arXiv subjects

Michael D. Graham

Publications and source records attributed to Michael D. Graham.

At least 55 records · Page 3Linked to original sources

arXiv2020

Discovering multiscale and self-similar structure with data-driven wavelets

Many materials, processes, and structures in science and engineering have important features at multiple scales of time and/or space; examples include biological tissues, active matter, oceans, networks, and images. Explicitly extracting, describing, and defining such features are difficult tasks, at least in part because each system has a unique set of features. Here, we introduce an analysis method that, given a set of observations, discovers an energetic hierarchy of structures localized in scale and space. We call the resulting basis vectors a "data-driven wavelet decomposition". We show that this decomposition reflects the inherent structure of the dataset it acts on, whether it has no structure, structure dominated by a single scale, or structure on a hierarchy of scales. In particular, when applied to turbulence---a high-dimensional, nonlinear, multiscale process---the method reveals self-similar structure over a wide range of spatial scales, providing direct, model-free evidence for a century-old phenomenological picture of turbulence. This approach is a starting point for the characterization of localized hierarchical structures in multiscale systems, which we may think of as the building blocks of these systems.

physics.flu-dyn↗

arXiv2020

Coil-stretch-like transition of elastic sheets in extensional flows

The conformation of a long linear polymer dissolved in fluid and exposed to an extensional flow is well-known to exhibit a "coil-stretch" transition, which for sufficiently long chains can lead to bistability. The present work reports computations indicating that an analogous "compact-stretched" transition arises in the dynamics of a thin elastic sheet. Sheets of nominally circular, square or rectangular shape are simulated in planar and biaxial flows using a finite element method for the sheet conformations and a regularized Stokeslet method for the fluid flow. If a neo-Hookean constitutive model is used for the sheet elasticity, the sheets will stretch without bound once a critical extension rate, as characterized nondimensionally by a capillary number, is exceeded. Nonlinear elasticity, represented with the Yeoh model, arrests the stretching, leading to a highly-stretched steady state once the critical capillary number is exceeded. For all shapes and in both planar and biaxial extension, a parameter regime exists in which both weakly stretched (compact) and strongly stretched states can be found, depending on initial conditions. I.e. this parameter regime displays bistability. As in the long-chain polymer case, the bistable behavior arises from the hydrodynamic interaction between distant elements of the sheet, and vanishes if these interactions are artificially screened by use of a Brinkman model for the fluid motion. While the sheets can transiently display wrinkled shapes, all final shapes in planar and biaxial extension are planar.

cond-mat.soft↗

arXiv2020

Deep learning to discover and predict dynamics on an inertial manifold

A data-driven framework is developed to represent chaotic dynamics on an inertial manifold (IM), and applied to solutions of the Kuramoto-Sivashinsky equation. A hybrid method combining linear and nonlinear (neural-network) dimension reduction transforms between coordinates in the full state space and on the IM. Additional neural networks predict time-evolution on the IM. The formalism accounts for translation invariance and energy conservation, and substantially outperforms linear dimension reduction, reproducing very well key dynamic and statistical features of the attractor.

cs.LG↗

arXiv2020

Self-sustained elastoinertial Tollmien-Schlichting waves

Direct simulations of two-dimensional plane channel flow of a viscoelastic fluid at Reynolds number Re = 3000 reveal the existence of a family of attractors whose structure closely resembles the linear Tollmien-Schlichting (TS) mode, and in particular exhibits strongly localized stress fluctuations at the critical layer position of the TS mode. At the parameter values chosen, this solution branch is not connected to the nonlinear TS solution branch found for Newtonian flow, and thus represents a solution family that is nonlinearly self-sustained by viscoelasticity. The ratio between stress and velocity fluctuations is in quantitative agreement for the attractor and the linear TS mode, and increases strongly with Weissenberg number, Wi. For the latter, there is a transition in the scaling of this ratio as Wi increases, and the Wi at which the nonlinear solution family comes into existence is just above this transition. Finally, evidence indicates that this branch is connected through an unstable solution branch to two-dimensional elastoinertial turbulence (EIT). These results suggest that, in the parameter range considered here, the bypass transition leading to EIT is mediated by nonlinear amplification and self-sustenance of perturbations that excite the Tollmien-Schlichting mode.

