Professional Education

  • Doctor of Philosophy, California Institute of Technology (2019)
  • Master of Science, California Institute of Technology (2016)
  • Bachelor of Science, Cornell University (2014)

2019-20 Courses

All Publications

  • Nonlinear microrheology of active Brownian suspensions SOFT MATTER Burkholder, E. W., Brady, J. F. 2020; 16 (4): 1034–46


    The rheological properties of active suspensions are studied via microrheology: tracking the motion of a colloidal probe particle in order to measure the viscoelastic response of the embedding material. The passive probe particle with size R is pulled through the suspension by an external force Fext, which causes it to translate at some speed Uprobe. The bath is comprised of a Newtonian solvent with viscosity ηs and a dilute dispersion of active Brownian particles (ABPs) with size a, characteristic swim speed U0, and a reorientation time τR. The motion of the probe distorts the suspension microstructure, so the bath exerts a reactive force on the probe. In a passive suspension, the degree of distortion is governed by the Péclet number, Pe = Fext/(kBT/a), the ratio of the external force to the thermodynamic restoring force of the suspension. In active suspensions, however, the relevant parameter is Ladv/l = UprobeτR/U0τR∼Fext/Fswim, where Fswim = ζU0 is the swim force that propels the ABPs (ζ is the Stokes drag on a swimmer). When the external forces are weak, Ladv≪l, the autonomous motion of the bath particles leads to "swim-thinning," though the effective suspension viscosity is always greater than ηs. When advection dominates, Ladv≫l, we recover the familiar behavior of the microrheology of passive suspensions. The non-Newtonian behavior for intermediate values of Ladv/l is determined by l/Rc = U0τR/Rc-the ratio of the swimmer's run length l to the geometric length scale associated with interparticle interactions Rc = R + a. The results in this manuscript are approximate as they are based on numerical solutions to mean-field equations that describe the motion of the active bath particles.

    View details for DOI 10.1039/c9sm01713e

    View details for Web of Science ID 000510894800016

    View details for PubMedID 31854425

  • What do AP physics courses teach and the AP physics exam measure? PHYSICAL REVIEW PHYSICS EDUCATION RESEARCH Burkholder, E. W., Wieman, C. E. 2019; 15 (2)
  • Demographic gaps or preparation gaps?: The large impact of incoming preparation on performance of students in introductory physics PHYSICAL REVIEW PHYSICS EDUCATION RESEARCH Salehi, S., Burkholder, E., Lepage, G., Pollock, S., Wieman, C. 2019; 15 (2)
  • Fluctuation-dissipation in active matter JOURNAL OF CHEMICAL PHYSICS Burkholder, E. W., Brady, J. F. 2019; 150 (18): 184901


    In a colloidal suspension at equilibrium, the diffusive motion of a tracer particle due to random thermal fluctuations from the solvent is related to the particle's response to an applied external force, provided this force is weak compared to the thermal restoring forces in the solvent. This is known as the fluctuation-dissipation theorem (FDT) and is expressed via the Stokes-Einstein-Sutherland (SES) relation D = kBT/ζ, where D is the particle's self-diffusivity (fluctuation), ζ is the drag on the particle (dissipation), and kBT is the thermal Boltzmann energy. Active suspensions are widely studied precisely because they are far from equilibrium-they can generate significant nonthermal internal stresses, which can break the detailed balance and time-reversal symmetry-and thus cannot be assumed to obey the FDT a priori. We derive a general relationship between diffusivity and mobility in generic colloidal suspensions (not restricted to near equilibrium) using generalized Taylor dispersion theory and derive specific conditions on particle motion required for the FDT to hold. Even in the simplest system of active Brownian particles (ABPs), these conditions may not be satisfied. Nevertheless, it is still possible to quantify deviations from the FDT and express them in terms of an effective SES relation that accounts for the ABPs conversion of chemical into kinetic energy.

    View details for DOI 10.1063/1.5081725

    View details for Web of Science ID 000470154100003

    View details for PubMedID 31091919

  • Do hydrodynamic interactions affect the swim pressure? SOFT MATTER Burkholder, E. W., Brady, J. F. 2018; 14 (18): 3581–89


    We study the motion of a spherical active Brownian particle (ABP) of size a, moving with a fixed speed U0, and reorienting on a time scale τR in the presence of a confining boundary. Because momentum is conserved in the embedding fluid, we show that the average force per unit area on the boundary equals the bulk mechanical pressure P∞ = p∞f + Π∞, where p∞f is the fluid pressure and Π∞ is the particle pressure; this is true for active and passive particles alike regardless of how the particles interact with the boundary. As an example, we investigate how hydrodynamic interactions (HI) change the particle-phase pressure at the wall, and find that Πwall = n∞(kBT + ζ(Δ)U0l(Δ)/6), where ζ is the (Stokes) drag on the swimmer, l = U0τR is the run length, and Δ is the minimum gap size between the particle and the wall; as Δ → ∞ this is the familiar swim pressure [Takatori et al., Phys. Rev. Lett., 2014, 113, 1-5].

    View details for DOI 10.1039/c8sm00197a

    View details for Web of Science ID 000432205300019

    View details for PubMedID 29683179

  • Tracer diffusion in active suspensions PHYSICAL REVIEW E Burkholder, E. W., Brady, J. F. 2017; 95 (5): 052605


    We study the diffusion of a Brownian probe particle of size R in a dilute dispersion of active Brownian particles of size a, characteristic swim speed U_{0}, reorientation time τ_{R}, and mechanical energy k_{s}T_{s}=ζ_{a}U_{0}^{2}τ_{R}/6, where ζ_{a} is the Stokes drag coefficient of a swimmer. The probe has a thermal diffusivity D_{P}=k_{B}T/ζ_{P}, where k_{B}T is the thermal energy of the solvent and ζ_{P} is the Stokes drag coefficient for the probe. When the swimmers are inactive, collisions between the probe and the swimmers sterically hinder the probe's diffusive motion. In competition with this steric hindrance is an enhancement driven by the activity of the swimmers. The strength of swimming relative to thermal diffusion is set by Pe_{s}=U_{0}a/D_{P}. The active contribution to the diffusivity scales as Pe_{s}^{2} for weak swimming and Pe_{s} for strong swimming, but the transition between these two regimes is nonmonotonic. When fluctuations in the probe motion decay on the time scale τ_{R}, the active diffusivity scales as k_{s}T_{s}/ζ_{P}: the probe moves as if it were immersed in a solvent with energy k_{s}T_{s} rather than k_{B}T.

    View details for DOI 10.1103/PhysRevE.95.052605

    View details for Web of Science ID 000401233600003

    View details for PubMedID 28618621