Brownian demixing and wall effects in sedimenting suspensions of orientable particles

Hoffman, Brendan D.; Shaqfeh, Eric S. G.

doi:10.1103/physreve.78.055301

Cited by 2 publications

(4 citation statements)

References 11 publications

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“…21 The rate of hopping from one well to the other is affected by various parameters of the system which include the length of the polymer 22 and the mixedness in planar flows. 23 Even though the controversy surrounding the existence of hysteresis has been removed, our present understanding is still limited to ideal solvents. There are still controversial results surrounding the effect of solvent quality on the coil stretch transition and hence hysteresis.…”

Section: Introductionmentioning

confidence: 99%

“…However the chains are kinetically trapped in two wells separated by the activation barrier and depending on the initial conformation of the polymer, the polymer lies preferentially in one of the two wells at some finite time . The rate of hopping from one well to the other is affected by various parameters of the system which include the length of the polymer and the mixedness in planar flows . Even though the controversy surrounding the existence of hysteresis has been removed, our present understanding is still limited to ideal solvents.…”

Section: Introductionmentioning

confidence: 99%

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Effect of Solvent Quality on the Coil−Stretch Transition

2010

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Polymers undergo a sharp coil−stretch transition in extension dominated flows when the strain rate exceeds a critical strain rate. We investigate this transition in both Θ solvents and good solvents using Brownian dynamics simulations. The polymer is represented by a bead−spring chain model undergoing elongational flow and solvent-mediated effects such as fluctuating hydrodynamic interactions (HI) and excluded volume (EV) are included rigorously. A 1-D energy landscape theory with an activation energy for transition is used to gain qualitative insights into the dynamics. A key factor in determining the influence of solvent quality is the use of a proper measure of solvent quality. , Contrary to earlier findings, it is observed that with improvement in solvent quality, the critical strain rate at which the coil to stretch transition takes place decreases. Furthermore, the solvent quality has a profound effect on the scaling of the critical strain rate with molecular weight and on both the transient and steady state properties of the system. Universal functions are shown to exist for the observed dynamic and static properties, which will prove useful in determining the operating parameters for experiments.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effect of Solvent Quality on the Coil−Stretch Transition

2010

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“…2 In situations where the microstructural variable does not respond instantaneously to the mean flow, the theory is more complex, but contains the same basic physical elements. 1, 3 The instability is again driven by velocity gradients perturbing the mobility in such a way that the concentration fluctuations amplify.…”

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confidence: 99%

“…6 Moreover, previous examinations of this type of structural instability show that a host of effects not examined here can play a role in wavenumber selection such as density stratification and boundary conditions at container walls. 2, 3 Before we conclude, we would like to revisit some simplifying assumptions we made in our linear stability analysis. As stated before, we assumed the microstructural variable ͓i.e., location of surfactant cap as shown in Figs.…”

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confidence: 99%

Lateral drift and concentration instability in a suspension of bubbles induced by Marangoni stresses at zero Reynolds number

Narsimhan

Shaqfeh

2010

Physics of Fluids

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We report a concentration instability at zero Reynolds number created by hydrodynamically interacting bubbles with surfactant. This instability is driven by Marangoni stresses that force bubbles to migrate in directions perpendicular to gravity. We characterize the lateral motion of a single buoyant bubble when it is subject to a weak, low wavenumber disturbance velocity. We use this result to determine which mean flow wavevectors amplify concentration fluctuations in a dilute suspension. The suspension is linearly unstable at small horizontal wavenumbers by a mechanism similar to the concentration instabilities demonstrated in suspensions of sedimenting nonspherical or deformable particles.It is now well known that hydrodynamic interactions between particles under the action of a body force can greatly alter a suspension's microstructure and even create concentration instabilities, particularly when the particles are characterized by an intrinsic microstructural variable such as orientation or shape deformation. 1-5 These instabilities share a common mechanism in the regime of dilute concentration and low particle Reynolds number, 1-5 and they are very important in describing the rates of sedimentation of fibers in suspension. 2,4,5 We describe another example of this instability that is perhaps not obviously related to the previous work in this area. As described below, buoyant bubbles contaminated with surfactant are subject to a concentration instability due to the Marangoni forces induced by hydrodynamic interactions.The simplest mathematical description of these instabilities is through a mean field theory, where the particles only interact through the mean flow. We assume the microstructural variable ͑deformation, orientation, etc.͒ changes instantaneously compared to the growth rate of concentration fluctuations caused by this variable ͑an assumption we justify at the end of the analysis͒. In this situation, the instability of a dilute, monodisperse suspension at low Reynolds number can be captured by a particle advection-diffusion equation coupled with an averaged momentum equation 2In Eq. ͑1͒, is the suspension concentration, F is the body force on a particle, M is the mobility of a particle, D is a hydrodynamic dispersion tensor, and uЈ is the mean disturbance velocity of the fluid caused by all particles. uЈ satisfies an averaged Stokes flow ͑2͒ which includes a body force proportional to the suspension concentration. 1-3 Hydrodynamic interactions occur between particles via uЈ, and these interactions amplify concentration fluctuations when the advection flux M · F + uЈ is larger than the diffusive flux −D · ٌ, and both point in opposite directions. Because of the microstructural variable describing the mobility of the particle, the particle's mobility is coupled to the mean velocity gradient via M = fٌ͑uЈ͒, and this coupling is what drives instability. For weakly deformable particles, M = M 0 ͑1+E͒, where E is the local rate of strain ͓i.e., 1 2 ٌ͑uЈ + ٌuЈ T ͔͒, and is a relaxation time-scale for the...

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Brownian demixing and wall effects in sedimenting suspensions of orientable particles

Cited by 2 publications

References 11 publications

Effect of Solvent Quality on the Coil−Stretch Transition

Effect of Solvent Quality on the Coil−Stretch Transition

Lateral drift and concentration instability in a suspension of bubbles induced by Marangoni stresses at zero Reynolds number

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