Calculating the motion of highly confined, arbitrary-shaped particles in Hele–Shaw channels

Abstract

We combine theory and numerical calculations to accurately predict the motion of anisotropic particles in shallow microfluidic channels, in which the particles are strongly confined in the vertical direction. We formulate an effective quasi-two-dimensional description of the Stokes flow around the particle via the Brinkman equation, which can be solved in a time that is two orders of magnitude faster than the three-dimensional problem. The computational speedup enables us to calculate the full trajectories of particles in the channel. To validate our scheme, we study the motion of dumbbell-shaped particles that are produced in a microfluidic channel using ‘continuous-flow lithography’. Contrary to what was reported in earlier work (Uspal et al. in Nat Commun 4:2666, 2013 ), we find that the reorientation time of a dumbbell particle in an external flow exhibits a minimum as a function of its disk size ratio. This finding is in excellent agreement with new experiments, thus confirming the predictive power of our scheme. Electronic supplementary material The online version of this article (10.1007/s10404-018-2092-y) contains supplementary material, which is available to authorized users.

Small asymmetric Brownian objects self-align in nanofluidic channels

“…We have fitted the analytical curves on our data set, where the fitting parameter is the reorientation relaxation timeτ. We find that this parameter is a monotonically decreasing function of R. We stress that this result is not in contradiction with recent work where the relaxation time shows a minimum forR = 1.9 23 , since their model of dumbbell particle is fundamentally different from our model. In our model we increaseR by decreasing the radius of one sphere, leading to a particle composed of two beads for allR.…”

“…Engineering particle trajectories in a device is now possible in three different ways, by means of external fields 11 , by taking advantage of hydrodynamic interactions in laminar flows, or by exploiting inertial effects in flow drag of finite Reynolds numbers 12 . The latter has been achieved with recent studies on flow sculpting [13][14][15] , while hydrodynamic interactions are exploited in laminar flows by engineering the geometry of the channel [16][17][18][19][20] or, alternatively, the shape of the sus- pended particles [21][22][23] . This work is concerned with the last of these and specifically with dumbbell shaped particles.…”

“…[22], where the authors investigated the non-Brownian regime. A recent work has further analysed this particular system, providing an alternative and more efficient theoretical framework to solve the Stokes flow around the particle 23 . Their study focuses on the already known phenomenon of self-orientation, the spontaneous alignment of the long axis of the particle with the flow direction, provided that the two disks have different radii (R 1 = R 2 ).…”

“…The experiments 22 were performed at very high Pe number (of the order of 10 4 ), which was essential to drag particles of few tens of microns in width and 100 microns in length, dimensions that are quite big if compared to the typical colloidal length scales (100 − 1000 nm). Similarly, in numerical studies [22][23][24] , the lack of thermal noise in the deterministic model limits the investigations to ideally infinite Pe and do not provide insights on the possibility of self-orientation of smaller objects. On the basis of these arguments, natural questions arise: is the selfalignment still possible for nano-particles or macromolecules with an asymmetric conformation?…”

Universal motion of mirror-symmetric microparticles in confined Stokes flow

“…To distinguish this drag from the drag due to the in-plane flow around the particle, we dub these two interactions “friction” and “flow” drag, respectively. Due to the strong particle confinement the velocity profile in the gaps is close to linear ( 38 , 52 ), allowing us to assume Couette flow in the gaps ( Fig. 1 F ).…”