The rheological behavior of a dilute emulsion comprised of neutrally buoyant drops suspended in an immiscible medium under the combined influence of a uniform electric field and simple shear flow is analyzed. Considering the drops and suspending medium as Newtonian and leaky dielectrics, the effective emulsion stress tensor is obtained when the fluid motion is governed by the Stokes equations. The present study takes into account an arbitrarily oriented uniform electric field in the plane of shear flow. A small-deformation analysis is performed to study this coupled electrohydrodynamic problem considering weak imposed shear flow and weak surface charge convection. Analytical expressions are obtained for the effective shear viscosity and normal stress differences of the dilute emulsion. The tilt angle (orientation angle of the applied electric field relative to the direction of shear flow) is found to affect the emulsion rheology. Key results show that the dilute emulsion exhibits non-Newtonian behavior such as shear-rate-dependent effective viscosity and nonzero first and second normal stress differences. In the absence of shape deformation and charge convection, a dilute emulsion displays shear thinning or shear thickening behavior depending on the drop polarization and tilt angle. The effective viscosity of the dilute emulsion can be lower or higher than the viscosity of the suspending medium depending on the electrical property ratios, tilt angle, and relative strength of the electric stress as compared with viscous stress. Surface charge convection significantly affects the electrohydrodynamic flow and thereby modifies the effective viscosity and normal stress differences. The applied electric field significantly affects the drop shape and orientation angle and thereby modifies the effective viscosity and normal stress differences. Both the surface charge convection and shape deformation can increase or decrease the effective viscosity and normal stress differences. Notably, the presence of surface charge convection and shape deformation leads to the generation of electric torque, which further results in a nonzero antisymmetric component of the emulsion stress tensor. We establish that fine-tuned rheology of a dilute emulsion can be obtained by proper choices of the tilt angle.

When a vortex refracts surface waves, the momentum flux carried by the waves changes direction and the waves induce a reaction force on the vortex. We study experimentally the resulting vortex distortion. Incoming surface gravity waves impinge on a steady vortex of velocity $U_0$ driven magnetohydrodynamically at the bottom of a fluid layer. The waves induce a shift of the vortex center in the direction transverse to wave propagation, together with a decrease in surface vorticity. We interpret these two phenomena in the framework introduced by Craik and Leibovich [A. D. D. Craik and S. Leibovich, J. Fluid Mech. 73, 401 (1976)]: We identify the dimensionless Stokes drift $S=U_s/U_0$ as the relevant control parameter, $U_s$ being the Stokes drift velocity of the waves. We propose a simple vortex line model that indicates that the shift of the vortex center originates from a balance between vorticity advection by the Stokes drift and self-advection of the vortex. The decrease in surface vorticity is interpreted as a consequence of vorticity expulsion by the fast Stokes drift, which confines it at depth. This purely hydrodynamic process is analogous to the magnetohydrodynamic expulsion of a magnetic field by a rapidly moving conductor through the electromagnetic skin effect. We study vorticity expulsion in the limit of fast Stokes drift and deduce that the surface vorticity decreases as $1/S$, a prediction that is compatible with the experimental data. Such wave-induced vortex distortions have important consequences for the nonlinear regime of wave refraction: The refraction angle rapidly decreases with wave intensity.

