Periodic and symmetric two-dimensional textures with various cross-sectional profiles have been employed to improve and optimize the physical response of the surfaces such as drag force, superhydrophobicity, and adhesion. While the effect of the height and spacing of the textures have been extensively studied, the effect of the shape of the textures has only been considered qualitatively. Here, a polynomial framework is proposed to mathematically define the cross-sectional profiles of the textures and offer a quantitative measure for comparing the physical response of the textured surfaces with various shapes. As a case study, textured surfaces designed with this framework are tested for their hydrodynamic frictional response in the cylindrical Couette flow regime in Taylor–Couette flows. With the reduction in torque as the objective, experimental and numerical results confirm that textures with height-to-half-spacing ratios of lower and equal to unity with concave profiles offer a lower torque compared to both smooth surfaces and triangular textures. In addition, across multiple polynomial orders, textures defined by second-order polynomials offer a wide range of responses, eliminating the need for considering polynomials of higher orders and complexity. While the case study here is focused on the laminar flow regime and the frictional torque, the same type of analysis can be applied to other surface properties and physical responses as we
Changes in the elastic properties of brain tissue have been correlated with injury, cancers, and neurodegenerative diseases. However, discrepancies in the reported elastic moduli of brain tissue are persistent, and spatial inhomogeneities complicate the interpretation of macroscale measurements such as rheology. Here we introduce needle induced cavitation rheology (NICR) and volume-controlled cavity expansion (VCCE) as facile methods to measure the apparent Young's modulus E of minimally manipulated brain tissue, at specific tissue locations and with sub-millimeter spatial resolution. For different porcine brain regions and sections analyzed by NICR, we found E to be 3.7 ± 0.7 kPa and 4.8 ± 1.0 kPa for gray matter, and white matter, respectively. For different porcine brain regions and sections analyzed by VCCE, we found E was 0.76 ± 0.02 kPa for gray matter and 0.92 ± 0.01 kPa for white matter. Measurements from VCCE were more similar to those obtained from macroscale shear rheology (0.75 ± 0.06 kPa) and from instrumented microindentation of white matter (0.97 ± 0.40 kPa) and gray matter (0.86 ± 0.20 kPa). We attributed the higher stiffness reported from NICR to that method's assumption of a cavitation instability due to a neo-Hookean constitutive response, which does not capture the strain-stiffening behavior of brain tissue under large strains, and therefore did not provide appropriate measurements. We demonstrate via both analytical modeling of a spherical cavity and finite element modeling of a needle geometry, that this strain stiffening may prevent a cavitation instability. VCCE measurements take this stiffening behavior into account by employing an incompressible one-term Ogden model to find the nonlinear elastic properties of the tissue. Overall, VCCE afforded rapid and facile measurement of nonlinear mechanical properties of intact, healthy mammalian brain tissue, enabling quantitative comparison among brain tissue regions and also between species. Finally, accurate estimation of elastic properties for this strain stiffening tissue requires methods that include appropriate constitutive models of the brain tissue response, which here are represented by inclusion of the Ogden model in VCCE.
Periodic surface microtextures of different shapes such as V grooves, semicircular grooves, or rectangular grooves have been studied under laminar and turbulent flow conditions to offer guides for designing optimized low-friction surfaces. In this work we investigate the efficacy of periodic streamwise-aligned surface features in reducing the torque exerted on a steadily rotating cylinder in Taylor-Couette flow. Using three-dimensional printed riblet-textured rotors and a bespoke Taylor-Couette cell, which can be mounted on a controlled stress rheometer, we measure the evolution in the torque acting on the inner rotor as a function of three different dimensionless parameters: (i) the Reynolds number characterizing the flow, (ii) the sharpness of the riblets, as defined by their aspect ratio (height to wavelength), and (iii) the axial scale of the riblets with respect to the size of the overall Taylor-Couette cell (the ratio of the riblet wavelength to the gap of the Taylor-Couette cell). Our experimental results in the laminar viscous flow regime show a reduction in torque up to 10% over a wide range of Reynolds numbers that is a nonmonotonic function of the aspect ratio of the grooves and independent of Red (the gap-based Reynolds number). However, after the transition to the Taylor vortex regime, the modification in torque also becomes a function of the Reynolds number while remaining a nonmonotonic function of the aspect ratio. Using finite-volume simulation of the three-dimensional swirling flow in the annular gap, we discuss the kinematic changes to the Taylor-Couette flow in the presence of the riblets compared to the case of smooth rotors and compute the resulting torque reduction as a function of the parameter space defined above. Good agreement between experiments and computational predictions is found for both azimuthal Couette flow and the Taylor vortex regime.
