Detachment velocity: A borderline between different types of particulate plugs Anubhav Rawat a, ⁎, Haim Kalman a,b a The Laboratory for conveying and Handling of Particulate Solids, Department of Mechanical Engineering, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel b Aaron Fish Chair in Mechanical Engineering – Fracture Mechanics abstract article info Article history: Received 20 March 2017 Received in revised form 21 June 2017 Accepted 10 August 2017 Available online 12 August 2017 Shaul & Kalman (2014–2015) defined three different types of plugs (Plug-I, II and III) of different particulate materials for dense phase pneumatic conveying. The Present experimental study is undertaken to determine the borderline between Plug-I and the other type of plugs. The borderline is established by using the concept of detachment velocity of the particles from the front of the plug. For the current study, thirty three particulate materials have been tested having the Archimedes number (Ar) in the range of 10 -3 to10 6 . The experiments conducted in three transparent Plexiglas pipes of diameters 1 in., 2 in. and 3 in. For each experiment, a single artificial plug of type I of varying length in the range of 10–100 cm was inserted into the test section of 1.5 m length. Further, as the plug flow is a low velocity phenomenon, the Reynolds number (R e ) during experimenta- tion, is varied in the range of 10 -3 to 10 2 . The results of the experiments show that for the particulate materials with Ar N 10 2 , first the phenomenon of detachment occurs at a corresponding velocity and on further increasing the flow rates the plug dissembled. The variation of the detachment velocity is found to be a power function of the Ar number (for Ar N 10 2 ), whereas, the detachment velocity is found to be independent of the pipe diameter and plug length. For materials with Ar b 10 2 no detachment of the particles from the plug front is observed and the plug starts to move as Plug-I at a critical air flow-rate and a critical plug length corresponding to respective material. © 2017 Elsevier B.V. All rights reserved. Keywords: Dense phase pneumatic conveying Plug flows Detachment velocity Archimedes number Threshold velocity 1. Introduction Pneumatic conveying of powders through pipelines has been a prevailing practice for transportation in industries. It is done either in dilute phase or in dense phase. These days a shift towards dense phase transportation is observed due to its inherited advantages of low cost and low wear. The most widely used form of dense phase conveying is plug flows, which have an added advantage of low particle attrition along with the other advantages of dense phase pneumatic conveying. Since the inception of idea of dense phase plug conveying plethora of models have been given for plug flows [4–7]. They all have given theoretical models for the propagation of single plugs through pipelines and pressure drop prediction for the plugs convey- ing. Recently, Shaul & Kalman [1–3] defined three different types of plugs of particulate materials as shown in Fig.1 for plug flow mode of dense phase pneumatic conveying. First type (Plug-I) is the one in which the plug covers the whole pipe cross-section and does not leave any stationary particle either behind or in front. However, it may contain a slope of particles in front and rear of the horizontal plug. In the second type (Plug-II) a stationary layer of particles is left at the rear of the plug, while the next plug picks it up. Whereas, third type of plugs (Plug-III) are the small plugs that move over a stationary bed of particles. Shaul & Kalman also gave pressure drop prediction equations for all three types of plugs. The pressure drop required for Plug-I is: ΔP TypeI ¼ 2μ 2 w ρ b g tanθ þ μ w ρ b g þ 4C w D   e 4μ wkL D - 4C w D -μ w ρ b g 1-ε ð Þ4μ w k D þ ε L e 4μ wkL D -1   ; ð1Þ where, μ w is coefficient of wall friction, ρ b is bulk density of the material (kg/m 3 ), g is gravitational acceleration (m/s 2 ), θ is repose angle of plug (degrees), C w is wall cohesion coefficient (Pa), D is internal pipe diameter (m), k is stress ratio, L is plug length (m) and ε is void fraction. For developing the above equation Shaul and Kalman [3] used the force balance given by previous researchers [4,6,8,9–13] based on analysis of the forces acting on a differential slice of a plug of particulate materials by employing the field of solid mechanics. The forces which were considered by various researchers for force balance were; Pressure Stresses (ΔP), Normal Stresses (σ a ) and Wall Shear Stresses (τ w ). Shaul and Kalman [1] modified the force balance by dividing the pressure Powder Technology 321 (2017) 293–300 ⁎ Corresponding author. E-mail addresses: rawat@post.bgu.ac.il (A. Rawat), hkalman@bgu.ac.il (H. Kalman). http://dx.doi.org/10.1016/j.powtec.2017.08.043 0032-5910/© 2017 Elsevier B.V. All rights reserved. Contents lists available at ScienceDirect Powder Technology journal homepage: www.elsevier.com/locate/powtec