, as the oil flowed downward, but it is order of a few hun-1023 dreds of micrometers when the emulsion drop is placed 1024 above it. However, this does not affect our qualitative obser-1025 vations: as the sample moves downward it seems to, The thickness of this layer could not be 1021 controlled, and it continuously decreased in time during the 1022 test
, Under these conditions, considering that there remains an 1031 oil layer of thickness of the same order as the usual slip 1032 layer, due to the much larger viscosity of the oil, its contribu-1033 tion to slip will be much weaker (for the same stress) than 1034 that of water, and we can conclude that wall slip is still gov-1035 erned by a slip layer roughly similar to the standard one 1036
, Indeed, as a first approximation, 1039 we can describe the process as the squeeze flow of a fluid 1040 layer between two disks of radius R situated at a distance b 1041 and approached to each other with a normal force F, More surprising is the removal of the oil layer between 1038 the emulsion and the wall
, This means that the oil 1050 layer cannot be removed by this simple effect. This suggests 1051 that there is a kind of attraction between the elements (drop-1052 lets) of the material and the solid surface, which tends to 1053 further push away the oil. This implies that in any case, some 1054 droplets will be positioned at a very short distance from the 1055 wall, and this effect plays a critical role in wall slip. our 1098 case. Here, in some cases, we observe a (nonphysical) more 1099 significant increase of the velocity toward the outer cylinder 1100 which a priori reflects the uncertainty on NMR measure-1101 ments. For larger rotation velocities, the evolution of the 1102 velocity profiles is completely different: there is now a 1103 sheared region along the inner wall, which grows in size as 1104 the velocity is increased, while the unsheared region progres-1105 sively disappears; at the same time, there is still some wall 1106 slip along each wall (see Fig. 17)
, We can now compare the slip velocity observed in the
, This is done by 1112 extracting the slip velocity (at both walls) from the profiles 1113 and associate them with the stress along each wall deduced 1114 from the torque measured from independent similar rheomet-1115 rical tests with the same geometry in a rheometer. We see 1116 that the slip velocity observed in both cases in the non-1117 yielding regime, Couette cell from NMR measurements with those deduced 1111 from rheometry in the nonyielding regime
, From direct measurements, Princen found that f varies concentrations. 1241 This is in total disagreement with our data (and those of
even if he did not withdraw the apparent slip yield 1243 stress), we essentially find no impact of the concentration of 1244 the emulsion ,
, it is remarkable that for our emulsions, 1253 according to proposed estimations [41,43], we expect varia-1254 tions of the osmotic pressure by a factor of several tens when 1255 increasing the emulsion concentration between 72% and 1256 92%, whereas we did not notice any impact of concentration 1257 on the apparent slip thickness, On the other side, if we now just consider the standard 1251 models assuming a balance between attractive and repulsive 1252 forces (see above)
, 1261 for a stress larger than the yield stress and thus leading to an 1262 elongational flow, the wall slip characteristics change 1263 abruptly: the apparent liquid layer thickness turns to a value 1264 several orders of magnitude larger than that for the shear 1265 flow below the yield stress
, This means that in that case there is a kind of irreversible 1267 detachment of the elements from the wall, implicitly 1268 meaning that they were somehow attached in the previous sit-1269 uation. This kind of attachment is further supported by the 1270 inclined plane tests with an initial oil layer
, This suggests that there are significant van der Waals 1274 attractive forces between the droplets and the wall, which 1275 leads to push them to be in contact (in fact, at a distance of a 1276 few molecules) around some point of their surface. Although 1277 we must admit that we cannot fully explain the origin of this 1278 effect
, As a counterpart, the area concerned 1282 would be rather limited. The resulting apparent liquid layer 1283 thickness would vary with the number of contacts, and thus 1284 would only slightly vary when the concentration is varied in 1285 the range tested. Finally, this scheme would explain that the 1286 elements tend to be able to remove at large distance from the 1287 wall when some critical force has been applied. In contrast, 1288 there should be a significant dependence with the droplet 1289 size, since the number of contact points decreases with r À3 . 1290 Note that we indeed observed an increase in apparent slip 1291 layer thickness
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