Roseanna N. Zia is an Associate Professor of Chemical Engineering at Stanford University and, by courtesy, Mechanical Engineering. She received her Ph.D. from the California Institute of Technology in Mechanical Engineering in 2011 with Professor John F. Brady, for development of theory in colloidal hydrodynamics and microrheology. Zia subsequently conducted post-doctoral study of colloidal gels at Princeton University, in collaboration with Professor William B. Russel. Zia began her faculty career at Cornell in January 2013, then subsequently moved her research group to Stanford University in 2017.

Dr. Zia’s research includes developing micro-continuum theory for structure-property relationships of flowing suspensions, elucidating the mechanistic origins of the colloidal glass transition, and microscopic modeling of reversibly bonded colloidal gels, which resulted in discovery that gel aging is actually ongoing but very slow phase separation and the finding that mechanical yield of colloidal gels is actually a non-equilibrium phase transition, triggered by changes in osmotic pressure. Her research group aims to unlock the fundamental connections between colloidal-scale physics and life-essential processes in biological cells using theoretical colloid physics, biological modeling, and high-fidelity computational models. Her group’s ultimate vision is to create a generalized platform for uncovering disease mechanisms and pathways for physics-based therapeutics.

Dr. Zia’s work has been recognized by several awards, including the PECASE Award, the ONR Director of Research Early Career Award, the Office of Naval Research (ONR) Young Investigator award, the NSF CAREER Award, the NSF BRIGE Award, the Publication Award from the Society of Rheology, and the Engineering Sonny Yau (’72) Teaching Award. Most recently she was named an Otterson Faculty Fellow at Stanford.

Dr. Zia serves as an Associate Editor for the Journal of Rheology, and on the Advisory Board of the AIChE Journal.

Academic Appointments

Honors & Awards

  • Otterson Faculty Fellow, Stanford University (2021)
  • Corrsin Lecturer, Johns Hopkins University (2020 - 2021)
  • PECASE Award, National Science Foundation (2019)
  • PECASE Award, Department of Defense (2019)
  • Director of Research Early Career Award, Office of Naval Research (2017)
  • Terman Faculty Fellow, Stanford University (2017)
  • Frontiers of Engineering, National Academy of Engineering (2015)
  • Sonny Yau ('72) Teaching Award, Cornell University College of Engineering (2015)
  • White House Workshop on the National Strategic Computing Initiative, Initiative held by Executive Order of President Barack Obama (2015)
  • Best Paper Award 01J Session, AIChE (2014)
  • Frontiers in Engineering Education, National Academy of Engineering (2014)
  • Young Investigator Award, Office of Naval Research (2014)
  • BRIGE Award, National Science Foundation (2013)
  • CAREER Award, National Science Foundation (2013)
  • Morgan Faculty Fellow, Cornell University (2013)
  • Publication of the Year, Journal of Rheology (2013)
  • Best Poster, Princeton University Symposium (2012)
  • Everhart Lecturer, California Institute of Technology (2011)
  • Graduate Dean's Award, California Institute of Technology (2011)
  • PEO Scholar Award, PEO (2010)
  • Best Overall Poster Award, California Institute of Technology Poster Symposium (2009)
  • Best Poster Award, Society of Rheology - International Congress on Rheology (2008)

Boards, Advisory Committees, Professional Organizations

  • Associate Editor, Journal of Rheology (2016 - Present)
  • Editorial Board Member, AIChE Journal (2020 - Present)
  • Editorial Board Member, Physics of Fluids (2016 - 2019)
  • Guest Editor, PLOS One (2017 - Present)
  • Meeting Programming Chair, Fluid Mechanics, AIChE (2021 - 2021)
  • Chair, Media & Science Relations Committee, American Physical Society Division of Fluid Dynamics (2019 - Present)
  • Vice Chair, Media and Science Relations Committee, APS DFD (2018 - 2019)
  • Fluids Programming Committee, AIChE (2015 - Present)
  • Program Comittee, American Physical Society DFD (2015 - 2018)
  • Liaison, AIP Publishing Partnerships Committee for Soc. Rheology (2016 - Present)
  • Chair, Electronic Publishing Committee (2013 - 2014)

Professional Education

  • PhD, California Institute of Technology, Mechanical Engineering (2011)

