Newtonian Fluid Mechanics Research Articles

Unraveling the liquid gliding on vibrating solid liquid interfaces with dynamic nanoslip enactment

Slip length describes the classical no-slip boundary condition violation of Newtonian fluid mechanics, where fluids glide on the solid surfaces. Here, we propose a new analytical model validated by experiments for characterization of the liquid slip using vibrating solid surfaces. Essentially, we use a microfluidic system integrated with quartz crystal microbalance (QCM) to investigate the relationship between the slip and the mechanical response of a vibrating solid for a moving fluid. We discover a liquid slip that emerges especially at high flow rates, which is independent of the surface wetting condition, having significant contributions to the changes in resonant frequency of the vibrating solid and energy dissipation on its surface. Overall, our work will lead to consideration of ‘missing slip’ in the vibrating solid-liquid systems such as the QCM-based biosensing where traditionally frequency changes are interpreted exclusively with mass change on the sensor surface, irrespective of the flow conditions.

On the relations between large-scale models of superfluid helium-4

Superfluid helium-4 is characterized by extremely small values of kinematic viscosity, and its thermal conductivity can be huge, orders of magnitude larger than that of water or air. Additionally, quantum vortices may exist within the fluid. Therefore, its behavior cannot be explained by using the classical tools of Newtonian fluid mechanics, and, over the years, a few alternative models have been proposed. In order to highlight similarities and differences between these models, we recast them within a unifying framework, the general equation for non-equilibrium reversible-irreversible coupling (GENERIC). We begin by comparing the original two-fluid model, developed by Tisza and Landau, with the Hall–Vinen–Bekarevich–Khalatnikov model, both prescribing two types of fluid motion and two fluid densities, at flow scales appreciably larger than the typical distance between quantum vortices. We find from the geometrical structure of the models that only one fluid density plays the role of state variable, which should be taken into account when choosing an adequate expression for the free energy. We also recast within the GENERIC framework the one-fluid model of superfluid helium-4, where the inviscid component of two-fluid models is replaced by a caloric quantity, such as entropy. We find that the corresponding geometrical structures are analogous, with the roles of density and entropy swapped. In short, our work demonstrates that the studied models are compatible with each other, at least when focusing on the reversible parts of the models.

Highly Spherical Nanoparticles Probe Gigahertz Viscoelastic Flows of Simple Liquids Without the No-Slip Condition.

Simple liquids are conventionally described by Newtonian fluid mechanics, based on the assumption that relaxation processes in the flow occur much faster than the rate at which the fluid is driven. Nanoscale solids, however, have characteristic mechanical response times on the picosecond scale, which are comparable to mechanical relaxation times in simple liquids; as a result, viscoelastic effects in the liquid must be considered. These effects have been observed using time-resolved optical measurements of vibrating nanoparticles, but interpretation has often been complicated by finite velocity slip at the liquid-solid interface. Here, we use highly spherical gold nanoparticles to drive flows that are theoretically modeled without the use of the no-slip boundary condition at the particle surface. We obtain excellent agreement with this analytical theory that considers both the compression and shear relaxation properties of the liquid.

Quartic Non-Polynomial Spline for Solving the Third-Order Dispersive Partial Differential Equation

In the present paper, we introduce a non-polynomial quadratic spline method for solving third-order boundary value problems. Third-order singularly perturbed boundary value problems occur frequently in many areas of applied sciences such as solid mechanics, quantum mechanics, chemical reactor theory, Newtonian fluid mechanics, optimal control, convection-diffusion processes, hydrodynamics, aerodynamics, etc. These problems have various important applications in fluid dynamics. The procedure involves a reduction of a third-order partial differential equation to a first-order ordinary differential equation. Truncation errors are given. The unconditional stability of the method is analysed by the Von-Neumann stability analysis. The developed method is tested with an illustrated example, and the results are compared with other methods from the literature, which shows the applicability and feasibility of the presented method. Furthermore, a graphical comparison between analytical and approximate solutions is also shown for the illustrated example.

