Transitions to vibro-fluidization in a deep granular bed Kenneth J. Ford ⁎, James F. Gilchrist, Hugo S. Caram Department of Chemical Engineering, Lehigh University, Bethlehem, PA,18015, USA abstract article info Article history: Received 18 December 2007 Received in revised form 2 November 2008 Accepted 14 November 2008 Available online 16 December 2008 Keywords: Granular media Vibro-fluidization Quasi-static Deep granular bed Vane granular state State transitions Vibration Power Torque Rheology Hysteresis Granular media subjected to vibration can approximate fluid behavior with sufficient vibration acceleration. Unlike gas fluidization, the transition from a static bed to a liquid-like state is poorly defined and has primarily studied previously in shallow or 2D granular beds. Three granular states are identified in this work: the static, the quasi-static, and the vibro-fluidized state. These states are characterized for a deep granular bed through quantitative measurements of the power or torque required to rotate a vane within the granular media. In this study, the vane is rotated while the bed is subjected to vibration at 10 Hz with acceleration in the range 0 ≤ Γ = ω 2 x max /g ≤ 4.0. We define a critical dimensionless vibration acceleration, Γ c , based on a dramatic decrease in vane power and the absence of a dynamic zero-shear rate torque, as the transition to vibro-fluidization. Typical of granular materials, significant hysteresis is observed in measuring these bed state transitions. These measurements of “granular rheology” provide a quantitative framework for defining these transitions. © 2008 Elsevier B.V. All rights reserved. 1. Introduction Considerable recent work has focused on the phase behavior and dynamics of granular materials and significant progress has been made [1]. The lack of constitutive equations to describe phase behavior and kinematics has led to an array of simulation and experimental techniques to determine the granular state [2–5]. This paper focuses on the granular bed phase behavior and kinematics that are of interest to industrial granular processes by adapting a vane shear experimental technique commonly used to test static soil samples to measure the state of a dynamic, vibrated deep granular bed. For many processes in the pharmaceutical, food/beverage, cosmetic, chemical, petroleum, polymer and ceramic industries, the goal is to achieve or maintain homogeneity of many granular ingredients during processes such as agglomeration, feed stream transport, chemical reactions, coating and others. Knowledge of the granular bed properties and state of the bed is crucial, therefore many experimental methods have been developed including: Bed dilation measurement [6], shear cells [7,8], solid objects moving through the bed [9], couette devices [10– 15], and rotating/oscillating rods [16–19] or impellers [20–22] and visual measurements of velocity and segregation [23–29]. The idea of characterizing granular rheology to better understand the behavior of these materials is controversial. While a major effort is underway to derive constitutive equations that describe the kinematics of these materials, there is still a great demand for simple experiments to catalog fundamental granular behavior. The deep granular bed in this paper experiences three phases or granular bed states: The static dense granular state when no granular rearrangement is present, a quasi-static granular state having a finite yield stress or zero shear-rate torque for vibration below a critical dimensionless vibration amplitude, Γ c , and a vibro-fluidized state above Γ c . A vane probe is used to measure the granular bed state under dynamic vibrated conditions. The vane was chosen for two reasons. Vanes are common in rheological measure- ments [30], akin to using cone-and-plate, cup and bob and Couette geometries to isolate the material performance upon deformation. The use of vanes was derived from an existing standard in testing mechanical behavior of soil [31,32] or manufactured food [33–36]. The second reason for choosing a vane probe is its similarity to many industrial granular processing devices, such as those found in pharmaceutical high shear granulators. One can envision partially decoupling the rotational motion and vertical motion to explore various dynamics. When the vane is smaller than the granular bed diameter, as in this paper, the vane can be placed to sample subregions of the bed to probe local behavior. To date, granular bed vibration research primarily focuses on two dimensional [24,37–40] and three dimensional [25–27,41–46] shallow Powder Technology 192 (2009) 33–39 ⁎ Corresponding author. E-mail address: kenneth_ford@merck.com (K.J. Ford). 0032-5910/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2008.11.017 Contents lists available at ScienceDirect Powder Technology journal homepage: www.elsevier.com/locate/powtec