Transport of inertial particles by viscous streaming in arrays of oscillating probes

A microfluidic array enabling generation of identical biochemical stimulating signals to trapped biological cells for single-cell dynamics

Microfluidic-based analyses of single-cell dynamics in response to dynamic biochemical signals are emerging as pivotal approaches for investigating the effects of extracellular microenvironmental biochemical factors on cellular structure, function, and behavior. However, current devices often fail to consistently apply identical dynamic biochemical signals to trapped cells. In this study, we introduce a novel radially distributed single-cell trapping microfluidic array, designed to quantitatively and consistently apply identical biochemical stimulating signals to each trapped cell. Numerical simulations were employed to optimize microchannel geometry, enhancing trapping efficiency while minimizing signal distortion. Experimental validation demonstrated the trapping success rate and the single-cell trapping efficiency exceeding 99% and 85%, respectively. The microarray's capability to deliver identical dynamic biochemical stimulating signals, with various waveforms, to each unit was confirmed through fluorescein transport tests. Furthermore, we examined the intracellular calcium dynamics of U-2 OS human osteosarcoma cells in response to dynamic ATP signals, observing both single-peak calcium responses and calcium oscillations, which were modelled by a second-order system with a natural frequency of 1.6 mHz. Overall, our proposed microfluidic array offers a robust and valuable framework for advancing the understanding of single-cell dynamics.

Oscillating viscous flow past a streamwise linear array of circular cylinders

This paper addresses the viscous flow developing about an array of equally spaced identical circular cylinders aligned with an incompressible fluid stream whose velocity oscillates periodically in time. The focus of the analysis is on harmonically oscillating flows with stroke lengths that are comparable to or smaller than the cylinder radius, such that the flow remains two-dimensional, time-periodic and symmetric with respect to the centreline. Specific consideration is given to the limit of asymptotically small stroke lengths, in which the flow is harmonic at leading order, with the first-order corrections exhibiting a steady-streaming component, which is computed here along with the accompanying Stokes drift. As in the familiar case of oscillating flow over a single cylinder, for small stroke lengths, the associated time-averaged Lagrangian velocity field, given by the sum of the steady-streaming and Stokes-drift components, displays recirculating vortices, which are quantified for different values of the two relevant controlling parameters, namely, the Womersley number and the ratio of the inter-cylinder distance to the cylinder radius. Comparisons with results of direct numerical simulations indicate that the description of the Lagrangian mean flow for infinitesimally small values of the stroke length remains reasonably accurate even when the stroke length is comparable to the cylinder radius. The numerical integrations are also used to quantify the streamwise flow rate induced by the presence of the cylinder array in cases where the periodic surrounding motion is driven by an anharmonic pressure gradient, a problem of interest in connection with the oscillating flow of cerebrospinal fluid around the nerve roots located along the spinal canal.

Multicurvature viscous streaming: Flow topology and particle manipulation

Viscous streaming refers to the rectified, steady flows that emerge when a liquid oscillates around an immersed microfeature. Relevant to microfluidics, the resulting local, strong inertial effects allow manipulation of fluid and particles effectively, within short time scales and compact footprints. Nonetheless, practically, viscous streaming has been stymied by a narrow set of achievable flow topologies, limiting scope and application. Here, by moving away from classically employed microfeatures of uniform curvature, we experimentally show how multicurvature designs, computationally obtained, give rise, instead, to rich flow repertoires. The potential utility of these flows is then illustrated in compact, robust, and tunable devices for enhanced manipulation, filtering, and separation of both synthetic and biological particles. Overall, our mixed computational/experimental approach expands the scope of viscous streaming application, with opportunities in manufacturing, environment, health, and medicine, from particle self-assembly to microplastics removal.

Particle slip velocity influences inertial focusing of particles in curved microchannels

Size based separation and identification of particles in microfluidics through purely hydrodynamic means has gained significant interest due to a number of possible biomedical applications. Curved micro-channels, particularly spiral micro-channels with rectangular cross-section and the dynamics of particles in such channels have been extensively researched to achieve size based separation of particles. In this paper we present evidence that sheds new light on the dynamics of particles in such curved channels; that a unique particle slip velocity is associated with the focusing positions in the cross sections, which leads to a balance of forces. Our experiments therefore imply that the forces acting on the particle lead to convergence to an attractor in both the physical space (the cross section of the channel) and the slip velocity space.

Steady streaming around a cylinder pair

The steady streaming motion that appears around a pair of circular cylinders placed in a small-amplitude oscillatory flow is considered. Attention is focused on the case where the Stokes layer thickness at the surface of the cylinders is much smaller than the cylinder radius, and the streaming Reynolds number is of order unity or larger. In that case, the steady streaming velocity that persists at the edge of the Stokes layer can be imposed as a boundary condition to numerically solve the outer streaming motion that it drives in the bulk of the fluid. It is investigated how the gap width between the cylinders and the streaming Reynolds number affect the flow topology. The results are compared against experimental observations.

Theoretical and experimental study of the dynamic response of absorber-based, micro-scale, oscillatory probes for contact sensing applications

This paper presents two models for predicting the frequency response of micro-scale oscillatory probes. These probes are manufactured by attaching a thin fiber to the free end of one tine of a quartz tuning fork oscillator. In these studies, the attached fibers were either 75 μm diameter tungsten or 7 μm diameter carbon with lengths ranging from around 1 to 15 mm. The oscillators used in these studies were commercial 32.7 kHz quartz tuning forks. The first theoretical model considers lateral vibration of two beams serially connected and provides a characteristic equation from which the roots (eigenvalues) are extracted to determine the natural frequencies of the probe. A second, lumped model approximation is used to derive an approximate frequency response function for prediction of tine displacements as a function of a modal force excitation corresponding to the first mode of the tine in the absence of a fiber. These models are used to evaluate the effect of changes in both length and diameter of the attached fibers. Theoretical values of the natural frequencies of different modes show an asymptotic relationship with the length and a linear relationship with the diameter of the attached fiber. Similar results are observed from experiment, one with a tungsten probe having an initial fiber length of 14.11 mm incrementally etched down to 0.83 mm, and another tungsten probe of length 8.16 mm incrementally etched in diameter, in both cases using chronocoulometry to determine incremental volumetric material removal. The lumped model is used to provide a frequency response again reveals poles and zeros that are consistent with experimental measurements. Finite element analysis shows mode shapes similar to experimental microscope observations of the resonating carbon probes. This model provides a means of interpreting measured responses in terms of the relative motion of the tine and attached fibers. Of particular relevance is that, when a "zero" is observed in the response of the tine, one mode of the fiber is matched to the tine frequency and is acting as an absorber. This represents an optimal condition for contact sensing and for transferring energy to the fiber for fluid mixing, touch sensing, and surface modification applications.