  Citation: Yan, Y.; Helmons, R.; Schott, D. The Inﬂuence of Particle Size on Sliding Wear of a Convex Pattern Surface. Minerals 2022, 12, 139. https://doi.org/10.3390/ min12020139 Academic Editor: Konstantinos Komnitsas Received: 20 December 2021 Accepted: 21 January 2022 Published: 25 January 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional afﬁl- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). minerals Article The Inﬂuence of Particle Size on Sliding Wear of a Convex Pattern Surface Yunpeng Yan 1, * , Rudy Helmons 1,2 and Dingena Schott 1 1 Department of Maritime and Transport Technology, Delft University of Technology, 2628 CD Delft, The Netherlands; R.L.J.Helmons@tudelft.nl (R.H.); D.L.Schott@tudelft.nl (D.S.) 2 Department of Mineral Processing and HSE, Norwegian University of Science and Technology, 7031 Trondheim, Norway * Correspondence: Y.Yan@tudelft.nl Abstract: Sliding wear of bulk handling equipment (e.g., shovel bucket, mill and transfer chute) can be dramatically reduced by using a convex pattern surface compared to a ﬂat surface, by adjusting the ﬂow behavior of particles moving along the convex pattern surface. To study the effect of particle size relative to the dimensions of the convex pattern surface, a coarse graining technique is applied. Comparisons of bulk ﬂow and wear behavior between the convex pattern and ﬂat surfaces illustrate the two-sided effect of the convex pattern surface on sliding wear. The bulk ﬂow behavior indicates that the particle size has a minor effect on the velocity and angular velocity of particles for the ﬂat surface, while it has a signiﬁcant effect on those of the convex pattern surface. The wear results show that the particle size has negligible inﬂuence on the sliding wear of a ﬂat surface and a linear relationship with the sliding wear of the convex pattern surface. The convex pattern surface can reduce the sliding wear through inﬂuencing the ﬂow behavior of the bulk material when the equivalent radius of the convex is larger than r 50 of particles. This research reveals the relationship between the dimensions of the convex pattern and the particle size on the sliding wear caused by the interaction between bulk material and bulk handling equipment. The relationship should be carefully considered for the applications of the convex pattern surface to bulk handling equipment. Keywords: particle size; coarse graining; sliding wear; convex pattern surface; interaction 1. Introduction The handling of bulk solids plays an important role in a variety of industries, such as the mining, agricultural, chemical, and pharmacological industries [1]. For the mining industry, the process of transferring bulk solids leads to surface wear of shovel buckets [2]. The vertical stirred mills are applied widely in mineral industries and the liner wear plays a signiﬁcant role in the maintenance and operational costs [3]. Severe wear has been found in several locations on bulk handling equipment, for example, silo walls and bottom sections of the transfer chute [4]. For transfer chutes, studies show that approximately 82% of the energy losses are attributed to the bulk material sliding along the bottom of the chute, and 9% of the losses are due to sliding against the side walls [5]. To reduce the wear caused by the interaction between bulk material (e.g., soil and iron ore) and equipment surface (e.g., shovel bucket and transfer chute), scientists have proposed biological wear-resistant surfaces inspired by the contacts between biological surfaces and the corresponding living environments. Inspired by the bionic design method, a convex pattern surface is introduced [6] and optimized [7] to reduce the sliding wear of the surfaces of bulk solids handing equipment by using a discrete element method (DEM). Many works [8–16] have been completed on the investigation of sliding wear caused by the bulk material based on the DEM method, while other studies [9,11–14,16] whilwhile seldom focused on the inﬂuence of particle size on sliding wear. Although the previous studies have shown that the convex pattern surface can signiﬁcantly reduce sliding wear Minerals 2022, 12, 139. https://doi.org/10.3390/min12020139 https://www.mdpi.com/journal/minerals