Current Research and Scholarly Interests

Colloidal gels, glasses, and suspensions form over 95% of biological fluids, most pharmaceutical fluids, and are ubiquitous across personal-care, agricultural, and industrial-coating materials. Despite the pervasiveness of these fluid-suspended, microscopically small particles (colloids), many of their behaviors have defied explanation – such as the sudden collapse of colloidal gels, vitrification that thwarts crystallization, and their physical role in biological cell function. In addition to these opportunities, the frontier of cellular biology resides at the colloidal scale, requiring a merger between physics and biology, which have evolved almost orthogonally since the 19th century. My lab focuses on unifying mesoscale physics and chemistry with cellular-level biology through novel theoretical modeling and large-scale computational simulations. Our work includes four areas: 1) constructing a micro-continuum theory of complex fluids to predict heterogenous flows of arbitrary composition; 2) mechanistically explaining non-equilibrium phase transitions in colloidal systems; 3) modeling confined and large-scale hydrodynamically-interacting colloidal suspensions; and 4) modeling the physics of living cells. I chose these areas specifically to support my group’s ultimate vision: accurate, physics-based modeling of whole-cell function where physical laws predict biological behavior.

Core Competencies: My lab’s expertise is in uncovering the physics of far-from-equilibrium behaviors of soft matter and explaining how they emerge from microscopic forces. We have developed three core competencies:
•Micro-continuum theory using energy and momentum methods. Theoretical modeling of colloids using microhydrodynamics is routine, but application to dense or heterogeneous suspensions is an immense challenge. Our energy methods are a powerful tool to encode complex boundary conditions yet preserve structural detail.
•Physics-based computational modeling. Computational modeling of suspensions is robust for small or unconfined systems, but current methods obtain large system size by sacrificing on the geometry or transport processes they represent. Our novel physics-based and deep-learning algorithms address these limitations.
•Physics-based modeling of biological cell functions. Biochemical models of life cannot explain many growth- or condition-dependent changes in biological cell function. We merge colloidal-scale modeling with biological process chemistry to reveal entirely new physics-based mechanisms of life-essential cell processes.

2020-21 Courses

Stanford Advisees

Graduate and Fellowship Programs

All Publications

  • Phase mechanics of colloidal gels: osmotic pressure drives non-equilibrium phase separation. Soft matter Johnson, L. C., Zia, R. N. 2021


    Although dense colloidal gels with interparticle bonds of order several kT are typically described as resulting from an arrest of phase separation, they continue to coarsen with age, owing to the dynamics of their temporary bonds. Here, k is Boltzmann's constant and T is the absolute temperature. Computational studies of gel aging reveal particle-scale dynamics reminiscent of condensation that suggests very slow but ongoing phase separation. Subsequent studies of delayed yield reveal structural changes consistent with re-initiation of phase separation. In the present study we interrogate the idea that mechanical yield is connected to a release from phase arrest. We study aging and yield of moderately concentrated to dense reversible colloidal gels and focus on two macroscopic hallmarks of phase separation: increases in surface-area to volume ratio that accompanies condensation, and minimization of free energy. The interplay between externally imposed fields, Brownian motion, and interparticle forces during aging or yield, changes the distribution of bond lengths throughout the gel, altering macroscopic potential energy. The gradient of the microscopic potential (the interparticle force) gives a natural connection of potential energy to stress. We find that the free energy decreases with age, but this slows down as bonds get held stretched by glassy frustration. External perturbations break just enough bonds to liberate negative osmotic pressure, which we show drives a cascade of bond relaxation and rapid reduction of the potential energy, consistent with renewed phase separation. Overall, we show that mechanical yield of reversible colloidal gels releases kinetic arrest and can be viewed as non-equilibrium phase separation.

    View details for DOI 10.1039/d0sm02180f

    View details for PubMedID 33554996

  • Faxen formulas for particles of arbitrary shape and material composition JOURNAL OF FLUID MECHANICS Dolata, B. E., Zia, R. N. 2021; 910
  • Vitrification is a spontaneous non-equilibrium transition driven by osmotic pressure. Journal of physics. Condensed matter : an Institute of Physics journal Wang, J. G., Zia, R. N. 2021