The trinity of so-called “canonical” wall-bounded turbulent flows, comprising the zero pressure gradient turbulent boundary layer, abbreviated ZPG TBL, turbulent pipe flow, and channel/duct flows has continued to receive intense attention as new and more reliable experimental data have become available. Nevertheless, the debate on whether the logarithmic part of the mean velocity profile, in particular the Kármán constant $\kappa$, is identical for these three canonical flows or flow-dependent is still ongoing. In this paper, the asymptotic matching requirement of equal $\kappa$ in the logarithmic overlap layer, which links the inner and outer flow regions, and in the expression for the centerline/free-stream velocity is reiterated and shown to preclude a universal logarithmic overlap layer in the three canonical flows. However, the majority of pipe and channel flow studies at friction Reynolds numbers ${\mathrm{Re}}_{\tau }$ below $\approx {10}^4$ extract from near-wall profiles the same $\kappa$ of 0.38–0.39 as in the ZPG TBL. This apparent contradiction is resolved by a careful reanalysis of high-quality mean velocity profiles in the Princeton “Superpipe” and other pipes, channels, and ducts, which shows that the mean velocity in a near-wall region extending to around 700 “+” units in channels and ducts and 500 “+” units in pipes is the same as in the ZPG TBL. In other words, all the “canonical” flow profiles contain the lower end of the ZPG TBL log-region, which starts at a wall distance of $150–200$ “+” units with a universal $\kappa$ of ${\kappa }_{\mathrm{ZPG}}\approx 0.384$. This interior log-region is followed by a second logarithmic region with a flow specific $\kappa >{\kappa }_{\mathrm{ZPG}}$, which increases monotonically with pressure gradient. This second, exterior log-layer is the actual overlap layer matching up to the outer expansion, which implies equality of the exterior $\kappa$ and ${\kappa }_{\mathrm{CL}}$ obtained from the evolution of the respective centerline velocity with Reynolds number. The location of the switch-over point implies furthermore that this second log-layer only becomes clearly identifiable, i.e., separated from the wake region, for ${\mathrm{Re}}_{\tau }$ well beyond ${10}^4$ (see Fig. 1). This explains the discrepancies between the Kármán constants of 0.38–0.39, extracted from near-wall pipe profiles below ${\mathrm{Re}}_{\tau }\approx {10}^4$ and the $\kappa$'s obtained from the evolution of the centerline velocity with Reynolds number. The same analysis is successfully applied to velocity profiles in channels and ducts even though experiments and numerical simulations have not yet reached Reynolds numbers where the different layers have even started to clearly separate.

We report an experimental investigation of the effect of finite depth on the statistical properties of wave turbulence at the surface of water in the gravity-capillary range. We tune the wave dispersion and the level of nonlinearity by modifying the depth of water and the forcing, respectively. We use space-time resolved profilometry to reconstruct the deformed surface of water. When decreasing the water depth, we observe a drastic transition between weak turbulence at the weakest forcing and a solitonic regime at stronger forcing. We characterize the transition between both states by studying their Fourier spectra. We also study the efficiency of energy transfer in the weak turbulence regime. We report a loss of efficiency of angular transfer as the dispersion of the wave is reduced until the system bifurcates into the solitonic regime.

We study the dynamical regimes of a density-stratified fluid confined between isothermal no-slip top and bottom boundaries (at temperatures $T_t$ and $T_b)$ via direct numerical simulation. The thermal expansion coefficient of the fluid is temperature dependent and chosen such that the fluid density is maximum at the inversion temperature $T_b>T_i>T_t$. Thus, the lower layer of the fluid is convectively unstable while the upper layer is stably stratified. We show that the characteristics of the convection change significantly depending on the degree of stratification of the stable layer. For strong stable stratification, the convection zone coincides with the fraction of the fluid that is convectively unstable (i.e., where $T>T_i)$, and convective motions consist of rising and sinking plumes of large density anomaly, as is the case in canonical Rayleigh-Bénard convection; internal gravity waves are generated by turbulent fluctuations in the convective layer and propagate in the upper layer. For weak stable stratification, we demonstrate that a large fraction of the stable fluid (i.e., with temperature $T<T_i)$ is instead destabilized and entrained by buoyant plumes emitted from the bottom boundary. The convection thus mixes cold patches of low density-anomaly fluid with hot upward plumes and the end result is that the $T_i$ isotherm sinks within the bottom boundary layer and that the convection is entrainment dominated. We provide a phenomenological description of the transition between the regimes of plume-dominated and entrainment-dominated convection through analysis of the differences in the heat transfer mechanisms, kinetic energy density spectra, and probability density functions for different stratification strengths. Importantly, we find that the effect of the stable layer on the convection decreases only weakly with increasing stratification strength, meaning that the dynamics of the stable layer and convection should be studied self-consistently in a wide range of applications.

We conduct a simple experiment and numerical simulation of two-dimensional granular discharge flow driven by gravity under the influence of an obstacle. According to previous work [Zuriguel et al., Phys. Rev. Lett. 107, 278001 (2011)], the clogging of granular discharge flow can be suppressed by putting a circular obstacle at a proper position. In order to investigate the details of the obstacle effect in granular flow, we focus on particle dynamics in this study. From the experimental and numerical data, we find that the obstacle remarkably affects the horizontal-velocity distribution and packing fraction in the vicinity of the exit. In addition to the circular obstacle, we utilize triangular, inverted-triangular, and horizontal-bar obstacles to discuss the obstacle-shape effect in granular discharge flow. Based on the investigation of dynamical quantities such as velocity distributions, granular temperature, and volume fraction, we find that the triangular obstacle or horizontal bar could be very effective in preventing the clogging. From the result obtained, we consider that the detouring of particles around the obstacle and resultant low packing fraction at the exit region effectively prevent the clogging in a certain class of granular discharge flow.

