PHYSICAL REVIEW LETTERS week ending VOLUME 92, NUMBER 5 6 FEBRUARY 2004 Vorticity Alignment and Negative Normal Stresses in Sheared Attractive Emulsions Alberto Montesi, Alejandro A. Pen˜a,* and Matteo Pasquali† Department of Chemical Engineering, Rice University, 6100 Main Street, Houston, Texas 77005, USA (Received 13 June 2003; published 6 February 2004) Attractive emulsions near the colloidal glass transition are investigated by rheometry and optical microscopy under shear. We find that (i) the apparent viscosity drops with increasing shear rate, then remains approximately constant in a range of shear rates, then continues to decay; (ii) the first normal stress difference N1 transitions sharply from nearly zero to negative in the region of constant shear viscosity; and (iii) correspondingly, cylindrical flocs form, align along the vorticity, and undergo a log- rolling movement. An analysis of the interplay between steric constraints, attractive forces, and composition explains this behavior, which seems universal to several other complex systems. DOI: 10.1103/PhysRevLett.92.058303 PACS numbers: 83.80.Iz, 83.50.Ax, 47.55.Dz Emulsions are relatively stable dispersions of drops of a Rheological measurements were carried out in a liquid into another liquid in which the former is partially strain-controlled rheometer using several geometries [1]. or totally immiscible. Stability is conferred by other Microscopic observations were performed using a cus- components, usually surfactants or finely divided solids, tomized rheo-optical cell consisting of two parallel which adsorb at the liquid-liquid interface and retard glass surfaces, with the upper one fixed to the micro- coalescence and other destabilizing mechanisms. scope (Nikon Eclipse E600) and the lower one set on a Emulsions can be regarded as repulsive or attractive, computer-controlled xyz translation stage (Prior Proscan depending on the prevailing interaction forces between H101). The glass surfaces were rendered hydrophobic to drops. In repulsive emulsions, droplets repel each other at prevent adhesion and spreading of water drops. All tests any center-to-center distance. On the other hand, attrac- were performed at 25:0 0:1 C. tive emulsions exhibit a potential well at a given distance Figure 1 shows plots of shear viscosity vs shear rate that exceeds the energy associated with random thermal _ for four water-in-oil emulsions with increasing vol- fluctuations. Consequently, drops in attractive emulsions ume fraction of the dispersed (water) phase . Emulsions form flocculates and gel-like structures, whereas droplets with 0:09, 0.32, and 0.73 exhibited a monotonic in repulsive emulsions do not. This Letter describes for viscosity decay characteristic of flocculated emulsions the first time unusual rheological and microstructural [2]. The shear thinning is related to the progressive features in emulsions under shear, such as alternating breakdown of flocs at low capillary number Ca changes in the sign of the first normal stress difference oil R=_ 1 and to the deformation of drops at mod- with increasing shear rate and formation of domains of erate Ca. The raise in with is a well-known effect drops that align perpendicularly to the direction of shear- caused by an increase in the population of droplets, ing. It is shown that these features result from the inter- which leads to higher hydrodynamic interactions among play between composition and attractive forces between drops and higher resistance to flow. The viscosity of the droplets. Significant similarities between these trends emulsion with 0:58 first decreased with increasing and those reported for different systems, such as liquid- crystalline polymers, colloidal suspensions, and poly- 1000 meric emulsions, are also mentioned. φ = 0.73 φ Experiments were performed on emulsions of bi- = 0.58 100 φ = 0.32 distilled water dispersed in a lubricant oil base provided φ 3 = 0.09 by Exxon Chemicals (oil 871 kg=m , oil 91 mPa s at 25 C, water=oil viscosity ratio 0:01). The emulsions 10 were stabilized using the nonionic surfactant SPAN 80 (Pa s) (sorbitan monooleate, Sigma) at a concentration of 5 wt %. η The interfacial tension was 1:3mN=m. Emulsification 1 was carried out by mixing in 1-in. diameter cylindrical plastic container and blending with a two-blade paddle for 10 min at 1500 rpm. Drops in these emulsions (mean 0.1 0.1 1. 10 100 radius R 8 m, geometric standard deviation 0:15) γ (1/s) form flocs due to micellar depletion attractions, because the concentration of surfactant is well above the critical FIG. 1. Steady shear viscosity of water-in-oil attractive emul- micellar concentration (<1wt%). sions at several water contents (large concentric cylinders). 