# Experimental Observations of Heat-Assisted Boycott Effect in Trapezoidal Enclosures
## 1 Introduction  
Sedimentation is used in various fields. In medicine, it assists in the analysis of urine sediments, facilitating the diagnosis of kidney disease [1]. In engineering, sedimentation is crucial for the construction of equipment such as settling tanks and lamella sedimentation tanks, used in wastewater treatment and drinking water, among other applications [2, 3, 4]. The velocity of sedimentation and the resulting quality of the clear fluid are critical, significantly impacting the processing capacity of the settling apparatuses. This underscores the need for ongoing innovation to improve the sedimentation process and its efficacy. Ref. [5] made a significant discovery, noting that the sedimentation of blood cells in an inclined tube occurs faster than in a vertical tube. Subsequently, models were developed to explain this phenomenon, referred to as the Boycott effect. The initial model, designated PNK, sought to provide a physical explanation for the Boycott effect. It was named in reference to the works of [6; 7], who aimed to clarify this phenomenon through kinematic analysis. This kinematic model asserts that the sedimentation rate in an inclined receptacle depends on the sedimentation rate in a vertical receptacle, the aspect ratio, and the angle of inclination relative to the horizontal one. Later, dynamic models emerged, including those proposed by [8; 9]. These models treat the suspension and sludge layers as a Newtonian fluid. Furthermore, dynamic models addressed the effects of shear stresses on the sludge layer. In addition, refs. [10; 11] developed dynamic models that investigated the impact of shear stresses on the sludge layer. From an industrial perspective, sedimentation has been used in process equipment for several decades. In 1880, ref. [12] emphasized the importance of understanding the mechanisms underlying the sedimentation process. Ref. [13] discusses sedimentation under various proposals aimed at improving the design of sedimentation tanks. The author asserts that the fundamental principle for clarifying a fluid through sedimentation is that each sediment particle descends through the fluid at a rate influenced by its size, weight, and the fluid's viscosity. This concept parallels Stokes velocity in dynamic models, where studies such as [14; 15] consider a correction factor related to particle concentration, commonly referred to as the hindered settling factor. This factor addresses the interactions between particles. To improve the sedimentation process on the equipment, ref. [16] conducted preliminary tests in 1964 to assess the efficiency of tube configurations for the removal of sludge. The tests indicated that the sludge could be effectively removed by periodically draining the tubes when they were slightly inclined in the direction of flow. The optimal angle of inclination for the removal of the gravity sludge was identified as \(5^{\circ}\) with respect to the horizontal position, eliminating the need for a mechanical removal of the sludge. Subsequently, ref. [17] presented operational experiences related to water treatment plants. The authors described two primary configurations of sedimentation tubes: (A) essentially horizontal and (B) strongly inclined, both requiring a prior flocculation process and subsequent filtering of the particle-free liquid, referred to as overflow. They concluded that a dedicated sludge removal device was unnecessary for inclined tubes. They suggested that increasing the inclination of the tubes between \(45^{\circ}\) and \(60^{\circ}\) would facilitate the continuous gravity drainage of a sedimentable material. In addition, they observed that the efficiency increased as the slope angle increased from \(35^{\circ}\) to \(45^{\circ}\) but decreased with increasing angle. This indicates that the angle of the tube is a critical factor in optimizing the efficiency of the equipment.