Dynamics of individual Brownian rods in a microchannel flow

Abstract

We study the orientational dynamics of heavy silica microrods flowing through a microfluidic channel. Comparing experiments and Brownian dynamics simulations we identify different particle orbits, in particular in-plane tumbling behavior, which cannot be explained by classical Jeffery theory, and we relate this behavior to the rotational diffusion of the rods. By constructing the full, three-dimensional, orientation distribution, we describe the rod trajectories and quantify the persistence of Jeffery orbits using temporal correlation functions of the Jeffery constant. We find that our colloidal rods lose memory of their initial configuration in about a second, corresponding to half a Jeffery period.Understanding the physics of a micron-scale, elongated particle moving in viscous flows is widely relevant. Examples include the effect of shape on nano-particle assisted drug delivery 1 , the dynamics of flowing suspensions of bacteria 2 , nanoengineering optically anisotropic devices 3 and the processing of food and pastes 4 . The orientational behaviour of a single, non-Brownian, ellipsoidal rod in a simple shear flow was analysed theoretically in a classic paper by Jeffery in 1922 5 who found that the orientation of an axisymmetric ellipsoid undergoes a periodic motion on the unit sphere. Assuming that the flow is in the x direction and that the shear gradient is along z [see also Fig. 1(a) for non-uniform shear], the specific orbit a particle follows is determined by its aspect ratio λ , the shear rateγ and the Jeffery constant C = n 2x + n 2 z /λ 2 /n y which depends on the initial orientation of the rod and ranges from -∞ to ∞. Here, the unit vector n = n xx + n yŷ + n zẑ points along the long axis of the particle. For C = ±∞ the rod rotates in the xz-plane. It is oriented along the direction of flow for most of the time, but periodically "tumbles", i.e. flips its orientation by 180 • . For smaller values of C, the motion has a finite y-component, and looks very similar to the trajectory of the paddles of a kayak if viewed from the side, hence the term "kayaking" for these orbits. At C = 0, the rod orients along the y-direction and only rotates around its long axis. This last type of motion is called "log-rolling", and has been shown to be unstable for rod-shaped particles 6 . Experiments on single rods, carried out in the non-Brownian regime, have demonstrated the applicability of Jeffery's ideas 7 .Subsequent research has shown how the many perturbations present in flowing channels can affect the reproducibility and longevity of the orbits. For example, even small deviations from a perfect axisymmetric rod shape can lead to the appearance of doubly periodic and chaotic orbits, and these have been studied both theoretically and experimentally [8][9][10] . The proximity of channel walls 11-15 , inertia 6 and the viscoelasticity of the shearing fluid 16 have also been shown to perturb the Jeffery solution. Furthermore, noise may also affect the orbits: for smaller rods, where Brownian motion (i.e. thermal noise)...

Holographic characterization and tracking of colloidal dimers in the effective-sphere approximation

“…The discrete points plotted in Fig. 6(b) are experimental results for P (θ) reported by Zöttl et al [38] for micrometer-scale colloidal rods being transported in a flow geometry very similar to ours. The orientation angles in this case were estimated with conventional microscopy by measuring the projected lengths of the colloidal rods.…”

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“…For nonchiral swimmers (ν = 0), noise affects the dynamics similar to passive elongated particles ( 44 ). Because of noise, trajectories now erratically move around between different Jeffery orbits ( 12 ), which strongly influences the orientation distribution function P (Ψ, Θ), as shown in Fig. 5C .…”

“…1 and 2 . ℋ is calculated from the translational diffusion tensor via Cholesky decomposition, where is a symmetric 3 by 3 matrix [see ( 45 )], and , Δ D = D 1 − D 2 , where D 1 = k B Ta −1 η −1 K 1 (α) and D 2 = k B Ta −1 η −1 K 2 (α) are the respective longitudinal and transversal diffusion coefficients of an ellipsoid of aspect ratio α with shape functions K 1 (α) > K 2 (α) [see ( 12 , 45 )] and with the effective particle (bacterium) radius , where V p is the volume of the particle (bacterium). We use room temperature; hence, k B T = 4.14 pN·nm and buffer viscosity η = 1.28 × 10 −3 Pa·s.…”

Signatures of elastoviscous buckling in the dilute rheology of stiff polymers

“…This dynamics is fundamentally altered in the presence of rotational diffusion. While the shear flow still results in quasi-periodic tumbling, the Brownian rod is now able to stochastically sample different orbits (Zöttl et al 2019), which results in an anisotropic orientational probability distribution ψ(p) at steady state, where p is a unit vector that identifies the orientation of the rod (Chen & Jiang 1999). This distribution leads to a mean orientation of the rod in the extensional quadrant, which gives rise to a contractile stresslet as the inextensible rod resists stretching by the flow.…”