Polarised light imaging microscopy, with the addition of a liquid crystal (LC) phase retarder, was used to determine the birefringence of silk fibres with high (∼1 μm) spatial resolution. The measurement was carried out with the silk fibres (the optical slow axis) and the slow axis of the LC-retarder set at parallel angles. The direct fit of the transmission data allowed for high fidelity determination of the birefringence Δn ≈ 1.63 × 10-2 (with ∼2% uncertainty) of the brown silk fibre, (Antheraea pernyi) averaged over the wavelength range λ = (425-625) nm. By measuring retardance at four separate wavelengths, it was possible to determine the true value of the birefringence of a thicker sample when an optical path may include a large number of wavelengths. The numerical procedures and required hardware are described for the do-it-yourself assembly of the imaging polariscope at a fractional budget compared to commercial units.

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Simple multi-wavelength imaging of birefringence:case study of silk.

Wormlike micellar (WLM) solutions are frequently used in enhanced oil and gas recovery applications in porous rock beds where complex microscopic geometries result in mixed flow kinematics with strong shear and extensional components. Experiments with WLM solutions through model microfluidic porous media have revealed a variety of complex flow phenomena, including the formation of stable gel-like structures known as a Flow-Induced Structured Phase (FISP), which undoubtedly play an important role in applications of WLM fluids, but are still poorly understood. A first step in understanding flows of WLM fluids through porous media can be made by examining the flow around a single micro-scale cylinder aligned on the flow axis. Here we study flow behavior of an aqueous WLM solution consisting of cationic surfactant cetyltrimethylammonium bromide (CTAB) and a stable hydrotropic salt 3-hydroxy naphthalene-2-carboxylate (SHNC) in microfluidic devices with three different cylinder blockage ratios, β. We observe a rich sequence of flow instabilities depending on β as the Weissenberg number (Wi) is increased to large values while the Reynolds number (Re) remains low. Instabilities upstream of the cylinder are associated with high stresses in fluid that accelerates into the narrow gap between the cylinder and the channel wall; vortex growth upstream is reminiscent of that seen in microfluidic contraction geometries. Instability downstream of the cylinder is associated with stresses generated at the trailing stagnation point and the resulting flow modification in the wake, coupled with the onset of time-dependent flow upstream and the asymmetric division of flow around the cylinder.

/pdf/flow-of-wormlike-micellar-solutions-around-confined-3ixljapc1x.pdf

Flow of wormlike micellar solutions around confined microfluidic cylinders

We employ a state-of-the-art microfabrication technique (selective laser-induced etching, SLE) to produce microfluidic cylinder geometries that explore new geometrical regimes. Using SLE, two microchannels are fabricated in monolithic fused silica substrate with height H = 2  mm and width W = 0.4  mm (aspect ratio α = H / W = 5 ) containing cylinders of radius r = 0.02  mm (blockage ratio β = 2 r / W = 0.1 ), centered at the channel mid-width, W/2. An ‘sc’ channel contains a single cylinder, while a ‘dc’ channel contains two axially-aligned cylinders separated by a distance L = 1  mm ( L = 50 r ). Compared with cylinder geometries fabricated by soft lithography (which typically have α ≪ 1 and β ≳ 0.5), these rigid glass devices provide a quasi-two-dimensional flow along the direction of the cylinder axis and also more clearly reveal the effects of the strong extensional wake regions located at the leading and trailing stagnation points. Using flow velocimetry and quantitative birefringence measurement techniques, we study the behaviour of a well-characterized viscoelastic polymer solution in flow around the cylinders. The small cylinder radii result in low inertia and very high elasticity numbers El ≈ 2400. For the sc device, we report strong flow modification effects around the cylinder as the flow rate is incremented. This is associated with the deformation of polymer molecules primarily in the upstream wake region, leading to the onset of a purely elastic flow asymmetry upstream of the cylinder. Stretched polymer molecules are advected around the cylinder and relax downstream of the cylinder, resulting in an extremely long elastic wake extending for  > 300r downstream. In the dc channel, at lower flow rates, similar flow modification effects are observed to develop around, and downstream of, both cylinders. However, at higher flow rates the wake of the first cylinder extends  > 50r downstream, and begins to interact with the second cylinder. The second cylinder becomes encapsulated by the wake of the first and is effectively obviated from the flow field. The results will be of relevance to understanding practical applications of viscoelastic fluids, for example in particle suspension and porous media flows, and also for benchmarking against numerical simulations using viscoelastic constitutive models.

