Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCoarse-graining the dynamics of immersed and driven fiber assemblies
81
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
An important class of fluid-structure problems involve the dynamics of ordered arrays of immersed, flexible fibers. While specialized numerical methods have been developed to study fluid-fiber systems, they become infeasible when there are many, rather than a few, fibers present, nor do these methods lend themselves to analytical calculation. Here, we introduce a coarse-grained continuum model, based on local-slender body theory, for elastic fibers immersed in a viscous Newtonian fluid. It takes the form of an anisotropic Brinkman equation whose skeletal drag is coupled to elastic forces. This model has two significant benefits: (1) the density effects of the fibers in a suspension become analytically manifest, and (2) it allows for the rapid simulation of dense suspensions of fibers in regimes inaccessible to standard methods. As a first validation, without fitting parameters, we achieve very reasonable agreement with 3D Immersed Boundary simulations of a bed of anchored fibers bent by a shear flow. Secondly, we characterize the effect of density on the relaxation time of fiber beds under oscillatory shear, and find close agreement to results from full numerical simulations. We then study buckling instabilities in beds of fibers, using our model both numerically and analytically to understand the role of fiber density and the structure of buckling transitions. We next apply our model to study the flow-induced bending of inclined fibers in a channel, as has been recently studied as a flow rectifier, examining the nature of the internal flows within the bed, and the emergence of inhomogeneous permeability. Finally, we extend the method to study a simple model of metachronal waves on beds of actuated fibers, as a model for ciliary beds. Our simulations reproduce qualitatively the pumping action of coordinated waves of compression through the bed.
rate research
Read More
A coarse-graining framework is implemented to analyze nonlinear processes, measure energy transfer rates and map out the energy pathways from simulated global ocean data. Traditional tools to measure the energy cascade from turbulence theory, such as spectral flux or spectral transfer rely on the assumption of statistical homogeneity, or at least a large separation between the scales of motion and the scales of statistical inhomogeneity. The coarse-graining framework allows for probing the fully nonlinear dynamics simultaneously in scale and in space, and is not restricted by those assumptions. This paper describes how the framework can be applied to ocean flows. Energy transfer between scales is not unique due to a gauge freedom. Here, it is argued that a Galilean invariant subfilter scale (SFS) flux is a suitable quantity to properly measure energy scale-transfer in the Ocean. It is shown that the SFS definition can yield answers that are qualitatively different from traditional measures that conflate spatial transport with the scale-transfer of energy. The paper presents geographic maps of the energy scale-transfer that are both local in space and allow quasi-spectral, or scale-by-scale, dynamics to be diagnosed. Utilizing a strongly eddying simulation of flow in the North Atlantic Ocean, it is found that an upscale energy transfer does not hold everywhere. Indeed certain regions, near the Gulf Stream and in the Equatorial Counter Current have a marked downscale transfer. Nevertheless, on average an upscale transfer is a reasonable mean description of the extra-tropical energy scale-transfer over regions of O(10^3) kilometers in size.
We numerically investigate both single and multiple droplet dissolution with droplets consisting of lighter liquid dissolving in a denser host liquid. The significance of buoyancy is quantified by the Rayleigh number Ra which is the buoyancy force over the viscous damping force. In this study, Ra spans almost four decades from 0.1 to 400. We focus on how the mass flux, characterized by the Sherwood number Sh, and the flow morphologies depend on Ra. For single droplet dissolution, we first show the transition of the Sh(Ra) scaling from a constant value to $Shsim Ra^{1/4}$, which confirms the experimental results by Dietrich et al. (J. Fluid Mech., vol. 794, 2016, pp. 45--67). The two distinct regimes, namely the diffusively- and the convectively-dominated regime, exhibit different flow morphologies: when Ra>=10, a buoyant plume is clearly visible which contrasts sharply to the pure diffusion case at low Ra. For multiple droplet dissolution, the well-known shielding effect comes into play at low Ra so that the dissolution rate is slower as compared to the single droplet case. However, at high Ra, convection becomes more and more dominant so that a collective plume enhances the mass flux, and remarkably the multiple droplets dissolve faster than a single droplet. This has also been found in the experiments by Laghezza et al. (Soft Matter, vol. 12, 2016, pp. 5787--5796). We explain this enhancement by the formation of a single, larger plume rather than several individual plumes. Moreover, there is an optimal Ra at which the enhancement is maximized, because the single plume is narrower at larger Ra, which thus hinders the enhancement. Our findings demonstrate a new mechanism in collective droplet dissolution, which is the merging of the plumes, that leads to non-trivial phenomena, contrasting the shielding effect.
A liquid droplet, immersed into a Newtonian fluid, can be propelled solely by internal flow. In a simple model, this flow is generated by a collection of point forces, which represent externally actuated devices or model autonomous swimmers. We work out the general framework to compute the self-propulsion of the droplet as a function of the actuating forces and their positions within the droplet. A single point force, F with general orientation and position, r_0, gives rise to both, translational and rotational motion of the droplet. We show that the translational mobility is anisotropic and the rotational mobility can be nonmonotonic as a function of | r_0|, depending on the viscosity contrast. Due to the linearity of the Stokes equation, superposition can be used to discuss more complex arrays of point forces. We analyse force dipoles, such as a stresslet, a simple model of a biflagellate swimmer and a rotlet, representing a helical swimmer, driven by an external magnetic field. For a general force distribution with arbitrary high multipole moments the propulsion properties of the droplet depend only on a few low order multipoles: up to the quadrupole for translational and up to a special octopole for rotational motion. The coupled motion of droplet and device is discussed for a few exemplary cases. We show in particular that a biflagellate swimmer, modeled as a stresslet, achieves a steady comoving state, where the position of the device relative to the droplet remains fixed. In fact there are two fixpoints, symmetric with respect to the center of the droplet. A tiny external force selects one of them and allows to switch between forward and backward motion.
We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids. We focus on capsules and vesicles, whose discretization is particularly challenging due to the higher-order derivatives that appear in their formulations. In two-dimensional settings, we employ cubic B-splines with periodic knot vectors to obtain discretizations of closed curves with C^2 inter-element continuity. In three-dimensional settings, we use analysis-suitable bi-cubic T-splines to obtain discretizations of closed surfaces with at least C^1 inter-element continuity. Large spurious changes of the fluid volume inside closed co-dimension one solids is a well-known issue for IB methods. The DCIB method results in volume changes orders of magnitude lower than conventional IB methods. This is a byproduct of discretizing the velocity-pressure pair with divergence-conforming B-splines, which lead to negligible incompressibility errors at the Eulerian level. The higher inter-element continuity of divergence-conforming B-splines is also crucial to avoid the quadrature/interpolation errors of IB methods becoming the dominant discretization error. Benchmark and application problems of vesicle and capsule dynamics are solved, including mesh-independence studies and comparisons with other numerical methods.
A Particle Tracking Velocimetry experiment has been performed in a turbulent flow at intermediate Reynolds number. We present experimentally obtained stretching rates for particle pairs in the inertial range. When compensated by a characteristic time scale for coarse-grained strain we observe constant stretching. This indicates that the process of material line stretching taking place in the viscous subrange has its counterpart in the inertial subrange. We investigate both forwards and backwards dispersion. We find a faster backwards stretching and relate it to the problem of relative dispersion and its time asymmetry.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
