About

Paul B. Umbanhowar is a Research Professor in the Department of Mechanical Engineering at Northwestern University. He holds a PhD from The University of Texas at Austin (1996), an MS from Boston University (1991), and a BA from Carleton College (1987). His research focuses on granular materials, examining the interaction of legged devices and animals with unconsolidated substrates, as well as the dependence of drag force and penetration resistance on granular material state and intruder geometry and kinematics. He investigates segregation, mixing, and flow in shaken, tumbled, fluidized, and stirred granular ensembles, along with pattern formation and its connection to continuum theories of discrete particulate systems. Another area of interest is motion control and self-assembly/organization through vibrational manipulation of contact interactions mediated by friction and impact.

Research topics

• Materials science
• Mechanics
• Physics
• Mathematics
• Thermodynamics
• Geotechnical engineering
• Geometry
• Chemical physics
• Statistical physics
• Geology
• Geography
• Classical mechanics
• Composite material
• Chemistry

Selected publications

• Stripes, squares, hexagons, and localized structures in vertically vibrated granular layers

  2026-02-19

  book-chapter

  Experiments on granular layers in wide, evacuated containers reveal that, when the acceleration amplitude exceeds a critical value (2.5 g), standing wave patterns spontaneously form and oscillate at half the excitation frequency. The patterns are arrays of squares at low frequencies and stripes at high frequencies. When the acceleration amplitude is decreased slightly below that at which the patterns initially form, highly localized, stable, standing wave excitations can emerge. At acceleration amplitudes well beyond the onset of stripes and squares, there are transitions to hexagons and more complicated patterns.

  PublisherDOI

• Percolation of a cohesive fine particle in a static bed

  arXiv (Cornell University) · 2026-05-19

  preprintOpen access

  Percolation of fine particles (fines) in a static bed of larger particles is central to many industrial and natural processes. Non-cohesive fines either pass through the bed or become trapped depending on multiple factors including particle sizes, friction and restitution coefficients, and size-polydispersity. Here we consider the additional factor of cohesion. We use the discrete element method to simulate gravity-driven percolation of cohesive fine particles through a static bed of randomly packed large particles; fines interact with bed particles but not with each other. A large-to-fine particle diameter ratio of 7 geometrically permits non-cohesive fines to pass the narrowest pore throats formed by the large particles so they can freely percolate. However, sufficiently large cohesion and friction lead to non-geometric trapping. Fines are trapped when they fail to rebound after a collision, due to large cohesion, low restitution, and low collision velocity, and any subsequent rolling or sliding is insufficient to cause detachment. This establishes a sequence of local interactions -- collision, adhesion, and post-contact motion -- that governs the ultimate fate of a fine particle. A collisional model that incorporates a trapping probability per collision and a collision frequency predicts the trapping distance in the regime dominated by collision-induced trapping. For non-rebounding collisions, frictional effects are enhanced by cohesion and, when large enough, prevent the fine particle from subsequently detaching. A static equilibrium condition based on force balance predicts whether a fine particle remains stationary after contact. These results show that percolation of cohesive fine particles is not determined by geometric accessibility alone, but also by particle-scale interaction dynamics that can override geometric expectations.

  PublisherDOI

• Percolation of a cohesive fine particle in a static bed

  ArXiv.org · 2026-05-19

  articleOpen access

  Percolation of fine particles (fines) in a static bed of larger particles is central to many industrial and natural processes. Non-cohesive fines either pass through the bed or become trapped depending on multiple factors including particle sizes, friction and restitution coefficients, and size-polydispersity. Here we consider the additional factor of cohesion. We use the discrete element method to simulate gravity-driven percolation of cohesive fine particles through a static bed of randomly packed large particles; fines interact with bed particles but not with each other. A large-to-fine particle diameter ratio of 7 geometrically permits non-cohesive fines to pass the narrowest pore throats formed by the large particles so they can freely percolate. However, sufficiently large cohesion and friction lead to non-geometric trapping. Fines are trapped when they fail to rebound after a collision, due to large cohesion, low restitution, and low collision velocity, and any subsequent rolling or sliding is insufficient to cause detachment. This establishes a sequence of local interactions -- collision, adhesion, and post-contact motion -- that governs the ultimate fate of a fine particle. A collisional model that incorporates a trapping probability per collision and a collision frequency predicts the trapping distance in the regime dominated by collision-induced trapping. For non-rebounding collisions, frictional effects are enhanced by cohesion and, when large enough, prevent the fine particle from subsequently detaching. A static equilibrium condition based on force balance predicts whether a fine particle remains stationary after contact. These results show that percolation of cohesive fine particles is not determined by geometric accessibility alone, but also by particle-scale interaction dynamics that can override geometric expectations.