Steady viscoelastic flow around high-aspect-ratio, low-blockage-ratio microfluidic cylinders

We employ time-resolved flow velocimetry and birefringence imaging methods to study the flow of a well-characterized shear-banding wormlike micellar solution around a novel glass-fabricated microfluidic circular cylinder. In contrast with typical microfluidic cylinders, our geometry is characterized by a high aspect ratio α = H/W = 5 and a low blockage ratio β = 2r/W = 0.1, where H and W are the channel height and width, and the cylinder radius r = 20 μm. The small cylinder radius allows access up to very high Weissenberg numbers 1.9 ≤ Wi = λMU/r ≤ 3750 (where λM is the Maxwell relaxation time) while inertial effects remain entirely negligible (Reynolds number, Re < 10−4). At low Wi values, the flow remains steady and symmetric and a birefringent region (indicating micellar alignment and tensile stress) develops downstream of the cylinder. Above a critical value Wic ≈ 60 the flow transitions to a steady asymmetric state, characterized as a supercritical pitchfork bifurcation, in which the fluid takes a preferential path around one side of the cylinder. At a second critical value Wic2 ≈ 130, the flow becomes time-dependent, with a characteristic frequency f0 ≈ 1/λM. This initial transition to time dependence has characteristics of a subcritical Hopf bifurcation. Power spectra of the measured fluctuations become complex as Wi is increased further, showing a gradual slowing down of the dynamics and emergence of harmonics. A final transition at very high Wic3 corresponds to the re-emergence of a single peak in the power spectrum but at much higher frequency. We discuss this in terms of possible flow-induced breakage of micelles into shorter species with a faster relaxation time.

https://pubs.rsc.org/en/content/articlepdf/2019/sm/c8sm02099j

Flow of wormlike micellar solutions around microfluidic cylinders with high aspect ratio and low blockage ratio

Molecular conformations of individual polymers during flow through porous media are directly observed by single-DNA imaging in microfluidics. As the Weissenberg number increases during flow (Wi > 1), we observe two types of elastic instabilities: (a) stationary dead-zone and (b) time-dependant dead-zone washing. When stretched polymer chains enter a dead-zone, they first re-coil and, once inside the dead-zone, they rotate and re-stretch again. The probability distribution of DNA chains under the stretched condition inside the dead-zone is found to be heterogeneous with a broad distribution.

/pdf/polymer-conformation-during-flow-in-porous-media-27msva8tnr.pdf

Polymer conformation during flow in porous media

In this study, we demonstrate the use of a microscopic circular polariscope to measure the flow-induced birefringence in a microfluidic device that represents the kinematics of fluid motion optically. Unlike the commercial birefringence microscope employed in the previous studies, our approach is able to provide direct measurement of retardance, which quantifies the difference in refractive index of the fluid experienced by the ordinary and extraordinary rays, from one single image frame. This capability facilitates unsteady full-field quantitation of flow-induced birefringence in microfluidics that has never been achieved before. At low flow rates, we find that the value of the retardance is independent of the microfluidic design and proportional to the nominal strain rates. This linearity bridges the measurement of birefringence and the deformation rate in the microflow environment, which yields the stress information of the fluid flow. In addition, the μPIV results confirm that both extensional and shear strain rates contribute to the flow-induced birefringence so that the retardance distribution can be used to represent the field of the principal strain rate in a microfluidic device. The outcome of this study proves that our approach provides a non-invasive method that enables an intuitive full-field representation of stress in the instantaneous flow field in a microfluidic device.

/pdf/measurements-of-flow-induced-birefringence-in-microfluidics-4ws2s49ap1.pdf

Measurements of flow-induced birefringence in microfluidics

In this study, we employ the similarity transformation and the AC-circuit analogy to investigate the flow rectification property of a microdiffuser. Driven by an oscillating source, the transient two-dimensional radial flow of viscous fluid in a planar microdiffuser, which consists in a wedge-shaped domain bounded by two circular arcs, is solved. The ratio of flow impedances is determined to evaluate the performance of the flow rectification. By gauging the leverage between viscous and unsteady effects, we discuss the influences of the half angle, the Reynolds number, the excitation frequency, and the ratio of inlet to outlet radii in flow directing properties of the microdiffuser. We find that net flow in the expansion direction only occurs when the product of the half angle and the Reynolds number is small and the Womersley number is low. Moreover, the reversal Womersley number, at which preference of flowing direction switches, decreases with increasing the product of half angle and the Reynolds number or reducing the ratio of inlet to outlet radii. We find that a wider half angle, stronger oscillation, higher frequency, broader inlet, and longer microdiffuser all contribute to the augmentation of the transient inertia and lead to the promotion of converging flow. The specific goal of this study is to provide the means to manipulate the flow rectification effect of a microdiffuser by varying its geometry or the driving conditions.

Hung-Yen Huang

Papers

Measurements of flow-induced birefringence in microfluidics

An analytical model for flow rectification of a microdiffuser driven by an oscillating source