    Persistent dynamics in colloidal glasses suggest the existence of a non-equilibrium driving force for structural relaxation during glassy aging. But the implicit assumption in the literature that colloidal glasses form within the metastable state bypasses the search for a driving force for vitrification and glassy aging and its connection with a metastable state. The natural relation of osmotic pressure to number-density gradients motivates us to investigate the osmotic pressure as this driving force. We use dynamic simulation to quench a polydipserse hard-sphere colloidal liquid into the putative glass region while monitoring structural relaxation and osmotic pressure. Following quenches to various depths in volume fraction φ (where φRCP≈0.678 for 7% polydispersity), the osmotic pressure overshoots its metastable value, then decreases with age toward the metastable pressure, driving redistribution of coordination number and interparticle voids that smooths structural heterogeneity with age. For quenches to 0.56≤φ≤0.58, accessible post-quench volume redistributes with age, allowing the glass to relax into a strong supercooled liquid and easily reach a metastable state. At higher volume fractions, 0.59≤φ<0.64, this redistribution encounters a barrier that is subsequently overcome by osmotic pressure, allowing the system to relax toward the metastable state. But for φ≥0.64, the overshoot is small compared to the high metastable pressure; redistribution of volume stops as particles acquire contacts and get stuck, freezing the system far from the metastable state. Overall, the osmotic pressure drives structural rearrangements responsible for both vitrification and glassy age-relaxation. We leverage the connection of osmotic pressure to energy density to put forth the mechanistic view that relaxation of structural heterogeneity in colloidal glasses occurs via individual particle motion driven by osmotic pressure, and is a spontaneous energy minimization process that drives the glass off and back to the metastable state. This connection of energy, pressure, and structure identify the glass transition, 0.63<φg≤0.64.

    View details for DOI 10.1088/1361-648X/abeec0

    View details for PubMedID 33724236

  • "Dense diffusion" in colloidal glasses: short-ranged long-time self-diffusion as a mechanistic model for relaxation dynamics. Soft matter Wang, J. G., Li, Q., Peng, X., McKenna, G. B., Zia, R. N. 2020


    Despite decades of exploration of the colloidal glass transition, mechanistic explanation of glassy relaxation processes has remained murky. State-of-the-art theoretical models of the colloidal glass transition such as random first order transition theory, active barrier hopping theory, and non-equilibrium self-consistent generalized Langevin theory assert that relaxation reported at volume fractions above the ideal mode coupling theory prediction phig,MCT requires some sort of activated process, and that cooperative motion plays a central role. However, discrepancies between predicted and measured values of phig and ambiguity in the role of cooperative dynamics persist. Underlying both issues is the challenge of conducting deep concentration quenches without flow and the difficulty in accessing particle-scale dynamics. These two challenges have led to widespread use of fitting methods to identify divergence, but most a priori assume divergent behavior; and without access to detailed particle dynamics, it is challenging to produce evidence of collective dynamics. We address these limitations by conducting dynamic simulations accompanied by experiments to quench a colloidal liquid into the putative glass by triggering an increase in particle size, and thus volume fraction, at constant particle number density. Quenches are performed from the liquid to final volume fractions 0.56 ≤ phi ≤ 0.63. The glass is allowed to age for long times, and relaxation dynamics are monitored throughout the simulation. Overall, correlated motion acts to release dynamics from the glassy plateau - but only over length scales much smaller than a particle size - allowing self-diffusion to re-emerge; self-diffusion then relaxes the glass into an intransient diffusive state, which persists for phi < 0.60. We observe similar relaxation dynamics up to phi = 0.63 before achieving the intransient state. We find that this long-time self-diffusion is short-ranged: analysis of mean-square displacement reveals a glassy cage size a fraction of a particle size that shrinks with quench depth, i.e. increasing volume fraction. Thus the equivalence between cage size and particle size found in the liquid breaks down in the glass, which we confirm by examining the self-intermediate scattering function over a range of wave numbers. The colloidal glass transition can hence be viewed mechanistically as a shift in the long-time self-diffusion from long-ranged to short-ranged exploration of configurations. This shift takes place without diverging dynamics: there is a smooth transition as particle mobility decreases dramatically with concomitant emergence of a dense local configuration space that permits sampling of many configurations via local particle motion.

