The Orientation Distribution Of Fiber Suspensions And Its Effect On The Constitutive Relationship

Understanding the physical properties of fiber suspensions is currently of great interest in many areas. Different from spherical particle suspensions, the properties of fiber suspensions mostly rely on the orientation distribution of fibers due to their slender bodies. It is important to study the particle orientation distribution of fibers suspensions during flows.In this thesis, the particle orientation distribution of fiber suspensions as well as the bulk stresses of fiber suspensions is investigated. Three cases are treated, i.e. (1) dilute planar converging channel flow in laminar regime; (2) semi-dilute planar shear flow in laminar regime; (3) dilute planar shear flow in turbulent regime.In the dilute planar converging channel flow in laminar regime, the orientation distribution function (ODF) and the orientation tensor are numerically simulated, and the effective viscosity of the fiber suspensions are obtained. The calculation shows that the transient orientation distribution of fibers is dependent of time and the velocity gradients of converging channel flows. The orientation distribution of fibers approaches the steady state with relatively short time. The time reaching steady state depends on the magnitude of velocity gradients. The steady viscosity distribution in whole flow field depends on the converging angles of flow fields, but not on Reynolds numbers.There are two parts in the semi-dilute planar shear flow in laminar regime. In the part one, the equation for ODF, which includes the orientation diffusion terms, is numerically calculated. In addition, the model of orientation distribution is modified by considering the normal stresses, whose effect is expressed in terms of effective stretch strains. The relationship between the orientation distribution and fiber concentrations is studied. The calculated results of the components of orientation tensor are well compared with others' experimental data. In the part two, an experiment on the viscosity of the semi-dilute suspensions of aspect ratio of 10 is performed. Combined with others' measurements of viscosity with different aspectratios, a new expression for the shear viscosity of semi-dilute fiber suspensions is proposed.In the dilute planar shear flow in turbulent regime, the mean equation for ODF is derived first time by using Reynolds averaging method. By obtaining the analytic result of the fluctuation equation for ODF, the correlation terms in mean equation are related to the terms of the mean ODF. Thus, a self-governed equation for the mean ODF in dilute fiber suspensions in turbulent regime is derived. The governing equation is numerically simulated in a pipe flow and a channel flow. Some of the calculated results are compared with the measured data in the literature. The results show that the orientation distribution is dispersed due to the randomizing effect of the turbulence, and become broader with the increases of Reynolds numbers, which indicates that the additional shear stress increases while the normal stress difference decreases.