physics.flu-dyn↗

arXiv2020

Flow-induced segregation and dynamics of red blood cells in sickle cell disease

Blood flow in sickle cell disease (SCD) can substantially differ from normal blood flow due to significant alterations in the physical properties of the red blood cells (RBCs). Chronic complications, such as inflammation of the endothelial cells lining blood vessel walls, are associated with SCD, for reasons that are unclear. Here, detailed boundary integral simulations are performed to investigate an idealized model flow flow in SCD, a binary suspension of flexible biconcave discoidal fluid-filled capsules and stiff curved prolate capsules that represent healthy and sickle RBCs, respectively, subjected to pressure-driven flow in a planar slit. The key observation is that, unlike healthy RBCs that concentrate around the center of the channel and form an RBC-depleted layer (i.e. cell-free layer) next to the walls, sickle cells are largely drained from the bulk of the suspension and aggregate inside the cell-free layer, displaying strong margination. These cells are found to undergo a rigid-body-like rolling orbit near the walls. Furthermore, the additional shear stress on the walls induced by the presence of marginated cells is computed. Compared to the small fluctuations in wall shear stress for a suspension of healthy RBCs, large local peaks in wall shear stress are observed for the binary suspensions, due to the proximity of the marginated stiff cells to the walls. As endothelial cells are known to mechanotransduce physical forces such as aberrations in shear stress and convert them to physiological processes such as activation of inflammatory signals, these results may aid in understanding mechanisms for endothelial dysfunction associated with SCD.

physics.bio-ph↗

arXiv2019

Multiplicity of stable orbits for deformable prolate capsules in shear flow

This work investigates the orbital dynamics of a fluid-filled deformable prolate capsule in unbounded shear flow. The motion of the capsule is simulated using a model that incorporates shear elasticity, area dilatation, and bending resistance. Here the deformability of the capsule is characterized by capillary number Ca, which represents the ratio of viscous stresses to elastic restoring stresses. For a capsule with small bending stiffness, at a given Ca, the orientation converges over time towards a unique stable orbit independent of the initial orientation. With increasing Ca, four dynamical modes are found for the stable orbit: rolling, wobbling, oscillating-swinging, and swinging. For a capsule with large bending stiffness, multiplicity in the orbit dynamics is observed. When the viscosity ratio $λ\lesssim 1$, the long-axis of the capsule always tends towards a stable orbit in the flow-gradient plane, either tumbling or swinging, depending on Ca. When $λ\gtrsim 1$, the stable orbit of the capsule is a tumbling motion at low Ca, irrespective of the initial orientation. Upon increasing Ca, there is a symmetry-breaking bifurcation away from the tumbling orbit, and the capsule is observed to adopt multiple stable orbital modes including nonsymmetric precessing and rolling, depending on the initial orientation. As Ca further increases, the nonsymmetric stable orbit loses existence at a saddle-node bifurcation, and rolling becomes the only attractor at high Ca, whereas the rolling state coexists with the nonsymmetric state at intermediate values of Ca. A symmetry-breaking bifurcation away from the rolling orbit is also found upon decreasing Ca. The regime with multiple attractors becomes broader as the aspect ratio of the capsule increases, while narrowing as viscosity ratio increases. We also report the particle contribution to the stress, which also displays multiplicity.

physics.flu-dyn↗

arXiv2019

Critical-layer structures and mechanisms in elastoinertial turbulence

Simulations of elastoinertial turbulence (EIT) of a polymer solution at low Reynolds number are shown to display localized polymer stretch fluctuations. These are very similar to structures arising from linear stability (Tollmien-Schlichting (TS) modes) and resolvent analyses: i.e., critical-layer structures localized where the mean fluid velocity equals the wavespeed. Computation of self-sustained nonlinear TS waves reveals that the critical layer exhibits stagnation points that generate sheets of large polymer stretch. These kinematics may be the genesis of similar structures in EIT.