The inhomogeneous concentration distribution of erythrocytes and platelets in microchannel flows particularly in directions normal to the mean flow plays a significant role in hemostasis, drug delivery, and microfluidic applications. In this paper, we develop a coarse-grained theory to predict these distributions in pressure-driven channel flow at zero Reynolds number and compare them to experiments and simulations. We demonstrate that the balance between the deformability-induced lift force and the shear-induced diffusion created by hydrodynamic interactions in the suspension results in both a peak concentration of red blood cells at the channel center and a cell-free or Fahraeus-Lindqvist layer near the walls. On the other hand, the absence of a lift force and the strong red blood cell-platelet interactions result in an excess concentration of platelets in the cell-free layer. We demonstrate a strong role of hematocrit (i.e., erythrocyte volume fraction) in determining the cell-free layer thickness and the degree of platelet margination. We also demonstrate that the capillary number of the erythrocytes, based on the membrane shear modulus, plays a relatively insignificant role in the regimes that we have studied. Our theory serves as a good and simple alternative to large-scale computer simulations of the cross-stream transport processes in these mixtures.

We perform both high- and low-speed particle image velocimetry and torque measurements to characterize eight radial impeller types in an unbaffled stirred tank. The blade types consist of a set of regular flat blades, used as a baseline, regular blades of increased thickness, perforated blades, and fractal blades. We find a qualitative correlation between the blades' torque coefficient and both vortex coherence and turbulent kinetic energy, possibly explaining the torque differences of the tested impellers. Furthermore, we find that the proposed modifications increase the bulk turbulence levels and mass flow rates while at the same time reducing the shaft torque, showing promise for applications. Finally, we attempt a comparison between fractal and perforated geometries using data from this study and the literature.

We analyze one of the simplest active suspensions with complex dynamics: a suspension of immotile “extensor” particles that exert active extensile dipolar stresses on the fluid in which they are immersed. This is relevant to several experimental systems, such as recently studied tripartite rods that create extensile flows by consuming a chemical fuel. We first describe the system through a Doi-Onsager kinetic theory based on microscopic modeling. This theory captures the active stresses produced by the particles that can drive hydrodynamic instabilities, as well as the steric interactions of rodlike particles that lead to nematic alignment. This active nematic system yields complex flows and disclination defect dynamics very similar to phenomenological Landau–deGennes $Q$-tensor theories for active nematic fluids, as well as by more complex Doi-Onsager theories for polar microtubule–motor-protein systems. We apply the quasiequilibrium Bingham closure, used to study suspensions of passive microscopic rods, to develop a nonstandard $Q$-tensor theory. We demonstrate through simulation that this $BQ$-tensor theory gives an excellent analytical and statistical accounting of the suspension's complex dynamics, at a far reduced computational cost. Finally, we apply the $BQ$-tensor model to study the dynamics of extensor suspensions in circular and biconcave domains. In circular domains, we reproduce previous results for systems with weak nematic alignment, but for strong alignment we find unusual dynamics with activity-controlled defect production and absorption at the boundaries of the domain. In biconcave domains, a Fredericks-like transition occurs as the width of the neck connecting the two disks is varied.

The shear rheology of two-dimensional foam is investigated over a range of shear rates with the numerical DySMaL model, which features dynamically deformable bubbles. It is found that at low shear rates, the rheological behavior of the system can be characterized by a yield stress power-law constitutive equation that is consistent with experimental findings and can be understood in terms of soft glassy rheology models. At low shear rates, the system rheology is also found to be subject to a scaling law involving the bubble size, the surface tension, and the viscosity of the carrier fluid. At high shear rates, the model produces a dynamic phase transition with a sudden change in the flow pattern, which is accompanied by a drop in the effective viscosity. This phase transition can be linked to rapid changes in the average bubble deformation and nematic order of the system. It is very likely that this phase transition is a result of the model dynamics and does not happen in actual foams.

