Anti-electroviscous effect of near-surface 5CB liquid crystal and its boundary lubrication property

The rheological properties of the near-surface 5CB (4-pentyl-4′-cyanobiphenyl) liquid crystal (LC) under an external electric field (EEF) are investigated using a dynamic quartz crystal microbalance (QCM). The real-time film-forming process and shearing response of the EEF-induced absorbed LC liquid are studied. The results indicate that the EEF-induced adsorbed LC is composed of a bulk liquid layer and a near-surface boundary layer. Within the boundary layer, the nematic 5CB LC presents an anti-electroviscous effect which may be due to the EEF-induced ordered structure. According to the estimation from QCM measurements, this near-surface layer is about 100 nm thick under certain electric strength and is irreversible even after the EEF is removed. Based on a QCM model, the near-surface LC layer presents a decreased and irreversible viscosity as the EEF voltage increases against the reversible electro-viscous effect of the bulk 5CB liquid crystal measured by rheometer and Raman spectrum measurements. The anti-electroviscous effect of the near-surface 5CB layer is also proved by an improved boundary lubrication property tested on a tribometer. The coefficient of friction of 5CB LC after a preliminary induction of EEF is the lowest one compared to those without EEF and during the application of EEF. The unique anti-electroviscous property of near-surface 5CB LC revealed in this article suggests a potential method to actively reduce shear resistance in boundary lubrication and in microfluidics.     

Sharp-Interface Nematic-Isotropic Phase Transformations With Flow

We develop a sharp-interface theory for phase transformations between the isotropic and uniaxial nematic phases of a flowing liquid crystal. Aside from conventional evolution equations for the bulk phases and corresponding interface conditions, the theory includes a supplemental interface condition expressing the balance of configurational momentum. As an idealized illustrative application of the theory, we consider the problem of an evolving spherical droplet of the isotropic phase surrounded by the nematic phase in a radially-oriented state. For this problem, the bulk and interfacial equations collapse to a single nonlinear second-order ordinary differential equation for the radius of the droplet—an equation which, in essence, expresses the balance of configurational momentum on the interface. This droplet evolution equation, which closely resembles a previously derived and extensively studied equation for the expansion of contraction of a spherical gas bubble in an incompressible viscous liquid, includes terms accounting for the curvature elasticity and viscosity of the nematic phase, interfacial energy, interfacial viscosity, and the ordering kinetics of the phase transformation. We determine the equilibria of this equation and study their stability. Additionally, we find that motion of the interface generates a backflow, without director reorientation, in the nematic phase. Our analysis indicates that a backflow measurement has the potential to provide an independent means to determine the density difference between the isotropic and uniaxial nematic phases.     

Non-Newtonian flow in microporous structures under the electroviscous effect

Single phase non-Newtonian microporous flow combined with the electroviscous effect is investigated in the pore-scale under conditions of various rheological properties and electrokinetic parameters. The lattice Boltzmann method is employed to solve both the electric potential field and flow velocity field. The simulation of commonly used power-law non-Newtonian flow shows that the electroviscous effect on the flow depends on both the fluid rheological behavior and pore surface area ratio significantly. For the shear thinning fluid with power-law exponent n < 1, the fluid viscosity near the wall is smaller and the electrovicous effect plays a more important role compared to the Newtonian fluid and shear thickening fluid. The high pore surface area ratio in the porous structure increases the electroviscous force and the induced flow resistance becomes important even to the flow of Newtonian and shear thickening fluids.     

Jeffrey-Hamel flow of Leslie-Ericksen nematic liquids

A similarity solution of the Leslie-Ericksen equations for nematic liquid crystals is obtained for flow between converging and diverging planar walls (Jeffrey-Hamel flow). There are three regions in the flow: extensional or compressional flow near the centerline, shear near the wall, and a wall boundary layer in which elastic stresses control the transition from the wall-induced orientation to the bulk behavior. The boundary layer thickness is obtained in closed form; the scaling with the Ericksen number depends on whether or not the boundary layer extends into the region of extensional flow. Imposition of a magnetic field with an azimuthal component in a converging flow can result in a Freedericksz-like transition from radial to transverse orientation at the center line at a critical field strength. This transition provides a new means to measure the irrotational viscosity λ₂.     

Rheo-Dielectric behavior of low molecular weight liquid crystals.

Dielectric relaxation behavior was examined for 4-4′-n-pentyl-cyanobiphenyl (5CB) and 4-4′-n-heptyl-cyanobiphenyl (7CB) under flow. In quiescent states at all temperatures examined, both 5CB and 7CB exhibited dispersions in their complex dielectric constant ε*(ω) at characteristic frequencies ω _c above 10⁶ rad s^–1. This dispersion reflected orientational fluctuation of individual 5CB and 7CB molecules having large dipoles parallel to their principal axis (in the direction of C≡N bond). In the isotropic state at high temperatures, these molecules exhibited no detectable changes of ε*(ω) under flow at shear rates . In contrast, in the nematic state at lower temperatures the terminal relaxation intensity of ε*(ω) as well as the static dielectric constant ε′(0) decreased under flow at . This rheo-dielectric change was discussed in relation to the flow effects on the nematic texture (director distribution) and anisotropy in motion of individual molecules with respect to the director. Received: 14 April 1998 Accepted: 29 July 1998     

The Effect of Heavy Oil Viscosity Reduction by Solvent Dissolution on Natural Convection in the Boundary Layer of VAPEX

