Simple Models for Wall Effect in Fiber Suspension Flows

Abstract

Jeffery's equation describes the dynamics of a non-inertial ellipsoidal particle immersed in a Stokes liquid and is used in various models of fiber suspension flow. However, it is not valid in close neighbourhood of a rigid wall. Geometrically impossible orientation states with the fiber penetrating the wall can result from this model. This paper proposes a modification of Jeffery's equation in close proximity to a wall so that the geometrical constraints are obeyed by the solution. A class of models differing in the distribution between the translational and rotational part of the response to the contact is derived. The model is upscaled to a Fokker–Planck equation. Another microscale model is proposed where recoiling from the wall upon the collision is permitted. Numerical examples illustrate the dynamics captured by the models.

Local Distributions of Bubble Velocity and Interfacial Area in the Slender Particle-Containing Scrubbing–Cooling Chamber of an Entrained-Flow Gasifier

“…73 Although the increase of the fiber aspect ratio results in the decrease of fiber number density, the longer fiber lengths will make an increase in the number of small bubbles attaching to the fibers, thus reducing the velocity of the fiber-bubble agglomerate. In addition, the "pole vaulting" phenomenon 74 generated by slender particles will keep fibers away from the wall, which results in a decrease of small bubbles near the wall and the mean bubble velocity decreases correspondingly. For descending bubble velocity distributions shown in Figure 6b, the variations of the mean bubble velocity are consistent with those of rising bubbles in regions 1 and 3: the variation of the mean bubble velocity is inversely proportional to that of the fiber number density, which indicates that the movement of small bubbles is easy to be hindered by the fibers, resulting in a decrease in bubble velocity.…”

“…Although the increase of the fiber aspect ratio results in the decrease of fiber number density, the longer fiber lengths will make an increase in the number of small bubbles attaching to the fibers, thus reducing the velocity of the fiber-bubble agglomerate. In addition, the “pole vaulting” phenomenon generated by slender particles will keep fibers away from the wall, which results in a decrease of small bubbles near the wall and the mean bubble velocity decreases correspondingly.…”

Short fiber composite reinforcements

“…It is well-known that when fibres interact with a solid wall, departures from the Jeffery's trajectories and orbits are prone to occur (Moses et al, 2001). Few theoretical studies proposed modifications of Jeffery's equations to account for confinements and/or wall effects (Schiek and Shaqfeh, 1997;Ozolins and Strautins, 2014;Perez et al, 2016Scheuer et al, 2018, Laurencin et al, 2019. In these models, the particle rotary velocity is split into two terms: the Jeffery rotary component (equation (20.4)) and a confined component which depends on the type of flow and the position of touching walls.…”

A multi-scale description of orientation in simple shear flows of confined rod suspensions

“…While preparing this paper, it came to our attention that Eq. (12) had been derived independently in [26] using similar arguments but a different procedure.…”