The bacterium Helicobacter pylori causes ulcers in the stomach of humans by invading mucus layers protecting epithelial cells. It does so by chemically changing the rheological properties of the mucus from a high-viscosity gel to a low-viscosity solution in which it may self-propel. We develop a two-fluid model for this process of swimming under self-generated confinement. We solve exactly for the flow and the locomotion speed of a spherical swimmer located in a spherically symmetric system of two Newtonian fluids whose boundary moves with the swimmer. We also treat separately the special case of an immobile outer fluid. In all cases, we characterize the flow fields, their spatial decay, and the impact of both the viscosity ratio and the degree of confinement on the locomotion speed of the model swimmer. The spatial decay of the flow retains the same power-law decay as for locomotion in a single fluid but with a decreased magnitude. Independent of the assumption chosen to characterize the impact of confinement on the actuation applied by the swimmer, its locomotion speed always decreases with an increase in the degree of confinement. Our modeling results suggest that a low-viscosity region of at least six times the effective swimmer size is required to lead to swimming with speeds similar to locomotion in an infinite fluid, corresponding to a region of size above $\approx 25\mu \mathrm{m}$ for Helicobacter pylori.

Exact statistical equations are derived for turbulent advection of a passive scalar having diffusivity much larger than the kinematic viscosity, i.e., small Schmidt number. The equations contain all terms needed for precise direct numerical simulation (DNS) quantification. In the appropriate limit, the equations reduce to the classical theory for which the scalar spectrum is proportional to the energy spectrum multiplied by $k^{-4}$, which, in turn, results in the inertial-diffusive range power law, $k^{-17/3}$. The classical theory was derived for the case of isotropic velocity and scalar fields. The exact equations are simplified for less restrictive cases: (1) locally isotropic scalar fluctuations at dissipation scales with no restriction on symmetry of the velocity field, (2) isotropic velocity field with averaging over all wave-vector directions with no restriction on the symmetry of the scalar, motivated by that average being used for DNS, and (3) isotropic velocity field with axisymmetric scalar fluctuations, motivated by the mean-scalar-gradient-source case. The equations are applied to recently published DNSs of passive scalars for the cases of a freely decaying scalar and a mean-scalar-gradient source. New terms in the exact equations are estimated for those cases and are found to be significant; those terms cause the deviations from the classical theory found by the DNS studies. A new formula for the mean-scalar-gradient case explains the variation of the scalar spectra for the DNS of the smallest Schmidt-number cases. Expansion in Legendre polynomials reveals the effect of axisymmetry. Inertial-diffusive-range formulas for both the zero- and second-order Legendre contributions are given. Exact statistical equations reveal what must be quantified using DNS to determine what causes deviations from asymptotic relationships.

We present an experimental system that can be used to study the dynamics of a picoliter droplet (in-flight radius of $12.2\mu \mathrm{m})$ as it spreads over substrates with topographic variations. We concentrate on the spreading of a droplet within a recessed stadium-shaped pixel, with applications to the manufacture of polymer organic light-emitting-diode displays, and find that the sloping sidewall of the pixel can either locally enhance or hinder spreading depending on whether the topography gradient ahead of the contact line is positive or negative, respectively. Locally enhanced spreading occurs via the formation of thin pointed rivulets along the sidewalls of the pixel through a mechanism similar to capillary rise in sharp corners. We demonstrate that a simplified model involving quasistatic surface-tension effects within the framework of a thin-film approximation combined with an experimentally measured dynamic spreading law, relating the speed of the contact line to the contact angle, provides excellent predictions of the evolving liquid morphologies. A key feature of the liquid-substrate interaction studied here is the presence of significant contact angle hysteresis, which enables the persistence of noncircular fluid morphologies. We also show that the spreading law for an advancing contact line can be adequately approximated by a Cox-Voinov law for the majority of the evolution. The model does not include viscous effects in the bulk of the droplet and hence the time scales for the propagation of the thin pointed rivulets are not captured. Nonetheless, this simple model can be used very effectively to predict the areas covered by the liquid and may serve as a useful design tool for systems that require precise control of liquid on substrates.