    View details for DOI 10.1039/d0sm00999g

    View details for PubMedID 32696798

  • Heterogeneous dispersions as microcontinuum fluids JOURNAL OF FLUID MECHANICS Dolata, B. E., Zia, R. N. 2020; 888

    View details for DOI 10.1017/jfm.2020.6

    View details for Web of Science ID 000511479100001

  • Stress decomposition in LAOS of dense colloidal suspensions JOURNAL OF RHEOLOGY Ong, E. X., Ramaswamy, M., Niu, R., Lin, N. C., Shetty, A., Zia, R. N., McKinley, G. H., Cohen, I. 2020; 64 (2): 343–51

    View details for DOI 10.1122/1.5144520

    View details for Web of Science ID 000554596100010

  • Transient nonlinear microrheology in hydrodynamically interacting colloidal dispersions: flow cessation JOURNAL OF FLUID MECHANICS Mohanty, R. P., Zia, R. N. 2020; 884
  • Stress decomposition in LAOS of dense colloidal suspensions Journal of Rheology Ong, E. Y., Ramaswamy, M., Niu, R., Lin, N. Y., Shetty, A., Zia, R. N., McKinley, G. H., Cohen, I. 2020; 64 (2): 343-351
  • Colloidal hydrodynamics of biological cells: A frontier spanning two fields PHYSICAL REVIEW FLUIDS Maheshwari, A. J., Sunol, A. M., Gonzalez, E., Endy, D., Zia, R. N. 2019; 4 (11)
  • Sticky, active microrheology: Part 1. Linear-response. Journal of colloid and interface science Huang, D. E., Zia, R. N. 2019; 554: 580–91


    Attractive colloidal-scale forces between macromolecules in biological fluids are suspected to play a role in important system dynamics, including association times, spatially heterogeneous viscosity, and anomalous diffusion. Passive and active microrheology provide a natural connection between observable particle motion and viscosity in such systems via generalized Stokes-Einstein and Stokes' drag law relations. While such models are robust for purely repulsive colloidal-scale interactions, no such theory exists to model the effects of attractive forces. Here we present such a model for the linear-response regime, where a Brownian probe particle is driven gently through a complex fluid by an external force that weakly augments thermal fluctuations. As the probe moves through the bath, hard-sphere repulsion results in an accumulation of particles on its upstream face and a trailing depletion zone, producing particle drag that slows the probe. Linear-response viscosity can be inferred constitutively from this speed reduction. One expects attractive forces to make the suspension more viscous, but surprisingly, weak attractions exerted by upstream particles actively pull the probe forward, giving it a "hypoviscous" environment through which it slides more easily. As attractions grow stronger, particles join to the probe in a long-lasting doublet, extracting particles from the upstream region and depositing them behind the probe. At a critical value of the second virial coefficient common to all potentials we studied, the distorted structure reverses direction, and continued growth of attraction strength causes the probe to drag a cluster of density along, dramatically increasing viscosity. But at this transition, the structure is neutral under the balance of attraction and repulsion, allowing the probe to "cloak" itself and move through the bath undetected and unhindered relative to hard-sphere dispersions. This poses an intriguing mechanism by which proteins or other macromolecules may change their surface chemistry in order to alter the viscosity of the surrounding medium to speed their own motion, or simply to pass undetected through a cell.

    View details for DOI 10.1016/j.jcis.2019.07.004

    View details for PubMedID 31326790

  • Influence of structure on the linear response rheology of colloidal gels JOURNAL OF RHEOLOGY Johnson, L. C., Zia, R. N., Moghimi, E., Petekidis, G. 2019; 63 (4): 583–608

    View details for DOI 10.1122/1.5082796

    View details for Web of Science ID 000492051800007

  • Toward a nonequilibrium Stokes-Einstein relation via active microrheology of hydrodynamically interacting colloidal dispersions JOURNAL OF COLLOID AND INTERFACE SCIENCE Chu, H. W., Zia, R. N. 2019; 539: 388–99
  • Sticky-probe active microrheology: Part 2. The influence of attractions on non-Newtonian flow. Journal of colloid and interface science Huang, D. E., Zia, R. N. 2019; 562: 293–306