(Keynote) Biosensor and Bioreactor Performance of a Chemically Modified Electrodynamic Microfluidic Channel

Numerous biological sensing devices have been developed for medical and health care purposes, to date. However, many cases demand a simple, inexpensive, and efficient device, concurrently performing the reaction, separation, and detection. Hence, we have established the separation detection method of molecules and nanoparticles using a symmetrical AC electric field applied electrochemical microfluidic device fabricated with a screen printing technique (EMC). The separation principle was also evaluated with the lateral movement of targets perpendicularly against the channel walls under the AC field, which was analyzed by simulation using the mathematically derived equation from Newtonian fluid mechanics.[1] The device can be used for various reactions and detections of complex biological species in the channel. Here, some applications will be introduced; 1) separation detection of cancer cells, 2) simultaneous analysis of glycated hemoglobin family, and 3) aptamer generation, separation, and biosensor fabrication.The circulating tumor cells (CTCs) are dare rare, and account for as low as one cell per 109 hematologic cells in the blood of metastatic cancer patients, and they are very similar in size as compared to some of the WBCs, hence, their separation is a tremendous challenge. To date, CellSearch® is the only FDA approved method for sorting CTCs from blood samples, where only cells of epithelial origin can be separated. Thus, a new robust method is demanded to separate and analyze the CTCs for the early-stage diagnosis of cancers. Here, the primary criterion for their separation is electrodynamic force to differentiate cells in size (or mass) and surface charge. To additionally enhance the performance, the channel wall inside was modified with a positively charged lipid to interact the cell surface. The separated cells in the channel were detected amperometrically at the channel end. Here, the electrochemically inactive cancer cells have been selectively detected in blood using electrochemically active drugs. The device was able to separate a single cell with 92.0 ± 0.5 % efficiency. 37 patient blood samples from different origins were separated and detected with the detection rate of 91%.[2]Glycated hemoglobin (HbA1c) is clinically important, since its concentration is directly or indirectly linked with various diseases including diabetes, nephropathy, retinopathy, atherosclerosis, and other perivascular diseases. Hence, the simultaneous detection of hemoglobin (Hb) and glycated hemoglobin fractions (HbA1c, HbAld1+2, HbAle, HbAld3a, HbAla+b, HbA2, and HbAld3b) is crucial. They were separated and detected using the EMC with a catalytic redox mediators-modified sensor. The different types of redox mediators were evaluated to achieve the efficient detection. Under optimized conditions, linear dynamic ranges for Hb and HbA1c among their fractions were obtained between 1.0×10−9 to 3.5 x 10-6 M and 3.0×10−9 to 0.6 x 10-6 M with the detection limit of 8.1×10−10 ± 3.0×10−11and 9.2×10−10 ± 5×10−11 M, respectively.In addition, we have demonstrated the device for the aptamer generation and isolation, where the generated them were applied for a model protein, PvLDH for malaria diagnosis. Here, the target protein bound on the EMC channel walls induced the specific binding of DNA library molecules. In case of 60 min inducing, the partitioning efficiency between target protein and the library was attained to be 1.67 x 107 with the background of 5.56 × 10-6, which was confirmed by the qPCR. The in situ method has successfully generated and separated five aptamers in different sequences by one round generation. The dissociation constants (Kd) of selected aptamers were determined employing both electrochemical impedance spectroscopy (EIS) and fluorescence method. The sensing performances of five aptamers were evaluated for the PvLDH detection after individual immobilization on the screen-printed array electrodes. The most sensitive one revealed the detection limit of 7.8 ± 0.4 fM. The reliability of the sensor was demonstrated by comparing with the other malaria sensors.Conclusively, the screen-printed electrochemical microfluidic channel with low potential AC electric field has been successfully demonstrated for the simultaneous detection of complex biological samples. It is respected to be applied in various research fields, such as bioreactor and biosensor, chemical reactor and sensor, medical device, separation science, etc.References M. M. Hossain, N G Gurudatt, K.D Seo, D.S. Park, H. Hong, E.S. Yeom, J. H. Shim, and Y.B. Shim, Anal. Chem. 91 (2019) 14109−14116.N.G. Gurudatt, S.Chung, J.M. Kim, M.H. Kim, D.K.Jung, J.Y. Han, Y.B. Shim, Biosensors and Bioelectronics 146 (2019) 111746.M.M. Hossain, J.M. Moon, N.G. Gurudatt, D.S. Park, C. S. Choi, Y.B. Shim, Biosensors and Bioelectronics 142 (2019) 111515.

