Modeling microflow and stirring around a microrotor in creeping flow using a quasi-steady-state analysis

Abstract

The microflow and stirring around paramagnetic particle microchains, referred to as microrotors, are modeled as a circular cylinder rotating about its radial axis at very low Reynolds number. Time scales for momentum transfer under these conditions are determined to be much smaller than those for boundary movement, hence a quasi-steady approximation can be used. The flow is derived at every instant from the case of a steady motion of a horizontally translating cylinder, with the rotation approximated to a series of differential incremental translations. A numerical simulation is used to determine the pathlines and material lines of virtual point fluid elements, which were analyzed to understand the behavior of the flow around the microrotor. The results indicate the flow to be unsteady, with chaotic advection observed in the system. The fluid motion is primarily two-dimensional, parallel to the rotational plane, with mixing limited to the immediate area around the rotating cylinder. Fluid layers, up to many cylinder diameters, in the axial direction experience the disturbance. Elliptic and star shaped pathlines, including periodic orbits, are observed depending on the fluid element's initial location. The trajectories and phase angles compare well with the experimental results, as well as with data from particle dynamics simulations. Material lines and streaklines display stretching and folding, which are indicative of the chaotic behavior and stirring characteristics of the system. The material lines have similar lengths for the same amount of rotation at different speeds, and the effect of rotational speeds appears to be primarily to change the time of mixing. The results are expected to help in the design of a particle microrotor based sensing technique.

Integrated lab-on-chip biosensing systems based on magnetic particle actuation – a comprehensive review

“…To understand the dynamic behavior of the chains in more detail, models have been developed in which particle chains were treated as three-dimensional circular cylinders, 38 as chains of circles in two dimensions 17,39 and finally as chains of spheres in three dimensions. [40][41][42][43] To characterize the chain behavior, most studies 17,39,40,44 used the dimensionless Mason number, which is the ratio between the rotational shear forces (i.e.…”

A well‐mixed, polymer‐based microbioreactor with integrated optical measurements

“…This vertical flow contributes to the oxygen mass transportation from the top PDMS membrane to the DO sensor located at the bottom of the reactor. Vuppu et al (2004) also simulated the rotation of a mm-scale rotor; but their rotational flow is in the regime of very low Reynolds number (maximal Re n of $0.05) and viscous forces dominate over inertial forces with poor mixing as the consequence. Flow in the present microbioreactor has a significantly higher Reynolds number (Re n of 30$130) and the convective inertial force dominates in this laminar and transitional flow regime.…”

Demonstration of sandwich and competitive modulated supraparticle fluoroimmunoassay applied to cardiac proteinbiomarkermyoglobin

“…In addition, capture and formation of supraparticle structures, modulation strategies (magnetic field strength and frequency or complex waveform), and signal capture and processing (or image analysis) can all dramatically impact the performance of the technique. Capture and formation strategies have been discussed elsewhere, in some depth, 31,33,34,[36][37][38][39][40][41][42][43][44] whereas frequency or complex waveform strategies for modulation have not been addressed yet.…”

“…Existing flow-cell technologies have shown that containment and rotation of these structures is possible using a cell with a chamber volume of 5.3 nL. 38 Further development and incorporation of all of these technologies into a device would allow rapid analysis of serum samples leading to quicker AMI diagnosis.…”