    We derive a theoretical framework for the non-Newtonian viscosity of a sticky, attractive colloidal dispersion via active microrheology by modeling detailed microscopic attractive and Brownian forces between particles. Actively forcing a probe distorts the surrounding arrangement of particles from equilibrium; the degree of this distortion is characterized by the Péclet number, Pe≡Fext/(2kT/a), where kT is the thermal energy and a the probe size. Similarly, the strength of attractive interactions relative to Brownian motion is captured by the second virial coefficient, B2. We formulate a Smoluchowski equation governing the pair configuration as it evolves with external and attractive forces. The microviscosity is then computed via non-equilibrium statistical mechanics. For active probe forcing, the familiar hard-sphere boundary-layer and wake structures emerge as Pe grows strong, but attractions alter its shape: changes in relative probe motion arising from its attraction to the bath particles can lead to a high-Pe, strong-attraction flipping of the microstructure, where an upstream depletion boundary layer forms, along with a downstream accumulation wake. This highly distorted structure is analyzed at the micro-mechanical level, where changes in the time spent upstream or downstream from a bath particle lead to hypo- and hyper-viscosity. When attractions are strong, separating the interparticle microviscosity into contributions from attractions and repulsions reveals an attractive undershoot and a repulsive overshoot, as advection grows strong enough to break interparticle bonds downstream and drain the wake. In contrast to linear-response rheology that is predictable entirely by B2 for short-ranged attractions, here the non-Newtonian viscosity is not, owing to the additional length scale introduced by the boundary layer. The ratio of external to attractive forces eventually supersedes B2 as the relevant predictor of structure and rheology. This behavior may provide interesting connections to active motion in biological systems where attractive forces are present.

    View details for DOI 10.1016/j.jcis.2019.11.057

    View details for PubMedID 31841889

  • Toward a nonequilibrium Stokes-Einstein relation via active microrheology of hydrodynamically interacting colloidal dispersions. Journal of colloid and interface science Chu, H. C., Zia, R. N. 2018; 539: 388–99


    We derive a theoretical model for the nonequilibrium stress in a flowing colloidal suspension by tracking the motion of a single embedded probe. While Stokes-Einstein relations connect passive, observable diffusion of a colloidal particle to properties of the suspending medium, they are limited to linear response. Actively forcing a probe through a suspension produces nonequilibrium stress that at steady state can be related directly to observable probe motion utilizing an equation of motion rather than an equation of state, giving a nonequilibrium Stokes-Einstein relation [J. Rheol., 2012, 56, 1175-1208]. Here that freely-draining theory is expanded to account for hydrodynamic interactions. To do so, we construct an effective hydrodynamic resistance tensor, through which the particle flux is projected to give the advective and diffusive components of a Cauchy momentum balance. The resultant phenomenological relation between suspension stress, viscosity and diffusivity is a generalized nonequilibrium Stokes-Einstein relation. The phenomenological model is compared with the statistical mechanics theory for dilute suspensions as well as dynamic simulation at finite concentration which show good agreement, indicating that the suspension stress, viscosity, and force-induced diffusion in a flowing colloidal dispersion can be obtained simply by tracking the motion of a single Brownian probe.

    View details for PubMedID 30597285

  • Exploring the validity of time-concentration superposition in glassy colloids: Experiments and simulations PHYSICAL REVIEW E Peng, X., Wang, J., Li, Q., Chen, D., Zia, R. N., McKenna, G. B. 2018; 98 (6)
  • The Impact of Hydrodynamics on Viscosity Evolution in Colloidal Dispersions: Transient, Nonlinear Microrheology AICHE JOURNAL Mohanty, R. P., Zia, R. N. 2018; 64 (8): 3198–3214

    View details for DOI 10.1002/aic.16123

    View details for Web of Science ID 000441215000026

  • Physical biology of the cancer cell glycocalyx NATURE PHYSICS Kuo, J., Gandhi, J. G., Zia, R. N., Paszek, M. J. 2018; 14 (7): 658–69
  • Yield of reversible colloidal gels during flow start-up: release from kinetic arrest. Soft matter Johnson, L. C., Landrum, B. J., Zia, R. N. 2018