The Influence of Magnetic Fields and Heat and Mass Transfer on Peristaltic Flow Through a Porous Channel

This paper discusses the effects of both magnetic fields and heat and mass transfer on the flows of a peristaltic nature with incompressible Newtonian fluid mechanics in a channel. The study was conducted under the assumption of a low Reynolds number and a long wavelength. The analytical solution was deduced from velocity and temperature. The outcomes for velocity and temperature, presented analytically, were evaluated in a numerical form and discussed briefly. Non-dimensional wave amplitude impact, the magnetic field, Grashof number, and the volume rate of flow in the waveform were analyzed theoretically and computed numerically. The expressions for velocity, pressure gradient, pressure rise, temperature, fractional force of the internal and outer channels, and shear stress were sketched for various embedded parameters; afterward, they were accordingly interpreted. Results of a numerical nature were given and illustrated graphically in every case. The results acquired in the presence and lack of magnetic field were compared against each other. The outcomes imply that the effects of the magnetic field and heat and mass transfer were evident in the phenomena. The effects of various involved criteria manifesting in the solutions were meticulously assayed.

Electrodynamic Force Derived in-Channel Separation and Detection of Au Nanoparticles Using an Electrochemical AC Microfluidic Channel.

In this study, we have established the separation of Au nanoparticles (AuNPs) using a symmetrical AC electric field applied-electrochemical microfluidic device composed of carbon channel and detection electrodes. The lateral movement of AuNPs in the channel under the AC field was analyzed by simulation using the mathematically derived equations, which were formulated from Newtonian fluid mechanics. It shows that the nanoparticles are precisely separated according to their respective mass or size difference in a short time. The experimental parameters affecting the separation and detection of AuNPs were optimized in terms of applied frequency, amplitude, flow rate, buffer concentration, pH dependency, and temperature. The final separation was performed at 1.0 V amplitude with 8.0 MHz frequency at 0.4 μL/min flow rate for the separation, and the potential of 1.0 V was applied for the amperometric detection of AuNPs in a 0.1 M PBS. Before and after the separation, AuNPs (diameter range: 3-60 nm) were confirmed by UV-visible spectroscopy and transmission electron microscopy. In this case, the separation resolution was 3 nm with an enhanced separation efficiency of up to 597,503 plates/m for the AuNPs. In addition, the amperometric current response of the detection electrode under the AC field application was also enhanced by the sensitivity 5-fold compared with the absence of the AC field.

Investigation of Lubrication Characteristics for a Soft Contact Lens

It is popular to wear the contact lens nowadays. Also, the output value of the contact lens is estimated more than 4 billion NT dollar every year. Because the phenomena of the contact lenses are very complicated, the relevant mechanisms are not well understood. Thus, the security of contact lens needs to be further investigated. In the lubricated mechanism of the contact lens, there is a layer of tear between the contact lens and cornea. The contact lens’ behavior is akin to that of a slider bearing. The lens represents the slider, the eye plays the role of the stationary pad, and the tear film is the lubricant. Hence, hydrodynamics and contact mechanisms of a contact lens are quite a fascinating subject that is relevant to the science of tribology. In the paper, the lubrication mechanisms include the partial hydrodynamic lubrication (contact lens roughness), contact mechanics and Newtonian fluid mechanics have been established. The parameters of roughness, flow factor, tear film geometry, and hydrodynamic pressure distribution are discussed. The developed technology increases the safety of contact lens.