Numerical simulations are performed to study the effects of proposed subsurface explosions for ejecting low-density regolith (that is, layers of rocky, granular material covering bedrock) from the surface of asteroids and comets. The numerical model solves two sets of coupled Euler equations, one for the gaseous phase and one for the granular phase, and is valid for a wide range of particle volume fractions. The specific conditions simulate an explosion in which the regolith, here a granular-gas mixture, consists of spherical particles with diameters of $1\mu \mathrm{m}$ and the gas above and inside of the particle layer is at 10 Pa and 100 K. A preliminary one-dimensional computation describes the structure of a granular shock formed from a spherical explosion. The two-dimensional axisymmetric calculations show that the explosion creates a cavity in the granular phase, and this cavity expands radially until it breaks through the surface. A blast wave is created during the explosion, initiating the particle motions and forming a granular shock. The particles accumulate behind the granular shock to form a region with high particle volume fractions. An increase in gas-phase velocity at the contact surface is due to a sudden reduction of gas-phase volume, which is called the “nozzling effect.” A weak shock in the gas phase is induced by the granular shock, which propagates radially. As the initial particle volume fraction increases, the propagation velocity of the granular shock increases. It is shown that there is a power-law relation between the explosion radius and time, and that this result is consistent with the blast-wave theory. At lower background temperatures, the velocities of both phases decrease, and this leads to more compact structures in the granular phase.

The dependence of the heat transfer, as measured by the nondimensional Nusselt number $\text{Nu}$, on Ekman pumping for rapidly rotating Rayleigh-Bénard convection in an infinite plane layer is examined for fluids with Prandtl number $\text{Pr}=1$. A joint effort utilizing simulations from the composite non-hydrostatic quasi-geostrophic model and direct numerical simulations (DNS) of the incompressible fluid equations has mapped a wide range of the Rayleigh number $\text{Ra}$-Ekman number $E$ parameter space within the geostrophic regime of rotating convection. Corroboration of the $\text{Nu}\text{−}\text{Ra}$ relation at $E={10}^{-7}$ from both methods along with higher $E$ covered by DNS and lower $E$ by the asymptotic model allows for this extensive range of the heat transfer results. For stress-free boundaries, the relation $\text{Nu}-1\propto {\left(\text{Ra}{E}^{4/3}\right)}^{\alpha }$ has the dissipation-free scaling of $\alpha =3/2$ for all $E\le {10}^{-7}$. This is directly related to a geostrophic turbulent interior that throttles the heat transport supplied to the thermal boundary layers. For no-slip boundaries, the existence of ageostrophic viscous boundary layers and their associated Ekman pumping yields a more complex two-dimensional surface in $\text{Nu}(E,\text{Ra})$ parameter space. For $E<{10}^{-7}$ results suggest that the surface can be expressed as $\text{Nu}-1\propto [1+P\left(E\right)]{\left(\text{Ra}{E}^{4/3}\right)}^{3/2}$ indicating the dissipation-free scaling law is enhanced by Ekman pumping by the multiplicative prefactor $[1+P(E\left)\right]$ where $P\left(E\right)\approx 5.97E^{1/8}$. It follows for $E<{10}^{-7}$ that the geostrophic turbulent interior remains the flux bottleneck in rapidly rotating Rayleigh-Bénard convection. For $E\sim {10}^{-7}$, where DNS and asymptotic simulations agree quantitatively, it is found that the effects of Ekman pumping are sufficiently strong to influence the heat transport with diminished exponent $\alpha \approx 1.2$ and $\text{Nu}-1\propto {\left(\text{Ra}{E}^{4/3}\right)}^{1.2}$.

Near a fluid-solid interface, the fluid spatial density profile is highly nonuniform at the molecular scale. This nonuniformity can have profound effects on the dynamical behavior of the fluid and has been shown to play an especially important role when modeling a wide variety of nanoscale heat and momentum transfer phenomena. We use molecular-mechanics arguments and molecular-dynamics (MD) simulations to develop a better understanding of the structure of the first fluid layer directly adjacent to the solid in the layering regime, as delineated by a nondimensional number that compares the effects of wall-fluid interaction to thermal energy. Using asymptotic analysis of the Nernst-Planck equation, we show that features of the fluid density profile close to the wall, such as the areal density of the first layer ${\mathrm{\Sigma }}_{\text{FL}}$ (defined as the number of atoms in this layer per unit of fluid-solid interfacial area), can be expressed as polynomial functions of the fluid average density ${\rho }_{\text{ave}}$. This is found to be in agreement with MD simulations, which also show that the width of the first layer $h_{\text{FL}}$ is a linear function of the average density and only a weak function of the temperature $T$. These results can be combined to show that, for system average densities corresponding to a dense fluid (${\rho }_{\text{ave}}\ge 0.7$), the ratio $\mathcal{C}\equiv \frac{{\mathrm{\Sigma }}_{\text{FL}}}{{\rho }_{\text{ave}}{h}_{\text{FL}}}$, representing a density enhancement with respect to the bulk fluid, depends only weakly on temperature and is essentially independent of density. Further MD simulations suggest that the above results, nominally valid for large systems (solid in contact with semi-infinite fluid), also describe fluid-solid interfaces under considerable nanoconfinement, provided ${\rho }_{\text{ave}}$ is appropriately defined.