    Yield of colloidal gels during start-up of shear flow is characterized by an overshoot in shear stress that accompanies changes in network structure. Prior studies of yield of reversible colloidal gels undergoing strong flow model the overshoot as the point at which network rupture permits fluidization. However, yield under weak flow, which is of interest in many biological and industrial fluids shows no such disintegration. The mechanics of reversible gels are influenced by bond strength and durability, where ongoing rupture and re-formation impart aging that deepens kinetic arrest [Zia et al., J. Rheol., 2014, 58, 1121], suggesting that yield be viewed as release from kinetic arrest. To explore this idea, we study reversible colloidal gels during start-up of shear flow via dynamic simulation, connecting rheological yield to detailed measurements of structure, bond dynamics, and potential energy. We find that pre-yield stress grows temporally with the changing roles of microscopic transport processes: early time behavior is set by Brownian diffusion; later, advective displacements permit relative particle motion that stretches bonds and stores energy. Stress accumulates in stretched, oriented bonds until yield, which is a tipping point to energy release, and is passed with a fully intact network, where the loss of very few bonds enables relaxation of many, easing glassy arrest. This is immediately followed by a reversal to growth in potential energy during bulk plastic deformation and condensation into larger particle domains, supporting the view that yield is an activated release from kinetic arrest. The continued condensation of dense domains and shrinkage of network surfaces, along with a decrease in the potential energy, permit the gel to evolve toward more complete phase separation, supporting our view that yield of weakly sheared gels is a 'non-equilibrium phase transition'. Our findings may be particularly useful for industrial or other coatings, where weak, slow application via shear may lead to phase separation, inhibiting smooth distribution.

    View details for DOI 10.1039/c8sm00109j

    View details for PubMedID 29869670

  • Gravitational collapse of colloidal gels: non-equilibrium phase separation driven by osmotic pressure SOFT MATTER Padmanabhan, P., Zia, R. 2018; 14 (17): 3265–87


    Delayed gravitational collapse of colloidal gels is characterized by initially slow compaction that gives way to rapid bulk collapse, posing interesting questions about the underlying mechanistic origins. Here we study gel collapse utilizing large-scale dynamic simulation of a freely draining gel of physically bonded particles subjected to gravitational forcing. The hallmark regimes of collapse are recovered: slow compaction, transition to rapid collapse, and long-time densification. Microstructural changes are monitored by tracking particle positions, coordination number, and bond dynamics, along with volume fraction, osmotic pressure, and potential energy. Together these reveal the surprising result that collapse can occur with a fully intact network, where the tipping point arises when particle migration dissolves strands in a capillary-type instability. While it is possible for collapse to rupture a gel network into clusters that then sediment, and hydrodynamic interactions can make interesting contributions, neither is necessary. Rather, we find that the "delay" arises from gravity-enhanced coarsening, which triggers the re-emergence of phase separation. The mechanism of this transition is a leap toward lower potential energy of the gel, driven by bulk negative osmotic pressure that condenses the particle phase: the gel collapses in on itself under negative osmotic pressure allowing the gel, to tunnel through the equilibrium phase diagram to a higher volume fraction "state". Remarkably, collapse stops when condensation stops, when gravitational advection produces a positive osmotic pressure, re-arresting the gel.

    View details for DOI 10.1039/c8sm00002f

    View details for Web of Science ID 000431422500007

    View details for PubMedID 29637976

  • Equilibrium structure and diffusion in concentrated hydrodynamically interacting suspensions confined by a spherical cavity JOURNAL OF FLUID MECHANICS Aponte-Rivera, C., Su, Y., Zia, R. N. 2018; 836: 413–50
  • Y Non-equilibrium pair interactions in colloidaldispersions JOURNAL OF FLUID MECHANICS Dolata, B. E., Zia, R. N. 2018; 836: 694–739
  • Active and Passive Microrheology: Theory and Simulation ANNUAL REVIEW OF FLUID MECHANICS, VOL 50 Zia, R. N., Davis, S. H., Moin, P. 2018; 50: 371–405
  • The non-Newtonian rheology of hydrodynamically interacting colloids via active, nonlinear microrheology JOURNAL OF RHEOLOGY Chu, H. W., Zia, R. N. 2017; 61 (3): 551–74

    View details for DOI 10.1122/1.4981819

    View details for Web of Science ID 000400620400011

  • Pair mobility functions for rigid spheres in concentrated colloidal dispersions: Stresslet and straining motion couplings JOURNAL OF CHEMICAL PHYSICS Su, Y., Swan, J. W., Zia, R. N. 2017; 146 (12): 124903


