Abstract
Describing the orientation state of the particles is often critical in fibre suspension applications. Macroscopic descriptors, the so-called second-order orientation tensor (or moment) leading the way, are often preferred due to their low computational cost. Closure problems however arise when evolution equations for the moments are derived from the orientation distribution functions and the impact of the chosen closure is often unpredictable. In this work, our aim is to provide macroscopic simulations of orientation that are cheap, accurate and closure-free. To this end, we propose an innovative data-based approach to the upscaling of orientation kinematics in the context of fibre suspensions. Since the physics at the microscopic scale can be modelled reasonably enough, the idea is to conduct accurate offline direct numerical simulations at that scale and to extract the corresponding macroscopic descriptors in order to build a database of scenarios. During the online stage, the macroscopic descriptors can then be updated quickly by combining adequately the items from the database instead of relying on an imprecise macroscopic model. This methodology is presented in the well-known case of dilute fibre suspensions (where it can be compared against closure-based macroscopic models) and in the case of suspensions of confined or electrically-charged fibres, for which state-of-the-art closures proved to be inadequate or simply do not exist.
Highlights
In processes involving fibre suspensions, predicting the evolution of particle orientation is critical since the rheology of the material and its final properties depend on the microstructure
Only the diagonal components of the orientation tensors are depicted: the solid colour lines correspond to the discrete orientation tensor using the confined kinematics Eq (16); the discontinuous colour lines to the discrete orientation tensor using Jeffery’s kinematics Eq (1); the discontinuous dashed colour lines correspond to the data-driven orientation tensor and the discontinuous grey lines correspond to the closure-based macroscopic models
Among the databases at our disposal, we identify the ones that best match the value of the current parameters (for example if (Nt, electric field intensity (Et)) = (225, 35) we keep the four databases built for N = 200 and 300 and E = 30 and 40 NC−1) and compute the weights needed for a bilinear interpolation of these results
Summary
In processes involving fibre suspensions ( e.g. composite manufacturing, papermaking, biological and pharmaceutical applications, food-processing and cosmetics industries, etc.), predicting the evolution of particle orientation is critical since the rheology of the material and its final properties depend on the microstructure. The time evolution of the second-order orientation tensor is readily obtained using Jeffery’s kinematics Eq (1). Closures for the sixth-order orientation tensor: such as LIN6, QUAD6, HYBR6 [Advani and Tucker (1990)], or even invariant-based fitted closures INV6 and IBF6 [Jack and Smith (2005, 2006)]. We propose a methodology aimed at providing data-driven macroscopic simulations of orientation kinematics that are cheap and closure-free. Its relevance is shown in the case of confined fibre suspensions, for which closures proved to be inadequate [Perez, Scheuer, Abisset-Chavanne et al (2016); Scheuer, Abisset-Chavanne, Chinesta et al (2016)] We apply this framework in a more complex case involving semi-concentrated suspensions of electrically-charged rods, for which no reliable macroscopic model is available.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
