Pressure-Driven Suspension Flow near Jamming Sangwon Oh, 1 Yi-qiao Song, 1 Dmitry I. Garagash, 2 Brice Lecampion, 3 and Jean Desroches 3 1 Schlumberger-Doll Research, One Hampshire Street, Cambridge, Massachusetts 02139, USA 2 Department of Civil and Resource Engineering, Dalhousie University, Halifax, Canada 3 Schlumberger, 1 Cours du Triangle, Paris la Défense 92936, France (Received 23 October 2014; revised manuscript received 15 January 2015; published 23 February 2015) We report here magnetic resonance imaging measurements performed on suspensions with a bulk solid volume fraction (ϕ 0 ) up to 0.55 flowing in a pipe. We visualize and quantify spatial distributions of ϕ and velocity across the pipe at different axial positions. For dense suspensions (ϕ 0 > 0.5), we found a different behavior compared to the known cases of lower ϕ 0 . Our experimental results demonstrate compaction within the jammed region (characterized by a zero macroscopic shear rate) from the jamming limit ϕ m ≈ 0.58 at its outer boundary to the random close packing limit ϕ rcp ≈ 0.64 at the center. Additionally, we show that ϕ and velocity profiles can be fairly well captured by a frictional rheology accounting for both further compaction of jammed regions as well as normal stress differences. DOI: 10.1103/PhysRevLett.114.088301 PACS numbers: 47.57.Gc, 47.80.Jk, 82.70.Kj Non-Brownian suspensions are known to exhibit jam- ming at a solid volume fraction ϕ m between that of a random loose packing ϕ rlp ≈ 0.55 and a random close packing ϕ rcp ≈ 0.64 [1]. The most recent direct measure- ment of the jamming limit for suspensions of monodisperse spheres, ϕ m ¼ 0.58–0.60 [2–4], confirms that ϕ m is below ϕ rcp , as previously suggested in [5]. However, the under- standing of the transition between the flowing state and the jammed state (also known as the quasistatic regime) remains incomplete. For example, particle migration toward the center line and the associated formation of a density gradient in pipe flow of suspensions have been observed since the early work of Cox and Mason [6–10]. But previous measurements, which can be reproduced by current suspension models accounting for shear-induced particle migration, are limited to bulk values ϕ 0 ≤ 0.45 (0.5 for slot flow [7]), significantly smaller than the jamming and the random-close-pack limits [9,11]. Furthermore, the small dimension of the centrally jammed plug (often comparable to the particle size) in these measurements does not allow for a clear resolution of the solid volume fraction and its variation across the plug, and, particularly, its relation to the jamming ϕ m and random-close-pack ϕ rcp limits. Granular rheology has been successful in explaining a wide range of dry granular flows using a friction law [a relation between the shear stress τ and the compressive particle stress normal to the slip plane, σ 0 n , via a friction coefficient μðI Þ¼ τ=σ 0 n ] and a solid volume fraction law [ϕ ¼ ϕðI Þ] formulated in terms of a dimensionless control parameter I. Defining I as the ratio of the microscopic to macroscopic time scales of particles’ rearrangement in dry granular flow [12,13] allowed its extension to Stokesian suspensions [2] using a microscopic time scale relevant to suspended particles. The resulting expression for a suspension viscous number is I ¼ η f _ γ =σ 0 n , capturing the competing effects of viscous shear stress in the fluid phase (η f _ γ , where η f is the base fluid viscosity and _ γ the shear rate) and of the particle stress normal to the flow. Universal relationships between ϕ, μ, and I have been found using particle-stress-controlled rheological measurements [2], see Fig. 1. These relationships indicate that ϕ approaches ϕ m as I goes to zero (i.e., when the suspension stops flowing, e.g., when σ 0 n becomes much larger than the viscous shear stress), while μ linearly decreases down to a finite value as ϕ reaches ϕ m . Lecampion and Garagash [14] suggested that μ could further decrease in the jammed region (where I ¼ 0) in relation to further slurry compaction from ϕ m to the random close packing limit ϕ rcp [14]. The underlying mechanism associated with the compaction of the non- flowing pack can be related to microscopic “in cage” particle rearrangements enabled by velocity fluctuations in the surrounding flowing material, similar to the static granular pack compaction in tapping experiments [15]. Such granular rheology successfully predicts the pipe flow behavior (velocity and solid volume fraction radial dependence) at moderate ϕ 0 ≤ 0.45 (see, for example, [9] in [14]). In this Letter, we describe magnetic resonance imaging (MRI) measurements on pipe flow of suspensions at higher ϕ 0 , close to the jamming limit, and present observations of significant deviation from the moderate ϕ 0 behavior observed previously. Namely, we observe further compac- tion in the jammed region with ϕ varying from ϕ m to ϕ rcp , and the formation of a solidlike plug at ϕ rcp in the pipe center. We argue that the mechanism proposed in [14] for the compaction of jammed regions can partially explain the formation of that solid plug. 1 H MRI experiments were performed on a flowing sus- pension of polymonobutyl ether (PME) from Sigma-Aldrich PRL 114, 088301 (2015) PHYSICAL REVIEW LETTERS week ending 27 FEBRUARY 2015 0031-9007=15=114(8)=088301(5) 088301-1 © 2015 American Physical Society