058303-1 0031-9007=04=92(5)=058303(4)$22.50 2004 The American Physical Society 058303-1 PHYSICAL REVIEW LETTERS week ending VOLUME 92, NUMBER 5 6 FEBRUARY 2004 shear rate (6 10ÿ5 < Ca < 6 10ÿ4), then remained involves the formation of domains with characteristic size relatively constant (610ÿ4 <Ca<610ÿ3), and then influenced by the gap size. ÿ3 continued to diminish (6 10 < Ca < 0:3). This Figure 3 shows and N1 as a function of the effective _ trend has been reported, but not explained, in a few between parallel plates for an emulsion with 0:58. N1 attractive emulsions [3]. Here we explain the microstruc- evolved from nearly zero to negative, then from negative tural mechanism of the transition in the trend of ,the to positive as _ was increased; the sharp transition to corresponding anomalous behavior of N1, and the depen- negative values of N1 occurred concomitantly with the dence of these phenomena on the composition of the plateau in at each gap size. Experiments with the cone- emulsion. and-plate geometry (CP), where _ is uniform across the The rheological behavior of an emulsion made of two sample, showed the same effects. Table I reports the Newtonian liquids shifts from viscous to predominantly minimum value of negative normal stresses N1;min as a elastic because of changes in the arrangement of droplets function of the gap between the parallel plates, together from dilute (uncaged) to caged, to packed, to compressed with the measurement obtained with the CP geometry. as the volume fraction of internal phase grows [4]. In N1;min was always negative and above the sensitivity of dilute emulsions viscoelasticity may arise from the de- the instrument and grew with decreasing gap. formation of the interfaces of drops [5]. At the colloidal The same trends in N1 reported in Fig. 3 were also glass transition ( g 0:58), droplets are caged in- observed in tests on emulsions with 0:52 and 0.62, definitely by their neighbors and random thermal fluctua- with comparable minimum values of N1 (also shown in tions do not disrupt such cages. The volume fraction for Table I). At 0:73 and 0.75 the transition to negative close packing of monodisperse hard spheres cp ranges N1 was much less pronounced and observed in a much between 0.64 (random packing) and 0.74 (ordered pack- narrower region of effective _ . Emulsions with 0:32 ing). When >cp, the interfaces deform due to com- did not exhibit any of these features, and N1 ’ 0 at all _ . pression of drops against drops. Figure 1 shows that a These results indicate that the onset of negative N1 is region of constant occurs for attractive emulsions in the favored by the caged configuration that droplets adopt transition from uncaged to compressed. The effect is most near the glass transition. The data reported in Fig. 3 and pronounced when g. Table I were obtained after preshearing the emulsion for Figure 2 shows the shear viscosity of emulsions at 60 s at _ 100 sÿ1. This protocol was adopted to im- 0:58, measured with concentric cylinders (CC) and par- prove the reproducibility of N1 measurements. We ob- allel plates (PP) at several gaps. A region of constant served similar trends for N1 in emulsions that were not viscosity was observed in all cases. The range of shear presheared, but the reproducibility of N1 values was poor. rates in which such a phenomenon was observed shifted We have also formulated and tested repulsive emulsions toward higher _ as the gap size was reduced. Figure 2 also with anionic surfactants that matched the composition, shows that remained constant in a wider range of _ at a the viscosity ratio of the phases, and the interfacial ten- narrower gap. Noticeably, the shear stress in the region sion of the attractive emulsions studied here. The effects of constant always ranged between 6 and 30 Pa, inde- described above were not observed in such repulsive pendently of geometry and gap size. This suggests that the emulsions, thus confirming the key role of attractive onset of a plateau in is related to changes in the micro- forces. structure of the emulsion and that the structural transition 10000 100 1000 f = Gap = 1.00 mm CC 100 Gap = 0.25 mm 70 1000 10 100 |N 1 100 f = (Pa) | s) . a Gap = 1.00 mm 1 (Pa s) (P PP Gap = 0.50 mm η η . 0.4 Gap = 0.25 mm 1 10 f 10 0.2 1 0.1 1 0.01 0.1 1 10 100 1000 0.1 . γ 0.1 1. 10 100 (1/s) γ (1/s) FIG. 3. Shear viscosity (squares) and magnitude of the first FIG. 2. Effect of gap on shear viscosity of emulsions with normal stress difference (circles) vs shear rate in an emulsion 0:58 for two geometries. The plots are shifted by a factor with 0:58 (parallel-plate geometry, gap 0:65 mm). of f (indicated for each curve) to facilitate interpretation.