Stability analysis of a class of non-newtonian fluids based on generalized vector variational-like inequalities on riemannian manifold

Fluid mechanics is a branch of mechanics. It is the science of studying fluid phenomena and related mechanical behaviors. So far, the mutual soaking and fusion between fluid mechanics and other disciplines have formed many branches, many physicists and Mathematicians are working on this aspect of research. The classical Newtonian fluid mechanics believe that in parallel flow, the shear force is proportional to the shear rate, and the proportional coefficient is called the viscosity coefficient. In recent years, with the increasing importance of non-Newtonian fluids, people have found that research on non-Newtonian flow is necessary. The variational inequalities based on Riemannian manifolds were first proposed by S.Z.Németh. S.Z.Németh studied the existence of solutions to variational inequalities on Hadamard manifolds. For the equivalence of non-differentiable vector optimization problems on Riemannian manifolds and generalized weak vector variational-like inequalities, we give some new conclusions.

Wax Deposition Modeling with Considerations of Non-Newtonian Characteristics: Application on Field-Scale Pipeline

Wax removal by pigging is costly in sub-sea oil production. Cost-effective scheduling of pigging can be achieved based on the deposition rate predicted by wax deposition models. Conventional wax deposition models predict wax deposition rates on the basis of Newtonian fluid mechanics. Such an approach can become invalid for highly waxy crude oils with non-Newtonian rheology. In this investigation, different simulation techniques, including large eddy simulation, Reynolds-averaged Naiver–Stokes equations, and the law of the wall, were applied to model non-Newtonian pipe flow. It was discovered that the law of the wall method is the best method to calculate the velocity profile, shear stress and the turbulent momentum diffusivity in turbulent non-Newtonian pipe flow of waxy oil. An enhanced wax deposition model considering the non-Newtonian characteristics of waxy oil using the law of the wall method was developed and applied to predict wax deposition rates in a field-scale pipeline.

The fluid dynamics of the chocolate fountain

We consider the fluid dynamics of the chocolate fountain. Molten chocolate is a mildly shear-thinning non-Newtonian fluid. Dividing the flow into three main domains—the pumped flow up the centre, the film flow over each dome, and the freely falling curtain flow between the domes—we generate a wide-ranging study of Newtonian and non-Newtonian fluid mechanics. The central pumped flow is a benchmark to elucidate the effects of shear-thinning. The dome flow can be modelled as a thin-film flow with the leading-order effects being a simple balance of gravity and viscosity. Finally, the curtain flow is analytically intractable but is related to the existing theory of water bells (both inviscid and viscous). In pipe flow, Newtonian fluids exhibit a parabolic velocity profile; shear-thinning makes the profile more blunted. In thin-film flow over the dome, gravitational and viscous effects balance and the dome shape is not important beyond the local slope. We find that the chocolate thins and slows down as it travels down the dome. Finally, in the curtain flow, we predict the shape of the falling sheet for an inviscid fluid, and compare this with the literature to predict the shape for a viscous fluid, having shown that viscous forces are too great to ignore. We also find that the primary effect driving the shape of the curtain (which falls inwards towards the axis of the fountain) is surface tension. We find that the three domains provide excellent introductions to non-Newtonian mechanics, the important mathematical technique of scaling, and how to manipulate existing data to make our own predictions. We also find that the topic generates interest among the public in our engagement work.

Viscoelastic Flows in Simple Liquids Generated by Vibrating Nanostructures

Newtonian fluid mechanics, in which the shear stress is proportional to the strain rate, is synonymous with the flow of simple liquids such as water. We report the measurement and theoretical verification of non-Newtonian, viscoelastic flow phenomena produced by the high-frequency (20GHz) vibration of gold nanoparticles immersed in water-glycerol mixtures. The observed viscoelasticity is not due to molecular confinement, but is a bulk continuum effect arising from the short time scale of vibration. This represents the first direct mechanical measurement of the intrinsic viscoelastic properties of simple bulk liquids, and opens a new paradigm for understanding extremely high frequency fluid mechanics, nanoscale sensing technologies, and biophysical processes.

