# Experimental Observations of Heat-Assisted Boycott Effect in Trapezoidal Enclosures
## 1 Introduction
Some stability issues arise during sedimentation processes where the Boycott effect is applied, particularly at the interface between the particle-free layer and the suspension layer. This phenomenon has been studied by several authors. For instance, ref. [9] observed the mixing between these layers during their experiments with cocurrent, countercurrent, and crossflow feeding. This mixing was attributed to gravity waves developing in the upper part of the channel. One of their key conclusions was that a lamella settler should operate in a way that ensures the suspension layer descends through the channel without expanding. Ref. [18] conducted both theoretical and experimental studies on flow stability in lamella settlers operating under supercritical conditions, aiming to optimize their use in engineering applications. Their analysis indicated that for low angles relative to the horizontal (\(\theta\leq 10^{\circ}\)), instability is primarily driven by an inflection point caused by shear stress. Conversely, at higher angles (\(\theta>10^{\circ}\)), gravity becomes the dominant destabilizing mechanism. Notably, the critical angle between these mechanisms depends on the channel geometry, with a narrower spacing between plates (\(b\)) resulting in higher velocities and, thus, greater shear stresses. In addition, refs. [19; 20] performed linear stability analyses in batch cells (closed at one end), focusing on the interface between the particle-free layer and the suspension layer. Their models considered the continuity of stresses and velocities at the interface, along with no-slip conditions on the walls. Ref. [20] further demonstrated that very tall and narrow vessels significantly improve sedimentation rates and enhance the stability of inclined settler systems, consistent with earlier findings by [21]. Additional related works are discussed in the review by [22]. Research efforts aim to improve the efficacy of sedimentation processes. For example, refs. [23; 24] analyzed the efficacy of sedimentators by investigating the relationship between the concentrations at the inlet and outlet, evaluating various models and considering geometric influences. Modifications to sedimentation tubes have also been proposed, as documented in [25]. These modifications include inclined tubes with square cross sections. Furthermore, the work of [26] presents triangular section modules. Studies such as those by [27] assess the impact of incorporating an arched plate into the settling tank on the overall settling efficiency. Currently, computational fluid dynamics (CFD) techniques are increasingly utilized in simulating and enhancing sedimentation processes. An example of CFD application is found in the work of [28], who simulated modifications to the design of the sedimentation tank inlet by elongating the inclined section and connecting it to a vertical section. Furthermore, ref. [29] used a CFD simulation with two turbulence models in three feeding configurations to evaluate their impact on inclined plate sedimentators. The results were subsequently validated through experimentation. Although many studies use models based on the Navier-Stokes equations, there are works that employed the Lattice Boltzmann Method (LBM), such as the one conducted by [30], who studied the Boycott effect in a cell with different inclination angles and compared it with the predictions of the PNK model, showing good qualitative and quantitative agreements. Similarly, ref. [31] employed 2D CFD-DEM simulations to investigate sedimentation dynamics in inclined cells under various inclination angles. Their study included a comparison with the PNK model, observing the generation of local vortices during the early stages of sedimentation.