On the use of rough geometries in rheometry Claudia Carotenuto, Mario Minale ⇑ Dept. of Industrial and Information Engineering, Second University of Naples, Real Casa dell’Annunziata, via Roma 29, 81031 Aversa (CE), Italy article info Article history: Received 5 February 2013 Received in revised form 29 March 2013 Accepted 2 April 2013 Available online 2 May 2013 Keywords: Wall slip Suspensions Rough surfaces Sandpapers Porous media abstract Multiphase fluids, like suspensions, often show wall slip. This is induced by depletion of particle concen- tration in proximity of wall surfaces. The rheometrical data can be corrected for wall slip in a post pro- cessing analysis. Alternatively, it is typically tried to suppress wall slip using modified devices, like rough geometries. We here investigate whether rough geometries themselves affect the rheological measure- ments. To this end, we glue sandpaper on the smooth surfaces of a plate–plate device. We use two com- mercial sandpapers and we measure five different Newtonian fluids proving that the fluids actually flow within the sandpaper roughness. This shows up as an apparent wall slip that we characterise. We, then, observe that the same happens also with a model suspension made of hollow glass beads in a Newtonian fluid. Finally, we propose two experimental procedures to correctly infer the rheological properties of a fluid when rough geometries are used. The first is more time consuming and accurate, the second is fast, only requires a single measurement and, in any case, is quite robust. Ó 2013 Elsevier B.V. All rights reserved. 1. Introduction When dealing with multiphase fluids like suspensions one often faces difficulties related to the so called ‘‘wall slip’’. It is an appar- ent discontinuity of the fluid velocity in proximity of a solid sur- face, i.e., macroscopically the velocity profile intersects a still solid surface at a finite velocity level. The physical origin of the apparent wall slip in multiphase fluids, like suspensions, is related to particles concentration depletion near the surface, as clearly shown in the sketch of Fig. 1a. Indeed, if the particles are homoge- neously distributed in the liquid, no elements can be centred at a distance from the surface smaller than the particle radius and thus the particle concentration must reduce while approaching the solid surface [1]. The suspension viscosity decreases as the concentra- tion decreases [2] and so, at a constant shear stress, the shear rate of the ‘‘depleted’’ layer adjacent to the surface can be much higher than that of the bulk causing the apparent wall slip [3]. This phe- nomenon can also be enhanced by the flow that may induce a migration of particles towards the low shear rate region, i.e., away from the solid surface [4]. Wall slip can be detected either directly, by looking at the periphery of the sample (e.g., [5]), with the NMR (e.g., [6]) or with laser doppler anemometry (e.g., [7,8]), or indirectly with rheologi- cal tests (e.g., [9–11]). In the latter case, in experiments conducted at a same stress, the measured viscosity varies with the imposed gap. Indeed, given the fluid and the measurement device, since the slip velocity is constant [12], the measured apparent shear rate increases as the gap decreases (Fig. 2). Consequently, the apparent viscosity, g A , hyperbolically decreases with the imposed gap, H [13] g A ¼ g H H þ h e ; ð1Þ where g is the material viscosity, g A is calculated as sH/V R (s is the imposed stress and V R the measured velocity of the instrument upper plate), and h e is the extrapolation length. The extrapolation length is shown in Fig. 2, it is independent of the gap size and repre- sents the distance between the lower plate and the point where the bulk velocity extrapolates to zero (h e ¼ V R = _ c  H). It is clear that the larger the gap, the smaller the viscosity reduction due to wall slip. To inhibit wall slip, or to reduce it, modified surfaces are typi- cally used. The basic idea is sketched in Fig. 1b: If rough surfaces are adopted, particles penetrate the roughness and the suspension solid concentration is approximately homogeneous beyond the envelope of the wall roughness. The fluid within the solid rough- ness is then considered not to move relatively to it and thus the wall roughness envelope forms an equivalent rigid boundary for the bulk fluid. The choice of the correct roughness is then very important and a practical selection criterion is to use a roughness equal to the maximum element size, for a material with a wide ele- ment size distribution, or to use a roughness equal to several times the element dimension, for a monodisperse material [12]. It must be said, however, that this criterion only gives a very qualitative indication to ensure that the particles effectively enter into the material asperities. Several roughed geometries have been pro- posed, like the so-called ‘‘serrated plates’’, ‘‘grooved plates’’ or ‘‘rough plates’’. An alternative cheap solution to the latters is to glue some sandpaper on each smooth plate. Beside the cheapness, 0377-0257/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jnnfm.2013.04.004 ⇑ Corresponding author. Tel.: +39 081 5010292; fax: +39 081 5010204. E-mail address: mario.minale@unina2.it (M. Minale). Journal of Non-Newtonian Fluid Mechanics 198 (2013) 39–47 Contents lists available at SciVerse ScienceDirect Journal of Non-Newtonian Fluid Mechanics journal homepage: http://www.elsevier.com/locate/jnnfm