We develop a linearly scaling variant of the force coupling method [K. Yeo and M. R. Maxey, J. Fluid Mech. 649, 205–231 (2010)] for computing hydrodynamic interactions among particles confined to a doubly periodic geometry with either a single bottom wall or two walls (slit channel) in the aperiodic direction. Our spectrally accurate Stokes solver uses the fast Fourier transform in the periodic xy plane and Chebyshev polynomials in the aperiodic z direction normal to the wall(s). We decompose the problem into two problems. The first is a doubly periodic subproblem in the presence of particles (source terms) with free-space boundary conditions in the z direction, which we solve by borrowing ideas from a recent method for rapid evaluation of electrostatic interactions in doubly periodic geometries [Maxian et al., J. Chem. Phys. 154, 204107 (2021)]. The second is a correction subproblem to impose the boundary conditions on the wall(s). Instead of the traditional Gaussian kernel, we use the exponential of a semicircle kernel to model the source terms (body force) due to the presence of particles and provide optimum values for the kernel parameters that ensure a given hydrodynamic radius with at least two digits of accuracy and rotational and translational invariance. The computation time of our solver, which is implemented in graphical processing units, scales linearly with the number of particles, and allows computations with about a million particles in less than a second for a sedimented layer of colloidal microrollers. We find that in a slit channel, a driven dense suspension of microrollers maintains the same two-layer structure as above a single wall, but moves at a substantially lower collective speed due to increased confinement.
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Driven dynamics in dense suspensions of microrollers
We perform detailed computational and experimental measurements of the driven dynamics of a dense, uniform suspension of sedimented microrollers driven by a magnetic field rotating around an axis parallel to the floor. We develop a lubrication-corrected Brownian dynamics method for dense suspensions of driven colloids sedimented above a bottom wall. The numerical method adds lubrication friction between nearby pairs of particles, as well as particles and the bottom wall, to a minimally-resolved model of the far-field hydrodynamic interactions. Our experiments combine fluorescent labeling with particle tracking to trace the trajectories of individual particles in a dense suspension, and to measure their propulsion velocities. Previous computational studies [B. Sprinkle et al. , J. Chem. Phys. , 2017, 147 , 244103] predicted that at sufficiently high densities a uniform suspension of microrollers separates into two layers, a slow monolayer right above the wall, and a fast layer on top of the bottom layer. Here we verify this prediction, showing good quantitative agreement between the bimodal distribution of particle velocities predicted by the lubrication-corrected Brownian dynamics and those measured in the experiments. The computational method accurately predicts the rate at which particles are observed to switch between the slow and fast layers in the experiments. We also use our numerical method to demonstrate the important role that pairwise lubrication plays in motility-induced phase separation in dense monolayers of colloidal microrollers, as recently suggested for suspensions of Quincke rollers [D. Geyer et al. , Phys. Rev. X , 2019, 9 (3), 031043].
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- NSF-PAR ID:
- 10225647
- Date Published:
- Journal Name:
- Soft Matter
- Volume:
- 16
- Issue:
- 34
- ISSN:
- 1744-683X
- Page Range / eLocation ID:
- 7982 to 8001
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Summary A hybrid computational method coupling the lattice‐Boltzmann (LB) method and a Langevin‐dynamics (LD) method is developed to simulate nanoscale particle and polymer (NPP) suspensions in the presence of both thermal fluctuation and long‐range many‐body hydrodynamic interactions (HIs). Brownian motion of the NPP is explicitly captured by a stochastic forcing term in the LD method. The LD method is two‐way coupled to the nonfluctuating LB fluid through a discrete LB forcing source distribution to capture the long‐range HI. To ensure intrinsically linear scalability with respect to the number of particles, a Eulerian‐host algorithm for short‐distance particle neighbor search and interaction is developed and embedded to LB‐LD framework. The validity and accuracy of the LB‐LD approach are demonstrated through several sample problems. The simulation results show good agreements with theory and experiment. The LB‐LD approach can be favorably incorporated into complex multiscale computational frameworks for efficiently simulating multiscale multicomponent particulate suspension systems such as complex blood suspensions.
