The behavior of suspensions and macromolecular solutions in crossflow microfiltration

Viscoelastic instabilities are of practical importance, and are the subject of growing interest. Reviewed here are the fresh developments as well as earlier work in this area, organized into the following categories: instabilities in Taylor-Couette flows, instabilities in cone-and-plate and plate-and-plate flows, instabilities in parallel shear flows, extrudate distortions and fracture, instabilities in shear flows with interfaces, instabilities in extensional flows, instabilities in multidimensional flows, and thermohydrodynamic instabilities. Emphasized in the review are comparisons between theory and experiment and suggested directions for future work.

Instabilities in viscoelastic flows

Circulating tumor cells (CTCs) are rare cancer cells that are shed from primary or metastatic tumors into the peripheral blood circulation. Phenotypic and genetic characterization of these rare cells can provide important information to guide cancer staging and treatment, and thus further research into their characteristics and properties is an area of considerable interest. In this protocol, we describe detailed procedures for the production and use of a label-free spiral microfluidic device to allow size-based isolation of viable CTCs using hydrodynamic forces that are present in curvilinear microchannels. This spiral system enables us to achieve ≥ 85% recovery of spiked cells across multiple cancer cell lines and 99.99% depletion of white blood cells in whole blood. The described spiral microfluidic devices can be produced at an extremely low cost using standard microfabrication and soft lithography techniques (2-3 d), and they can be operated using two syringe pumps for lysed blood samples (7.5 ml in 12.5 min for a three-layered multiplexed chip). The fast processing time and the ability to collect CTCs from a large patient blood volume allows this technique to be used experimentally in a broad range of potential genomic and transcriptomic applications.

Ultra-fast, label-free isolation of circulating tumor cells from blood using spiral microfluidics

A general stability analysis is given of the Kevin-Helmholtz instability, for the case of sheared MHD flow of finite thickness in a compressible plasma which allows for the arbitrary orientation of the magnetic field, velocity flow, and wave vector in the plane perpendicular to the velocity gradient. The stability problem is reduced to the solution of a single second-order differential equation including a gravitational term to represent the coupling between the Kelvin-Helmholtz mode and the interchange mode. Compressibility and a magnetic field component parallel to the flow are found to be stabilizing effects, with destabilization of only the fast magnetosonic mode in the transverse case, and the presence of both Alfven and slow magnetosonic components in the parallel case. Analysis results are used in a discussion of the stability of sheared plasma flow at the magnetopause boundary and in the solar wind.

Nonlocal stability analysis of the MHD Kelvin‐Helmholtz instability in a compressible plasma

When Segre and Silberberg in 1961 witnessed particles in a laminar pipe flow congregating at an annulus in the pipe, scientists were perplexed and spent decades learning why such behavior occurred, finally understanding that it was caused by previously unknown forces on particles in an inertial flow. The advent of microfluidics opened a new realm of possibilities for inertial focusing in the processing of biological fluids and cellular suspensions and created a field that is now rapidly expanding. Over the past five years, inertial focusing has enabled high-throughput, simple, and precise manipulation of bodily fluids for a myriad of applications in point-of-care and clinical diagnostics. This review describes the theoretical developments that have made the field of inertial focusing what it is today and presents the key applications that will make inertial focusing a mainstream technology in the future.

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Inertial Focusing in Microfluidics

Experimental work due to Prof. J. Eustice has shown that there is no marked critical velocity for a fluid flowing through a curved pipe. If the pipe is straight there is a sudden increase in the loss of head as soon as the velocity exceeds its critical value; below the critical the loss of head varies as the first power of the velocity, but above it approximately as the second power. But if the pipe is curved there does not appear to be such a sudden change at any velocity of flow. One possibility is that flow through a curved pipe is stream-line at velocities much greater than the critical for a straight pipe, but experiment seems to show that the critical velocity is smaller in a curved pipe than in a straight one. If then the motion in a curved pipe becomes unstable at a velocity somewhat less than the critical for a straight pipe, the absence of a sudden increase in the loss of head in this region suggests that the stream-line motion in a curved pipe (unlike that in a straight pipe) is unstable for small disturbances. A similar problem shows that it is not unlikely that curvature may have such an effect: it is believed that uniform shearing motion between flat plates is stable for small disturbances, but Prof. G. I. Taylor has shown that shearing motion between concentric cylinders can in certain conditions become unstable for small disturbances. A theoretical investigation of the stability of flow in a curved pipe is certain to be a matter of great difficulty, and therefore a simplified form of the problem, the stability of flow under pressure through a curved channel ( i. e. , between concentric cylinders), is here considered. It is shown that the motion can become unstable for a small disturbance of exactly the type found by Taylor to be possible in motion between rotating cylinders.

W. R. Dean

Papers

Fluid Motion in a Curved Channel