The microstructure and shear rheology of highly concentrated, jammed suspensions of soft particles are shown to depend on polydispersity and shear rate from computational simulations. Rich behavior is observed depending on the degree of polydispersity and the shear rate. Glassy suspensions with a low degree of polydispersity evolve to face-centered cubic and hexagonal close-packed structures at low and high shear rates, respectively. The structural rearrangement occurs over several units of strain and reduces the shear stress and elastic energy. Suspensions with a higher degree of polydispersity exhibit a microstructural transition from a glass to a layeredlike structure for sufficiently high shear rates. In this case, the soft particles first rearrange themselves in the flow-vorticity plane during an induction time (or strain) before layers parallel to the flow-vorticity plane are formed. The induction strain decays exponentially with shear rate revealing that the devitrification of monodisperse and polydisperse suspensions is a shear-activated process. Finally, a generic dynamical state diagram is found that depends on the polydispersity and the ratio of viscous to elastic forces due to shear.

We present detailed observations of the shock waves emitted at the collapse of single cavitation bubbles using simultaneous time-resolved shadowgraphy and hydrophone pressure measurements. The geometry of the bubbles is systematically varied from spherical to very nonspherical by decreasing their distance to a free or rigid surface or by modulating the gravity-induced pressure gradient aboard parabolic flights. The nonspherical collapse produces multiple shocks that are clearly associated with different processes, such as the jet impact and the individual collapses of the distinct bubble segments. For bubbles collapsing near a free surface, the energy and timing of each shock are measured separately as a function of the anisotropy parameter $\zeta$, which represents the dimensionless equivalent of the Kelvin impulse. For a given source of bubble deformation (free surface, rigid surface, or gravity), the normalized shock energy depends only on $\zeta$, irrespective of the bubble radius $R_0$ and driving pressure $\mathrm{\Delta }p$. Based on this finding, we develop a predictive framework for the peak pressure and energy of shock waves from nonspherical bubble collapses. Combining statistical analysis of the experimental data with theoretical derivations, we find that the shock peak pressures can be estimated as jet impact-induced hammer pressures, expressed as $p_h=0.45{\left(\rho c^2\mathrm{\Delta }p\right)}^{1/2}{\zeta }^{-1}$ at $\zeta >{10}^{-3}$. The same approach is found to explain the shock energy decreasing as a function of ${\zeta }^{-2/3}$.

A thin liquid film with nonzero curvature at its free surface spontaneously flows to reach a flat configuration, a process driven by Laplace pressure gradients and resisted by the liquid's viscosity. Inspired by recent progresses on the dynamics of liquid droplets on soft substrates, we here study the relaxation of a viscous film supported by an elastic foundation. Experiments involve thin polymer films on elastomeric substrates, where the dynamics of the liquid-air interface is monitored using atomic force microscopy. A theoretical model that describes the coupled evolution of the solid-liquid and the liquid-air interfaces is also provided. In this soft-levelling configuration, Laplace pressure gradients not only drive the flow, but they also induce elastic deformations on the substrate that affect the flow and the shape of the liquid-air interface itself. This process represents an original example of elastocapillarity that is not mediated by the presence of a contact line. We discuss the impact of the elastic contribution on the levelling dynamics and show the departure from the classical self-similarities and power laws observed for capillary levelling on rigid substrates.

Propulsion through fluids is a key component in the life cycle of many microbes, be it in development, infection, or simply finding nutrients. In systems of biomedical relevance, this propulsion is often through polymer suspensions that endow the fluid with complex non-Newtonian properties, such as shear-thinning and viscoelastic behavior. Due to the complexity of three-dimensional (3D) non-Newtonian modeling, two-dimensional (2D) undulatory propulsion has recently been extensively studied as a means of garnering physical intuition for these systems. However, while streamlines, swimming speeds, and swimmer trajectories are strikingly similar in 2D and 3D Newtonian calculations, behavior in non-Newtonian fluids depends upon flow derivatives, such as the shear rate, which are radically different. Taking shear thinning as an example rheology, prevalent in biological fluids such as physiological mucus, this Rapid Communication demonstrates how failing to account for this difference can misguide our understanding of 3D non-Newtonian swimming.