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Hypothesis: The dip coating of suspensions made of monodisperse non-Brownian spherical particles dispersed in a Newtonian fluid leads to different coating regimes depending on the ratio of the particle diameter to the thickness of the film entrained on the substrate. In particular, dilute particles dispersed in the liquid are entrained only above a threshold value of film thickness. In the case of anisotropic particles, in particular fibers, the smallest characteristic dimension will control the entrainment of the particle. Furthermore, it is possible to control the orientation of the anisotropic particles depending on the substrate geometry. In the thick film regime, the Landau-Levich-Derjaguin model remains valid if one account for the change in viscosity. Experiment: To test the hypotheses, we performed dip-coating experiments with dilute suspensions of non-Brownian fibers with different length-to-diameter aspect ratios. We characterize the number of fibers entrained on the surface of the substrate as a function of the withdrawal velocity, allowing us to estimate a threshold capillary number below which all the particles remain in the liquid bath. Besides, we measure the angular distribution of the entrained fibers for two different substrate geometries: flat plates and cylindrical rods. We then measure the film thickness for more concentrated fiber suspensions. Findings: The entrainment of the fibers on a flat plate and a cylindrical rod is primarily controlled by the smaller characteristic length of the fibers: their diameter. At first order, the entrainment threshold scales similarly to that of spherical particles. The length of the fibers only appears to have a minor influence on the entrainment threshold. No preferential alignment is observed for non-Brownian fibers on a flat plate, except for very thin films, whereas the fibers tend to align themselves along the axis of a cylindrical rod for a large enough ratio of the fiber length to the radius of the cylindrical rod. The Landau-Levich-Derjaguin law is recovered for more concentrated suspension by introducing an effective capillary number accounting for the change in viscosity.more » « less
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Understanding the orientation dynamics of anisotropic colloidal particles is important for suspension rheology and particle self-assembly. However, even for the simplest case of dilute suspensions in shear flow, the orientation dynamics of non-spherical Brownian particles are poorly understood. Here we analytically calculate the time-dependent orientation distributions for non-spherical axisymmetric particles confined to rotate in the flow–gradient plane, in the limit of small but non-zero Brownian diffusivity. For continuous shear, despite the complicated dynamics arising from the particle rotations, we find a coordinate change that maps the orientation dynamics to a diffusion equation with a remarkably simple ratio of the enhanced rotary diffusivity to the zero shear diffusion: $D_{eff}^{r}/D_{0}^{r}=(3/8)(p-1/p)^{2}+1$ , where $p$ is the particle aspect ratio. For oscillatory shear, the enhanced diffusion becomes orientation dependent and drastically alters the long-time orientation distributions. We describe a general method for solving the time-dependent oscillatory shear distributions and finding the effective diffusion constant. As an illustration, we use this method to solve for the diffusion and distributions in the case of triangle-wave oscillatory shear and find that they depend strongly on the strain amplitude and particle aspect ratio. These results provide new insight into the time-dependent rheology of suspensions of anisotropic particles. For continuous shear, we find two distinct diffusive time scales in the rheology that scale separately with aspect ratio $p$ , as $1/D_{0}^{r}p^{4}$ and as $1/D_{0}^{r}p^{2}$ for $p\gg 1$ . For oscillatory shear flows, the intrinsic viscosity oscillates with the strain amplitude. Finally, we show the relevance of our results to real suspensions in which particles can rotate freely. Collectively, the interplay between shear-induced rotations and diffusion has rich structure and strong effects: for a particle with aspect ratio 10, the oscillatory shear intrinsic viscosity varies by a factor of ${\approx}2$ and the rotational diffusion by a factor of ${\approx}40$ .more » « less
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$N_1$ $N_2$ $15\,\% \leq \phi \leq 50\,\%$ $Mn$ $Mn < 1$ $N_1$ $N_2$ $\phi < 30\,\%$ $\phi \ge 30\,\%$ $Mn \ge 1$ $\phi \ge 30\,\%$ $\phi = 50\,\%$ $N_1$ $N_2$ $Mn \gg 1$ $Mn = 1$
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/D0SM00879F
