The wall effect on the orientation of fibres in a shear flow Allan Carlsson 1 , Fredrik Lundell 1 and Daniel S¨oderberg 2 1 Department of Mechanics, School of Engineering Sciences Royal Institute of Technology, Stockholm, Sweden 2 STFI - Packforsk AB, Stockholm, Sweden ABSTRACT An experimental study concerning the orientation of fibres in a shear flow has been performed. The shear flow is gen- erated, by letting gravity drive a fibre sus- pension down an inclined plate. It is shown possible to influence the fibre orientation by modifying the surface structure of the inclined plate. ANNUAL TRANSACTIONS OF THE NORDIC RHEOLOGY SOCIETY, VOL. 14, 2006 INTRODUCTION The main intention of this study is to experimentally investigate the orientation of fibres, in a fibre suspension flowing close to a solid boundary. The fibre orientation has been determined in a plane parallel to the solid surface upon which the suspen- sion flows. Apart from performing exper- iments on a plain smooth surface, experi- ments has also been performed on a mod- ified structured surface, in order to see if this is a possible way of affecting the fibre orientation. The motion of an ellipsoid suspended in a laminar simple shear flow has been solved theoretically 1 . The expressions de- termining the motion are ˙ φ = - ˙ γ r 2 e +1 (r 2 e sin 2 φ + cos 2 φ) (1) ˙ θ =  r 2 e - 1 r 2 e +1  ˙ φ 4 sin2φsin2θ, (2) and are usually referred to as Jefferys equa- tions. The angles θ and φ are defined in Fig. 1. The shear rate is denoted by ˙ γ and r e is the aspect ratio of the ellipsoid, i.e. the length to diameter ratio. The motion is periodic and determined by the initial conditions. The period of the motion is T = 2π ˙ γ  r 2 e +1 r e  . (3) It has been shown possible to extend Jef- fery’s equations to be valid for any body with a fore-aft symmetry 2 , provided that an equivalent aspect ratio is found. In other words a relation must be found be- tween the aspect ratio of the particle r p and r e . It is thus possible to use the ex- pressions also for fibres. Experiments have been performed and have shown a good agreement with Jeffery’s equations 3, 4, 5 . However, no fibre-fibre interactions have been taken into account in Jeffery’s anal- ysis and there are no solid boundaries present. Experiments on a simple shear flow with a solid surface present have been performed 5 . In these studies the fibre ori- entation was measured in a plane perpen- dicular to the solid surface. In a region closer than one fibre length from the sur- face, it was concluded that Jeffery’s equa- tions could still be applied, provided that an effective increased shear rate was used. To the authors knowledge there is still a lack of experimental data dealing with the orientation of fibres in the plane parallel to a solid surface.