  PublisherOA PDF

• Lift and drag forces on a moving intruder in granular shear flow

  Journal of Fluid Mechanics · 2025-03-25 · 7 citations

  articleOpen access

  Lift and drag forces on moving intruders in flowing granular materials are of fundamental interest but have not yet been fully characterized. Drag on an intruder in granular shear flow has been studied almost exclusively for the intruder moving across flow streamlines, and the few studies of the lift explore a relatively limited range of parameters. Here, we use discrete element method simulations to measure the lift force, $F_{{L}}$ , and the drag force on a spherical intruder in a uniformly sheared bed of smaller spheres for a range of streamwise intruder slip velocities, $u_{{s}}$ . The streamwise drag matches the previously characterized Stokes-like cross-flow drag. However, $F_{{L}}$ in granular shear flow acts in the opposite direction to the Saffman lift in a sheared fluid at low $u_{{s}}$ , reaches a maximum value and then decreases with increasing $u_{{s}}$ , eventually reversing direction. This non-monotonic response holds over a range of flow conditions, and the $F_{{L}}$ versus $u_{{s}}$ data collapse when both quantities are scaled using the particle size, shear rate and overburden pressure. Analogous fluid simulations demonstrate that the flow around the intruder particle is similar in the granular and fluid cases. However, the shear stress on the granular intruder is notably less than that in a fluid shear flow. This difference, combined with a void behind the intruder in granular flow in which the stresses are zero, significantly changes the lift-force-inducing stresses acting on the intruder between the granular and fluid cases.

  PublisherOA PDFDOI

• Poster: Seeing the Unseen: Visualizing Particle Movement in Hydrogel Beds

  2025-11-23

  articleOpen accessSenior author
  PublisherDOI

• Diffusion in Granular Mixtures

  Diffusion fundamentals. · 2025-11-03

  articleOpen accessSenior author

  Granular materials, composed of discrete macroscopic particles such as sand, are ubiquitous in both natural and industrial contexts.These materials exhibit unique mechanical and transport properties due to their discrete nature and interparticle interactions through contact forces.Transport of fine particles within granular media plays a central role in processes ranging from chute flows and silos to geophysical flows and powder handling 1 .In such systems, the interplay of segregation 2 , confinement 3 , and diffusion 4 leads to complex dynamics that are not fully captured by existing models.A particular challenge arises at large particle size ratios, where fines can navigate void networks within the granular bed, resulting in transport mechanisms distinct from those in monodisperse or low size ratio systems 5 .We investigate fine particle diffusion across varying fine-particle concentrations using large-scale Discrete Element Method (DEM) simulations and find that the diffusion coefficient decreases with increasing concentration and size ratio.Drawing inspiration from kinetic theory, we develop a scaling framework that links particle concentration, size ratio, and bed geometry to diffusion behavior in dense granular beds.The framework has broad relevance for both industrial applications, such as mixers, separators, and hoppers, and fundamental studies of diffusion in heterogeneous media.