physics.flu-dyn↗

arXiv2018

Dynamics of deformable straight and curved prolate capsules in simple shear flow

This work investigates the motion of neutrally-buoyant, slightly deformable straight and curved prolate capsules in unbounded simple shear flow at zero Reynolds number using direct simulations. The curved capsules serve as a model for the typical crescent-shaped sickle red blood cells in sickle cell disease (SCD). The effects of deformability and curvature on the dynamics are revealed. We show that with low deformability, straight prolate spheroidal capsules tumble in the shear plane as their unique asymptotically stable orbit, which contrasts with that for rigid spheroids where infinitely many neutrally stable Jeffery orbits exist. The dynamics of curved prolate capsules are more complicated due to a combined effect of deformability and curvature. At short times, depending on the initial orientation, slightly deformable curved prolate capsules exhibit either a Jeffery-like motion such as tumbling or kayaking, or a non-Jeffery-like behavior in which the end-to-end vector of the capsule crosses the shear-gradient plane back and forth. At long times, however, a Jeffery-like quasi-periodic orbit is taken regardless of the initial orientation. We further show that the average of the long-time trajectory can be well approximated using the analytical solution for Jeffery orbits with an effective orbit constant $C_{\textnormal{eff}}$ and aspect ratio $\ell_{\textnormal{eff}}$. As the capsule becomes more deformable or curved, $C_{\textnormal{eff}}$ decreases, indicating a shift of the orbit towards log-rolling motion, while $\ell_{\textnormal{eff}}$ increases weakly as the degree of curvature increases but shows negligible dependency on deformability. As cell deformability, cell shape, and cell-cell interactions are all pathologically altered in blood disorders such as SCD, these results will have clear implications on improving our understanding of the pathophysiology of hematologic disease.

physics.flu-dyn↗

arXiv2018

Impacts of multiflagellarity on stability and speed of bacterial locomotion

Trajectories and conformations of uni- and multiflagellar bacteria are studied with a coarse-grained model of a cell comprised of elastic flagella connected to a cell body. The elasticities of both the hook protein (connecting cell body and flagellum) and flagella are varied. Flexibility plays contrasting roles for uni- and multiflagellar swimmers. For a uniflagellar swimmer, hook and/or flagellar buckling occurs above a critical flexibility relative to the torque exerted by the flagellar motor. Addition of a second flagellum greatly expands the parameter regime of stable locomotion, because flexible hooks that would lead to buckling instability in the uniflagellar case provide the flexibility required for flagellar bundling in the biflagellar case. Similar observations hold for tri- and quadriflagellar swimmers. Indeed the stability regimes for uni- and quadriflagellar swimming are virtually inverted -- to a first approximation what is stable in one case is unstable in the other. Swimming speed is also examined: it increases very weakly with number of flagella and a simple theory is developed that explains this observation.

physics.bio-ph↗

arXiv2018

Exact coherent states with hairpin-like vortex structure in channel flow

Hairpin vortices are widely studied as an important structural aspect of wall turbulence. The present work describes, for the first time, nonlinear traveling wave solutions to the Navier--Stokes equations in the channel flow geometry -- exact coherent states (ECS) -- that display hairpin-like vortex structure. This solution family comes into existence at a saddle-node bifurcation at Reynolds number Re=666. At the bifurcation, the solution has a highly symmetric quasistreamwise vortex structure similar to that reported for previously studied ECS. With increasing distance from the bifurcation, however, both the upper and lower branch solutions develop a vortical structure characteristic of hairpins: a spanwise-oriented "head" near the channel centerplane where the mean shear vanishes connected to counter-rotating quasistreamwise "legs" that extend toward the channel wall. At Re=1800, the upper branch solution has mean and Reynolds shear-stress profiles that closely resemble those of turbulent mean profiles in the same domain.

physics.flu-dyn↗

arXiv2017

Mechanistic constitutive model for wormlike micelle solutions with flow-induced structure formation

