Patrick T. Underhill

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.

Alternative spring force law for bead-spring chain models of the worm-like chain

We have developed a new spring force law which can be used in bead-spring chain models of the worm-like chain. The bead-spring chain has no bending potentials between the springs, and so differs from the current models only in the functional form of the force law. This new model can accurately represent a chain that contains many persistence lengths even if each spring represents only a few persistence lengths. We also discuss the assumptions in the model and other sources of possible error. The new force law significantly reduces the error compared with using the Marko-Siggia interpolation formula.

Development of bead-spring polymer models using the constant extension ensemble

We have examined a new method for generating coarse-grained models of polymers. The resulting models consist of bead-spring chains with the spring force law taken from the force-extension behavior in the constant extension ensemble. This method, called the polymer ensemble transformation method, is applied to the freely jointed chain. The resulting model illustrates why current bead-spring chain models are insufficient in describing polymer behavior at high discretization. Applying the method to the freely jointed chain with unequal rod lengths showed the effect of varying flexibility in the chain. The method was also used to generate a bead-spring model of F-actin, which shows how the method is not restricted to one molecular model and can even be applied to experimental data. The current limitations of the method are discussed, including the need for approximate bending potentials to model the worm-like chain with a bead-spring chain. We discuss practical issues such as using the bead-spring models in B...

Large-amplitude oscillatory shear rheology of dilute active suspensions

Suspensions of swimming microorganisms are a class of active suspensions that show an interesting rheological response in steady shear flow. In particular, the particle contribution to the viscosity can be negative, which has been calculated from models and measured experimentally. In this article, the material functions in large-amplitude oscillatory shear (LAOS) flow are calculated. In addition to the linear material functions, the nonlinearities are quantified analytically using the intrinsic nonlinear material functions. The particle contribution to both the storage and loss modulus can be negative. Since the suspending fluid is assumed Newtonian (and so has no storage modulus), the overall storage modulus can be negative. The intrinsic nonlinearities also show differences between passive and active suspensions. At small frequency, the active swimming can change the sign of the material functions. However, the viscous material functions are independent of the swimming motion at a very large frequency. The changes in sign of the material functions and the unique dependence on frequency may act as a rheological fingerprint of suspensions of swimming organisms.

Impact of external flow on the dynamics of swimming microorganisms near surfaces

Swimming microorganisms have been previously observed to accumulate along walls in confined systems both experimentally and in computer simulations. Here, we use computer simulations of dilute populations for a simplified model of an organism to calculate the dynamics of swimmers between two walls with an external fluid flow. Simulations with and without hydrodynamic interactions (HIs) are used to quantify their influence on surface accumulation. We found that the accumulation of organisms at the wall is larger when HIs are included. An external fluid flow orients the organisms parallel to the fluid flow, which reduces the accumulation at the walls. The effect of the flow on the orientations is quantified and compared to previous work on upstream swimming of organisms and alignment of passive rods in flow. In pressure-driven flow, the zero shear rate at the channel center leads to a dip in the concentration of organisms in the center. The curvature of this dip is quantified as a function of the flow rate. The fluid flow also affects the transport of organisms across the channel from one wall to the other.

Correlations and fluctuations of stress and velocity in suspensions of swimming microorganisms

Active systems, which are driven out of equilibrium, can produce long range correlations and large fluctuations that are not restricted by the fluctuation-dissipation theorem. We consider here the fluctuations and correlations in suspensions of swimming microorganisms that interact hydrodynamically. Modeling the organisms as force dipoles in Stokes flow and considering run-and-tumble and rotational diffusion models of their orientational dynamics allow derivation of closed form results for the stress fluctuations in the long-wave limit. Both of these models lead to Lorentzian distributions, in agreement with some experimental data. These fluctuations are not restricted by the fluctuation-dissipation theorem, as is explicitly verified by comparing the fluctuations with the viscosity of the suspension. In addition to the stress fluctuations in the suspension, we examine correlations between the organisms. Because of the hydrodynamic interactions, the velocities of two organisms are correlated even if the po...

Models of flexible polymers in good solvents: relaxation and coil–stretch transition

We analyze the impact of solvent quality on relaxation dynamics and the coil–stretch transition (CST) using Brownian dynamics simulations of a new bead–spring model. A new spring force relation, which can represent the polymer in theta to good solvent, is developed to obtain the force–extension (FE) behavior of molecules. Due to different regions of the FE curve, we find that the relaxation and CST behavior are altered. A simple force balance is used to explain different regions of the flow and relaxation behavior. Using a model that neglects conformation dependent drag, it is found that some molecules will have two different exponential decays in relaxation and the CST will be modified for others.

Brownian Dynamics Simulations of Polymers and Soft Matter

The Brownian dynamics (BD) simulation technique is a mesoscopic method in which explicit solvent molecules are replaced instead by a stochastic force. The technique takes advantage of the fact that there is a large separation in time scales between the rapid motion of solvent molecules and the more sluggish motion of polymers or colloids. The ability to coarse-grain out these fast modes of the solvent allows one to simulate much larger time scales than in a molecular dynamics simulation. At the core of a Brownian dynamics simulation is a stochastic differential equation which is integrated forward in time to create trajectories of molecules. Time enters naturally into the scheme allowing for the study of the temporal evolution and dynamics of complex fluids (e.g., polymers, large proteins, DNA molecules and colloidal solutions). Hydrodynamic and body forces, such as magnetic or electric fields, can be added in a straightforward way. Brownian dynamics simulations are particularly well suited to studying the structure and rheology of complex fluids in hydrodynamic flows and other nonequilibrium situations.

Role of linear viscoelasticity and rotational diffusivity on the collective behavior of active particles

A linear dynamics scheme has been used to quantify the impact of viscoelasticity of the suspending fluid on the collective structure of active particles, including rotational diffusivity. The linear stability examines the response near an isotropic state using a mean-field theory including far-field hydrodynamic interactions of the swimmers. The kinetic model uses three possible constitutive models, the Oldroyd-B, Maxwell, and generalized linear viscoelastic models inspired by fluids like saliva, mucus, and biological gels. The perturbation growth rate has been quantified in terms of wavenumber, translational diffusivity, rotational diffusivity, and material properties of the fluids. A key dimensionless group is the Deborah number, which compares the relaxation time of the fluid with the characteristic timescale of the instability. An advantage of the model formalism is the ability to calculate some properties analytically and others efficiently numerically in the presence of rotational diffusion. The dif...

Coarse-grained model of conformation-dependent electrophoretic mobility and its influence on DNA dynamics.

The electrophoretic mobility of molecules such as λ-DNA depends on the conformation of the molecule. It has been shown that electrohydrodynamic interactions between parts of the molecule lead to a mobility that depends on conformation and can explain some experimental observations. We have developed a new coarse-grained model that incorporates these changes of mobility into a bead-spring chain model. Brownian dynamics simulations have been performed using this model. The model reproduces the cross-stream migration that occurs in capillary electrophoresis when pressure-driven flow is applied parallel or antiparallel to the electric field. The model also reproduces the change of mobility when the molecule is stretched significantly in an extensional field. We find that the conformation-dependent mobility can lead to a new type of unraveling of the molecule in strong fields. This occurs when different parts of the molecule have different mobilities and the electric field is large.