    Accurate modeling of particle interactions arising from hydrodynamic, entropic, and other microscopic forces is essential to understanding and predicting particle motion and suspension behavior in complex and biological fluids. The long-range nature of hydrodynamic interactions can be particularly challenging to capture. In dilute dispersions, pair-level interactions are sufficient and can be modeled in detail by analytical relations derived by Jeffrey and Onishi [J. Fluid Mech. 139, 261-290 (1984)] and Jeffrey [Phys. Fluids A 4, 16-29 (1992)]. In more concentrated dispersions, analytical modeling of many-body hydrodynamic interactions quickly becomes intractable, leading to the development of simplified models. These include mean-field approaches that smear out particle-scale structure and essentially assume that long-range hydrodynamic interactions are screened by crowding, as particle mobility decays at high concentrations. Toward the development of an accurate and simplified model for the hydrodynamic interactions in concentrated suspensions, we recently computed a set of effective pair of hydrodynamic functions coupling particle motion to a hydrodynamic force and torque at volume fractions up to 50% utilizing accelerated Stokesian dynamics and a fast stochastic sampling technique [Zia et al., J. Chem. Phys. 143, 224901 (2015)]. We showed that the hydrodynamic mobility in suspensions of colloidal spheres is not screened, and the power law decay of the hydrodynamic functions persists at all concentrations studied. In the present work, we extend these mobility functions to include the couplings of particle motion and straining flow to the hydrodynamic stresslet. The couplings computed in these two articles constitute a set of orthogonal coupling functions that can be utilized to compute equilibrium properties in suspensions at arbitrary concentration and are readily applied to solve many-body hydrodynamic interactions analytically.

    View details for DOI 10.1063/1.4978622

    View details for Web of Science ID 000397929300067

    View details for PubMedID 28388164

  • Delayed yield in colloidal gels: Creep, flow, and re-entrant solid regimes JOURNAL OF RHEOLOGY Landrum, B. J., Russel, W. B., Zia, R. N. 2016; 60 (4): 783–807

    View details for DOI 10.1122/1.4954640

    View details for Web of Science ID 000379585600019

  • Active microrheology of hydrodynamically interacting colloids: Normal stresses and entropic energy density JOURNAL OF RHEOLOGY Chu, H. W., Zia, R. N. 2016; 60 (4): 755–81

    View details for DOI 10.1122/1.4953861

    View details for Web of Science ID 000379585600018

  • Simulation of hydrodynamically interacting particles confined by a spherical cavity PHYSICAL REVIEW FLUIDS Aponte-Rivera, C., Zia, R. N. 2016; 1 (2)
  • Force-induced diffusion in suspensions of hydrodynamically interacting colloids JOURNAL OF FLUID MECHANICS Hoh, N. J., Zia, R. N. 2016; 795: 739–83
  • Pair mobility functions for rigid spheres in concentrated colloidal dispersions: Force, torque, translation, and rotation JOURNAL OF CHEMICAL PHYSICS Zia, R. N., Swan, J. W., Su, Y. 2015; 143 (22): 224901


    The formulation of detailed models for the dynamics of condensed soft matter including colloidal suspensions and other complex fluids requires accurate description of the physical forces between microstructural constituents. In dilute suspensions, pair-level interactions are sufficient to capture hydrodynamic, interparticle, and thermodynamic forces. In dense suspensions, many-body interactions must be considered. Prior analytical approaches to capturing such interactions such as mean-field approaches replace detailed interactions with averaged approximations. However, long-range coupling and effects of concentration on local structure, which may play an important role in, e.g., phase transitions, are smeared out in such approaches. An alternative to such approximations is the detailed modeling of hydrodynamic interactions utilizing precise couplings between moments of the hydrodynamic traction on a suspended particle and the motion of that or other suspended particles. For two isolated spheres, a set of these functions was calculated by Jeffrey and Onishi [J. Fluid Mech. 139, 261-290 (1984)] and Jeffrey [J. Phys. Fluids 4, 16-29 (1992)]. Along with pioneering work by Batchelor, these are the touchstone for low-Reynolds-number hydrodynamic interactions and have been applied directly in the solution of many important problems related to the dynamics of dilute colloidal dispersions [G. K. Batchelor and J. T. Green, J. Fluid Mech. 56, 375-400 (1972) and G. K. Batchelor, J. Fluid Mech. 74, 1-29 (1976)]. Toward extension of these functions to concentrated systems, here we present a new stochastic sampling technique to rapidly calculate an analogous set of mobility functions describing the hydrodynamic interactions between two hard spheres immersed in a suspension of arbitrary concentration, utilizing accelerated Stokesian dynamics simulations. These mobility functions provide precise, radially dependent couplings of hydrodynamic force and torque to particle translation and rotation, for arbitrary colloid volume fraction ϕ. The pair mobilities (describing entrainment of one particle by the disturbance flow created by another) decay slowly with separation distance: as 1/r, for volume fractions 0.05 ≤ ϕ ≤ 0.5. For the relative mobility, we find an initially rapid growth as a pair separates, followed by a slow, 1/r growth. Up to ϕ ≤ 0.4, the relative mobility does not reached the far-field value even beyond separations of many particle sizes. In the case of ϕ = 0.5, the far-field asymptote is reached but only at a separation of eight radii and after a slow 1/r growth. At these higher concentrations, the coefficients also reveal liquid-like structural effects on pair mobility at close separations. These results confirm that long-range many-body hydrodynamic interactions are an essential part of the dynamics of concentrated systems and that care must be taken when applying renormalization schemes.