  PublisherOA PDFDOI

• Mobile-collector capture of particles in a chaotic flow

  PLoS ONE · 2025-08-07

  articleOpen accessCorresponding

  Removing dispersed material, such as pollutants, from dynamic fluid environments like the ocean or the atmosphere is challenging when the flow is chaotic. Here the capture of passive tracer particles by a mobile collector (MC) is studied in a model two-dimensional chaotic flow with vortices. Four simple capture strategies for determining the MC direction are considered, all of which rely on periodic measurement of the local particle distribution. The ultimate success of a strategy depends on its associated motion and detection parameters as well as the underlying fluid flow. When the flow is fully chaotic or the relative velocity of the MC is large, the four strategies exhibit nearly equal effectiveness. However, when the flow is less chaotic and the relative MC velocity is small, the collector can become trapped in or outside of a vortex. Changing the particle detection parameters can prevent trapping, which improves capture. In the absence of trapping and for both high and low relative velocities of the MC, a scaling analysis explains the dependence of the capture rate on the relevant dimensionless variables based on timescales for the mobile collector and the underlying flow. For a wide range of parameters and all four capture strategies, the capture timescale depends linearly on a combination of the characteristic kinematic timescale related to the relative motion of the collector and the gradient timescale related to the underlying flow field, confirming that the capture process is properly characterized.

  PublisherOA PDFDOI

• Improved velocity-Verlet algorithm for the discrete element method

  Computer Physics Communications · 2025-01-30 · 18 citations

  articleSenior authorCorresponding
  PublisherDOI

• Granular segregation across flow geometries: a closure model for the particle segregation velocity

  Journal of Fluid Mechanics · 2025-07-28 · 2 citations

  preprintOpen access

  Predicting particle segregation has remained challenging due to the lack of a general model for the segregation velocity that is applicable across a range of granular flow geometries. Here, a segregation-velocity model for dense granular flows is developed by exploiting force balance and recent advances in particle-scale modelling of the segregation driving and drag forces over the entire particle concentration range, size ratios up to 3 and inertial numbers as large as 0.4. This model is shown to correctly predict particle segregation velocity in a diverse set of idealised and natural granular flow geometries simulated using the discrete element method. When incorporated in the well-established advection–diffusion–segregation formulation, the model has the potential to accurately capture segregation phenomena in many relevant industrial applications and geophysical settings.

  PublisherOA PDFDOI

• Fine Particle Percolation Dynamics in Porous Media

  ArXiv.org · 2025-09-13

  preprintOpen accessSenior author

  The influences of restitution coefficient, $e_n$, inter-particle friction, $μ$, and size ratio, $R$, on gravity-driven percolation of fine particles through static beds of larger particles in the free-sifting regime ($R \gtrsim 6.5$) remain largely unexplored. Here we use discrete element method simulations to study the fine particle percolation velocity, $v_p$, and velocity fluctuations, $v_{rms}$, for $7 \le R \le 50$ and a range of $e_n$ and $μ$. Increasing $e_n$ increases velocity fluctuations and reduces percolation velocity. Increasing $μ$ decreases $v_{rms}$ but its influence on $v_p$ varies with $v_{rms}$, decreasing $v_p$ for low $v_{rms}$ and increasing $v_p$ for high $v_{rms}$. Although the influence of size ratio is weaker, larger values of $R$ increase both $v_p$ and $v_{rms}$. We also assess the influence of different excitation mechanisms, specifically using static, randomly excited, and sheared beds, finding that an inverse correlation between $v_p$ and $v_{rms}$ persists across all cases and is well-described by the Drude model, where increased scattering reduces mobility, when $v_{rms}$ is large. However, for weakly excited particles with low $v_{rms}$, the Drude analogy breaks down. In this regime, we introduce a staircase-inspired model that accounts for the gravitationally dominated percolation behavior. These findings provide fundamental insight into the mechanisms governing percolation dynamics in porous media and granular systems.

  PublisherOA PDFDOI

Recent grants

• UNS: Controlling mixing and segregation of granular media using unsteady flows

  NSF · $407k · 2015–2020

Frequent coauthors

• Richard M. Lueptow

  126 shared

• Julio M. Ottino

  120 shared

• Daniel I. Goldman

  33 shared

• Kevin Lynch

  24 shared

• Hongyi Xiao

  Friedrich-Alexander-Universität Erlangen-Nürnberg

  19 shared

• Yi Fan

  Liaoning Technical University

  19 shared

• H. Ungerechts

  Instituto de Radioastronomía Milimétrica

  17 shared

• Conor P. Schlick

  Northwestern University

  17 shared

Education

• PhD, Physics

  The University of Texas at Austin