can be imposed, which highlights the effect of the flow history on the effective surface tension measured.
The article is built as follows. In the first part, we present the fluids on which we performed measurements and the experimental setup. Then we describe the experimental results and in the next part we compare them to an elastoplastic model using only few ingredients. Finally we discuss the agreement between the experiments, the model and results from other works.
Ii Materials and methods
The simple fluids used here are deionized water (18 M