Micro-scale riblets are shown to systematically modify viscous skin friction in laminar flows at high Reynolds numbers. The textured denticles of native sharkskin are widely cited as a natural example of this passive drag reduction mechanism. Since the structure of a viscous boundary layer evolves along the plate, the local frictional drag changes are known empirically to be a function of the length of the plate in the flow direction, as well as the riblet spacing, and the ratio of the height to spacing of the riblets. Here, we aim to establish a canonical theory for high Reynolds number laminar flow over V-groove riblets to explore the self-similarity of the velocity profiles and the evolution of the total frictional drag exerted on plates of different lengths. Scaling analysis, conformal mapping, and numerical calculations are combined to show that the potential drag reduction achieved using riblet surfaces depends on an appropriately rescaled form of the Reynolds number and on the aspect ratio of the riblets (defined in terms of the ratio of the height to spacing of the texture). We show that riblet surfaces require a scaled Reynolds number lower than a maximum threshold to be drag-reducing and that the change in drag is a nonmonotonic function of the aspect ratio of the riblet texture. This physical scaling and the computational results presented here can be used to explain the underlying physical mechanism of this mode of passive drag reduction to rationalize the geometric dimensions of shark denticles, as well as the results of experiments with shark denticle replicas of various sizes, and guide designs for optimizing the textural parameters that result in friction-reducing surfaces.
Nearly three decades ago, the field of mechanics was cautioned of the obscure nature of cavitation processes in soft materials [A. Gent, Cavitation in rubber: a cautionary tale, Rubber Chem. Technol., 1990, 63, 49–53]. Since then, the debate on the mechanisms that drive this failure process is ongoing. Using a high precision volume controlled cavity expansion procedure, this paper reveals the intimate relationship between cavitation and fracture. Combining a Griffith inspired formulation for crack propagation, and a Gent inspired formulation for cavity expansion, we show that despite the apparent complexity of the fracture patterns, the pressure–volume response follows a predictable path. In contrast to available studies, both the model and our experiments are able to track the entire process including the unstable branch, by controlling the volume of the cavity. Moreover, this minimal theoretical framework is able to explain the ambiguity in previous experiments by revealing the presence of metastable states that can lead to first order transitions at onset of fracture. The agreement between the simple theory and all of the experimental results conducted in PDMS samples with shear moduli in the range of 25–246 [kPa] confirms that cavitation and fracture work together in driving the expansion process. Through this study we also determine the fracture energy of PDMS and show its significant dependence on strain stiffening.
Inspired by the design of the ribbed structure of shark skin, passive drag reduction methods using stream-wise riblet surfaces have previously been developed and tested over a wide range of flow conditions. Such textures aligned in the flow direction have been shown to be able to reduce skin friction drag by 4%–8%. Here, we explore the effects of periodic sinusoidal riblet surfaces aligned in the flow direction (also known as a “wrinkled” texture) on the evolution of a laminar boundary layer flow. Using numerical analysis with the open source Computational Fluid Dynamics solver OpenFOAM, boundary layer flow over sinusoidal wrinkled plates with a range of wavelength to plate length ratios (\(\lambda/L\)), aspect ratios (\(2A/\lambda\)), and inlet velocities are examined. It is shown that in the laminar boundary layer regime, the riblets are able to retard the viscous flow inside the grooves creating a cushion of stagnant fluid that the high-speed fluid above can partially slide over, thus reducing the shear stress inside the grooves and the total integrated viscous drag force on the plate. Additionally, we explore how the boundary layer thickness, local average shear stress distribution, and total drag force on the wrinkled plate vary with the aspect ratio of the riblets as well as the length of the plate. We show that riblets with an aspect ratio of close to unity lead to the highest reduction in the total drag, and that because of the interplay between the local stress distribution on the plate and stream-wise evolution of the boundary layer the plate has to exceed a critical length to give a net decrease in the total drag force.
The properties and behavior of a surface as well as its interaction with surrounding media depend on the inherent material constituency and the surface topography. Structured surface topography can be achieved via surface wrinkling. Through the buckling of a thin film of stiff material bonded to a substrate of a softer material, wrinkled patterns can be created by inducing compressive stress states in the thin film. Using this same principle, we show the ability to create wrinkled topologies consisting of a highly structured gradient in amplitude and wavelength, and one which can be actively tuned. The mechanics of graded wrinkling are revealed through analytical modeling and finite element analysis, and further demonstrated with experiments.