The objective of this project is to experimentally study the behavior of a flexible fibre in a shear flow. More simply, it will consist in making a fibre from a product used by dentists to make dental impressions. Then, we will then measure the Young's modulus of this fibre, characterize the shear flow by PIV (Particle Image Velocimetry) and finally observe the behavior of the particle when it is immersed in this flow using tracking methods.
Fibre-laden flows are encountered in the fabrication of several materials, including High Performance Fibre-reinforced Concrete (Fig. 1.(a), copyright: www.marseille-tourisme.com) and paper (Fig. 1.(b), copyright: Jan Homann, Wikipedia). Also, fibres are effective addictives which enhance the performance of simple and complex fluids where they are dispersed, such as water jets (Fig. 1.(c), (source: Karpikov, 2005)) and mascara (Fig1.(d), copyright: 3D Silk Fiber Mascara, Milky Spoon).
The theory of Jeffery (Jeffery, PRSA, 1922) still represents the most accurate description of the rotational dynamics of an ellipsoid or, through the equivalence of shape of Cox (Cox, JFM, 1971), a fibre suspended in a viscous shear flow. According to Jeffery and as confirmed experimentally in the following years (Taylor, PRSA, 1923; Trevelyan and S. G. Mason, JCS, 1951, Harris and Pittman, JCIS, 1974), an axisymmetrical particle under shear will determine a periodic dynamical system, where its extremities describe one out of infinite and equiprobable, closed orbits, i.e. the Jeffery orbits (see Video 1 for an example).
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As of today, the theory of Jeffery has been the foundation for the modelisation of the orientation of rigid fibres in turbulent flows, i.e. the flow regime of industrial interest (Parsa and Voth, PRL, 2014; Voth and Soldati ARFM, 2017; Shaik et al., PRF, 2020). Anyway, many questions concerning the particle dynamics still remain unanswered when fibres are not rigid but flexible, i.e. undergoing deformation within the flow.
The experiments of Forgacs and Mason, JCS, 1959 found that flexible fibres suspended in a viscous shear flow express a variety of different motions depending on the intensity ratio between the shear and the particle bending stiffness. Nevertheless, a lower viscous character of the fluid, and therefore a more intense inertial nature of the particles, could give raise to preferential dynamical states similarly to what suggested in the recent theoretical efforts of Dabade et al, JFM, 2016 and Einarsson et al., POF, 2016.
Therefore, this TAPIR aims at building a preliminary experimental characterisation of the rotation of flexible fibres suspended in a viscous shear flow, considering both a purely viscous and a small-inertial regime.
According to Jeffery, the period of rotation of a rigid axisymmetrical particle suspended in an unbounded viscous shear flow is:
Anyway, no model has been effectively derived for a flexible fibre, as previous experimental (Forgacs and Mason, JCS, 1959) and numerical (Zuk et al., JFM, 2021) could only identify universal features of the deformation of these particles within the shear flow. More in detail, Zuk and co-authors classified the possible deformation dynamics in terms of particle aspect ratio r and bending stiffness, finding that particles generally adopt one out of three possible configurations: coiled, locally bent and globally bent.
- Prepare the fibres for the experiments
- ⌛ Characterize the fibres: measurements of their shape, aspect ratio, density and Young's modulus.
- Prepare the fluids for the experiments: low and high viscosity;
- Characterize the fluids for the experiments: density and viscosity measurements;
- Characterize the viscous shear flow: PIV measurements;
- ⌛ Perform the experiments;
- Post-process the experiments: measurements of the orientation and deformation of the fibres;
- Anaylise the results and draw the conclusions (🥳).