Introduction to the Function of Bisokotuwa in Ancient Vewa

This brief paper deals with an introduction of analyzing the function of the Bisokotuwa, a structure found in ancient vewas (water reservoir) in Sri Lanka in the domain of modern Newtonian fluid mechanics and development of an analysis to investigate the possibility of using the Bisokotuwa as a flow rate meter in vewas.

Revisiting Newtonian and non-Newtonian fluid mechanics using computer algebra

This article illustrates how a computer algebra system, such as Maple®, can assist in the study of theoretical fluid mechanics, for both Newtonian and non-Newtonian fluids. The continuity equation, the stress equations of motion, the Navier–Stokes equations, and various constitutive equations are treated, using a full, but straightforward, notation. Programs are presented that can produce these equations in various coordinate systems, as is the algebra system used to obtain solutions for specific examples in parallel and rotational flow.

Characteristic scales and drag reduction evaluation in turbulent channel flow of nonconstant viscosity viscoelastic fluids

The polymer-induced drag reduction in turbulent viscoelastic channel flow is customarily investigated from first principles through direct numerical simulations. In contrast to Newtonian fluid mechanics, in viscoelastic fluid mechanics there are more parameters and those are typically referenced under standard, zero shear-rate conditions. For a nonconstant viscosity non-Newtonian fluid it is necessary to correlate the effective wall viscosity to the parameters of the model. This correlation can only be evaluated a posteriori based on the wall statistics. It is used here to relate the computational to the wall units. Furthermore, the relationship between the effective wall properties and the corresponding steady shear values is elucidated. Moreover, an accurate and robust procedure for evaluating the overall drag reduction is presented.

Purely viscous flow of a shear-thinning fluid between two rotating spheres

The steady-state flow of a non-Newtonian fluid in the space between two concentric spheres, both may rotate at constant angular velocities, is analyzed using a pseudo-spectral method based on Chebyshev polynomials. We focus our attention specifically upon the effect of shear thinning on the behavior of the system under investigation. The Carreau fluid, which is characterized by a power-law exponent n and a time constant λ, is selected as the representative case. We find that if the spheres are rotating at different directions, only one single vortex can exist if n is small. This is in contrast to the corresponding Newtonian fluid case, where two vortexes of opposite orientations are observed. This is an interesting discovery in the fundamental non-Newtonian fluid mechanics, which differs drastically from the conventional Newtonian fluid mechanics. Also, if the outer sphere is fixed, the torque required to rotate the inner sphere increases almost linearly with the increase of n. This information is of practical importance for the design of agitated polymeric reactors, for instance, among other potential engineering applications.

Discussion and Closure: Newtonian Fluid Mechanics Treatment of Debris Flows and Avalanches

Discussion and Closure: Newtonian Fluid Mechanics Treatment of Debris Flows and Avalanches

Closure to “Newtonian Fluid Mechanics Treatment of Debris Flows and Avalanches” by Bruce Hunt

Closure to “Newtonian Fluid Mechanics Treatment of Debris Flows and Avalanches” by Bruce Hunt

Newtonian fluid mechanics treatment of debris flows and avalanches : B. Hunt, Journal of Hydraulic Engineering — ASCE, 120(12), 1994, pp 1350–1363

Newtonian fluid mechanics treatment of debris flows and avalanches : B. Hunt, Journal of Hydraulic Engineering — ASCE, 120(12), 1994, pp 1350–1363

Newtonian Fluid Mechanics Treatment of Debris Flows and Avalanches

Calculations are carried out first for steady fully developed laminar flow on a slope. Application of this result to field data published in a previous paper by another author suggests that many debris flows are laminar. Then singular perturbation techniques are used to obtain first‐order solutions for unsteady non‐uniform flow from a point source on a steep slope. Solutions are obtained for both laminar and turbulent flows, and it is found that the laminar flow model gives the best description of laboratory data obtained by a previous investigator. A number of differences are observed in the behavior of the outer (kinematic wave) solutions for laminar and turbulent flow, and it is suggested that it is probably not possible to describe all debris flows and avalanches with laminar flow models. It is also suggested that more comparisons need to be made between theoretical results and field data measurements.