    View details for DOI 10.1063/1.4936664

    View details for Web of Science ID 000367194300050

    View details for PubMedID 26671398

  • Hydrodynamic diffusion in active microrheology of non-colloidal suspensions: the role of interparticle forces JOURNAL OF FLUID MECHANICS Hoh, N. J., Zia, R. N. 2015; 785: 189–218
  • A micro-mechanical study of coarsening and rheology of colloidal gels: Cage building, cage hopping, and Smoluchowski's ratchet JOURNAL OF RHEOLOGY Zia, R. N., Landrum, B. J., Russel, W. B. 2014; 58 (5): 1121–57

    View details for DOI 10.1122/1.4892115

    View details for Web of Science ID 000342206200004

  • Large amplitude oscillatory microrheology JOURNAL OF RHEOLOGY Swan, J. W., Zia, R. N., Brady, J. F. 2014; 58 (1): 1–41

    View details for DOI 10.1122/1.4826939

    View details for Web of Science ID 000329357400001

  • Far-from-equilibrium sheared colloidal liquids: Disentangling relaxation, advection, and shear-induced diffusion PHYSICAL REVIEW E Lin, N. C., Goyal, S., Cheng, X., Zia, R. N., Escobedo, F. A., Cohen, I. 2013; 88 (6): 062309


    Using high-speed confocal microscopy, we measure the particle positions in a colloidal suspension under large-amplitude oscillatory shear. Using the particle positions, we quantify the in situ anisotropy of the pair-correlation function, a measure of the Brownian stress. From these data we find two distinct types of responses as the system crosses over from equilibrium to far-from-equilibrium states. The first is a nonlinear amplitude saturation that arises from shear-induced advection, while the second is a linear frequency saturation due to competition between suspension relaxation and shear rate. In spite of their different underlying mechanisms, we show that all the data can be scaled onto a master curve that spans the equilibrium and far-from-equilibrium regimes, linking small-amplitude oscillatory to continuous shear. This observation illustrates a colloidal analog of the Cox-Merz rule and its microscopic underpinning. Brownian dynamics simulations show that interparticle interactions are sufficient for generating both experimentally observed saturations.

    View details for DOI 10.1103/PhysRevE.88.062309

    View details for Web of Science ID 000328697400003

    View details for PubMedID 24483446

  • Active microrheology: Fixed-velocity versus fixed-force PHYSICS OF FLUIDS Swan, J. W., Zia, R. N. 2013; 25 (8)

    View details for DOI 10.1063/1.4818810

    View details for Web of Science ID 000323946200029

  • Stress development, relaxation, and memory in colloidal dispersions: Transient nonlinear microrheology JOURNAL OF RHEOLOGY Zia, R. N., Brady, J. F. 2013; 57 (2): 457–92

    View details for DOI 10.1122/1.4775349

    View details for Web of Science ID 000314748100007

  • Microviscosity, microdiffusivity, and normal stresses in colloidal dispersions JOURNAL OF RHEOLOGY Zia, R. N., Brady, J. F. 2012; 56 (5): 1175–1208

    View details for DOI 10.1122/1.4722880

    View details for Web of Science ID 000306761300009

  • Modeling hydrodynamic self-propulsion with Stokesian Dynamics. Or teaching Stokesian Dynamics to swim PHYSICS OF FLUIDS Swan, J. W., Brady, J. F., Moore, R. S. 2011; 23 (7)

    View details for DOI 10.1063/1.3594790

    View details for Web of Science ID 000293478200002

  • Single-particle motion in colloids: force-induced diffusion JOURNAL OF FLUID MECHANICS Zia, R. N., Brady, J. F. 2010; 658: 188–210