We present a tensor constitutive model for predicting stress and flow-induced structure formation in dilute wormlike micellar solutions. The micellar solution is treated as a dilute suspension of rigid Brownian rods whose length varies dynamically. Consistent with the mechanism presented by Turner and Cates [J. Phys.:~Condens. Matter 4, 3719 (1992)], flow-induced alignment of the rods is assumed to promote increase of rod length that corresponds to the formation of flow-induced structures observed in experiments. At very high deformation rate, hydrodynamic stresses causes the rod length to decrease. These mechanisms are implemented in a phenomenological equation governing the evolution of rod length, with the number density of rods appropriately modified to ensure conservation of surfactant mass. The model leads first to an increase in both shear and extensional viscosity as deformation rate increases and then to a decrease at higher rates. If the rate constant for flow-induced rod growth is sufficiently large, the model predicts a multivalued relation between stress and deformation rate in both shear and uniaxial extension. Predictions for shear and extensional flow at steady state are in reasonable agreement with experimental results. By design, the model is simple enough to serve as a tractable constitutive relation for computational fluid dynamics studies.

physics.flu-dyn↗

arXiv2016

Low-dimensional representations of exact coherent states of the Navier-Stokes equations from the resolvent model of wall turbulence

We report that many exact invariant solutions of the Navier-Stokes equations for both pipe and channel flows are well represented by just few modes of the model of McKeon & Sharma J. Fl. Mech. 658, 356 (2010). This model provides modes that act as a basis to decompose the velocity field, ordered by their amplitude of response to forcing arising from the interaction between scales. The model was originally derived from the Navier-Stokes equations to represent turbulent flows and has been used to explain coherent structure and to predict turbulent statistics. This establishes a surprising new link between the two distinct approaches to understanding turbulence.

physics.flu-dyn↗

arXiv2015

Exact coherent states and connections to turbulent dynamics in minimal channel flow

Several new families of nonlinear three-dimensional travelling wave solutions to the Navier-Stokes equation, also known as exact coherent states, are computed for Newtonian plane Poiseuille flow. The symmetries and streak/vortex structures are reported and their possible connections to critical layer dynamics examined. While some of the solutions clearly display fluctuations that are localized around the critical layer (the surface on which the streamwise velocity matches the wave speed of the solution), for others this connection is not as clear. Dynamical trajectories along unstable directions of the solutions are computed. Over certain ranges of Reynolds number, two solution families are shown to lie on the basin boundary between laminar and turbulent flow. Direct comparison of nonlinear travelling wave solutions to turbulent flow in the same channel is presented. The state-space dynamics of the turbulent flow are organized around one of the newly-identified travelling wave families, and in particular the lower branch solutions of this family are closely approached during transient excursions away from the dominant behaviour. These observations provide a firm dynamical-systems foundation for prior observations that minimal channel turbulence displays time intervals of "active" turbulence punctuated by brief periods of "hibernation" (see e.g. Xi, L. and Graham, M. D., Phys. Rev. Lett., 104, 218301 (2010)). The hibernating intervals are approaches to lower branch nonlinear travelling waves. Representing these solutions on a Prandtl-von Karman plot illustrates how their bulk flow properties are related to those of Newtonian turbulence as well as the universal asymptotic state called maximum drag reduction (MDR) found in viscoelastic turbulent flow.

physics.flu-dyn↗

arXiv2012

Mechanism of margination in confined flows of blood and other multicomponent suspensions

Flowing blood displays a phenomenon called margination, in which leukocytes and platelets are preferentially found near blood vessel walls, while erythrocytes are depleted from these regions. Here margination is investigated using direct hydrodynamic simulations of a binary suspension of stiff (s) and floppy (f) capsules, as well as a stochastic model that incorporates the key particle transport mechanisms in suspensions -- wall-induced hydrodynamic migration and shear-induced pair collisions. The stochastic model allows the relative importance of these two mechanisms to be directly evaluated and thereby indicates that margination, at least in the dilute case, is largely due to the differential dynamics of homogeneous (e.g. s-s) and heterogeneous (s-f) collisions

cond-mat.soft↗

arXiv2012

Accelerated boundary integral method for multiphase flow in non-periodic geometries

An accelerated boundary integral method for Stokes flow of a suspension of deformable particles is presented for an arbitrary domain and implemented for the important case of a planar slit geometry. The computational complexity of the algorithm scales as O(N) or $O(N\log N$), where $N$ is proportional to the product of number of particles and the number of elements employed to discretize the particle. This technique is enabled by the use of an alternative boundary integral formulation in which the velocity field is expressed in terms of a single layer integral alone, even in problems with non-matched viscosities. The density of the single layer integral is obtained from a Fredholm integral equation of the second kind involving the double layer integral. Acceleration in this implementation is provided by the use of General Geometry Ewald-like method (GGEM) for computing the velocity and stress fields driven by a set of point forces in the geometry of interest. For the particular case of the slit geometry, a Fourier-Chebyshev spectral discretization of GGEM is developed. Efficient implementations employing the GGEM methodology are presented for the resulting single and the double layer integrals. The implementation is validated with test problems on the velocity of rigid particles and drops between parallel walls in pressure driven flow, the Taylor deformation parameter of capsules in simple shear flow and the particle trajectory in pair collisions of capsules in shear flow. The computational complexity of the algorithm is verified with results from several large scale multiparticle simulations.

cond-mat.soft↗

arXiv2011

Segregation by membrane rigidity in flowing binary suspensions of elastic capsules

Spatial segregation in the wall normal direction is investigated in suspensions containing a binary mixture of Neo-Hookean capsules subjected to pressure driven flow in a planar slit. The two components of the binary mixture have unequal membrane rigidities. The problem is studied numerically using an accelerated implementation of the boundary integral method. The effect of a variety of parameters was investigated, including the capillary number, rigidity ratio between the two species, volume fraction, confinement ratio, and the number fraction of the more floppy particle $X_f$ in the mixture. It was observed that in suspensions of pure species, the mean wall normal positions of the stiff and the floppy particles are comparable. In mixtures, however, the stiff particles were found to be increasingly displaced towards the walls with increasing $X_f$, while the floppy particles were found to increasingly accumulate near the centerline with decreasing $X_f$. The origins of this segregation is traced to the effect of the number fraction $X_f$ on the localization of the stiff and the floppy particles in the near wall region -- the probability of escape of a stiff particle from the near wall region to the interior is greatly reduced with increasing $X_f$, while the exact opposite trend is observed for a floppy particle with decreasing $X_f$. Simple model studies on heterogeneous pair collisions involving a stiff and a floppy particle mechanistically explain this observation. The key result in these studies is that the stiff particle experiences much larger cross-stream displacement in heterogeneous collisions than the floppy particle. A unified mechanism incorporating the wall-induced migration of deformable particles and the particle fluxes associated with heterogeneous and homogeneous pair collisions is presented.

cond-mat.soft↗

arXiv2010

Active and hibernating turbulence in minimal channel flow of Newtonian and polymeric fluids

Turbulent channel flow of drag-reducing polymer solutions is simulated in minimal flow geometries. Even in the Newtonian limit, we find intervals of "hibernating" turbulence that display many features of the universal maximum drag reduction (MDR) asymptote observed in polymer solutions: weak streamwise vortices, nearly nonexistent streamwise variations and a mean velocity gradient that quantitatively matches experiments. As viscoelasticity increases, the frequency of these intervals also increases, while the intervals themselves are unchanged, leading to flows that increasingly resemble MDR.

physics.flu-dyn↗

arXiv2008

Dynamics of confined suspensions of swimming particles

Low Reynolds number direct simulations of large populations of hydrodynamically interacting swimming particles confined between planar walls are performed. The results of simulations are compared with a theory that describes dilute suspensions of swimmers. The theory yields scalings with concentration for diffusivities and velocity fluctuations as well as a prediction of the fluid velocity spatial autocorrelation function. Even for uncorrelated swimmers, the theory predicts anticorrelations between nearby fluid elements that correspond to vortex-like swirling motions in the fluid with length scale set by the size of a swimmer and the slit height. Very similar results arise from the full simulations indicating either that correlated motion of the swimmers is not significant at the concentrations considered or that the fluid phase autocorrelation is not a sensitive measure of the correlated motion. This result is in stark contrast with results from unconfined systems, for which the fluid autocorrelation captures large-scale collective fluid structures. The additional length scale (screening length) introduced by the confinement seems to prevent these large-scale structures from forming.

physics.flu-dyn↗