We have studied the effect of viscosity on natural convection in the boundary layer of the vapor extraction (VAPEX) process. VAPEX is a heavy oil recovery method that uses solvents to reduce oil viscosity, and is a potential process in reservoirs where thermal recovery methods cannot be applied. Natural convection may happen in VAPEX if the solvents that are used to decrease oil viscosity increase the density of the oil. This can especially occur with $\text{ CO }_{2}$ CO 2 -based solvents. Reduction of the oil viscosity due to solvent dissolution can have a large impact on the onset of convection by decreasing the critical Rayleigh number. When the viscosity reduction is significant, the critical Rayleigh can decrease up to two orders of magnitude. The transverse Peclet number is also a crucial parameter in determining the critical Rayleigh and onset of convection. Our analysis shows that the longitudinal Peclet does not have a significant impact on the natural convention in VAPEX. When oil viscosity reduction is included in the analysis of boundary layer instability in VAPEX, natural convection may occur in high-permeable reservoirs (where Rayleigh number is high) leading to a greater oil production rate compared with current models where the effect of boundary layer instability has been ignored.     

The bulk electroviscous effect

Electroviscous stresses arise as hydrodynamic flows disturb the ionic (Debye) clouds that screen charged surfaces in electrolyte solutions. The contribution thereof to the effective bulk viscosity (also known as the second or volume viscosity) of two-phase suspensions is quantified here. Specifically, the bulk viscosity of two model suspensions is calculated: (1) a dilute dispersion of rigid charged spherical particles immersed in a compressible electrolyte that undergoes uniform dilatation and (2) a dilute suspension of charged gas bubbles expanding uniformly in an incompressible electrolyte. In both cases, it is assumed that the fluid flow only slightly drives the Debye cloud out of equilibrium, which formally requires that the ratio of the ion diffusion to flow time scales—a Péclet number—is small. For a suspension of rigid particles, the electroviscous contribution to the effective bulk viscosity is proportional to the particle volume fraction and decreases monotonically as the ratio of the particle radius to the Debye length increases. Similar behavior is well known for the electroviscous contribution to the effective shear viscosity of a dilute hard-sphere suspension; a quantitative comparison between the bulk and shear viscosities is made. In contrast, the electroviscous contribution to the bulk viscosity of a dilute suspension of bubbles is independent of the bubble volume fraction and attains a finite value in the limit of vanishing Debye length.     

A model for the shear viscosity of non-colloidal suspensions with Newtonian matrix fluids

We present a model for the shear viscosity of non-colloidal suspensions with Newtonian matrix fluids. The model is based on the original idea first presented by Brinkman (Applied Sci Research A1:27-34. 1947) for the viscous force exerted by a flowing fluid on a dense swarm of spherical particles. In particular, we consider an inertialess suspension in which the mean flow is driven by a pressure difference, and simultaneously, the suspension is subject to simple shear. Assuming steady state, incompressibility and taking into account a resistance force which is generated due to the presence of the particles in the flow, the three-dimensional governing equations for the mean flow around a single spherical particle are solved analytically. Self-consistency of the model provides a relationship between the resistance parameter and the volume fraction of the solid phase. A volume, or an ensemble, averaging of the total stress gives the bulk properties and an expression for the relative (bulk) viscosity of the suspension. The viscosity expression reduces to the Einstein limit for dilute suspensions and agrees well with empirical formulas from the literature in the semi-dilute and concentrated regimes. Since the model is based on a single particle and its average interaction with the other particles is isotropic, no normal stress differences can be predicted. A possible method of addressing this problem is provided in the paper.     

Mechanical and structural investigation of isotropic and anisotropic thermoplastic magnetorheological elastomer composites based on poly(styrene-b-ethylene-co-butylene-b-styrene) (SEBS)

Novel smart thermoplastic magnetorheological elastomer composites containing micron-sized magnetic carbonyl iron (CI) particles were prepared with a poly(styrene-ethylene-butylene-styrene) (SEBS) triblock copolymer utilized as the thermoplastic matrix rubber, and the structures and properties of the CI-SEBS composites were examined. The CI particles were uniformly dispersed in the composites prepared in the absence of the magnetic field at high temperatures T (>T $_{\rm g}^{\rm S})$ , and this isotropic composite exhibited a larger storage modulus G^?? compared to the SEBS matrix at room temperature (<?<T $_{\rm g}^{\rm S})$ where the EB phase therein was rubbery while the PS phase was in the glassy state. In contrast, the SEBS composite prepared under the magnetic field (with the intensity ???< 2.5?T) at high T (>T $_{\rm g}^{\rm S})$ contained a chain structure of CI particles. This chain structure became longer and better aligned on an increase of ?? up to a saturation of the particle magnetization and on an increase of the time interval of applying the field (that allowed the particles to move and equilibrate their aligned structure). The modulus G^?? of this ??pre-structured?? composite measured for both cases of ?? = 0 and ???> 0 in the direction perpendicular to the chain structure at room temperature was enhanced compared to G^?? of the isotropic composites. This difference of the filler effect (for ???=?0) and the magnetorheological effect (for ???> 0) between the pre-structured and isotropic composites was enhanced when the chain structure of the CI particles in the pre-structured composites became longer and better aligned. A mechanism(s) of this enhancement was discussed in relation to the morphologies (particle distribution) in the composites with the aid of a filler model and a molecular expression of the stress due to magnetically interacting particles.     

Solution of the heat-transfer equation for equilibrium turbulent boundary layers when the temperature distribution of the streamlined surface is arbitrary

We give an approximate solution of the heat-transfer equation for equilibrium turbulent boundary layers for which the velocity distribution and the coefficient of turbulent viscosity can be described by functions of two parameters. In [1–4] equilibrium turbulent boundary layers characterized by a constant dimensionless pressure gradient were investigated. The $$\beta = \frac{{\delta ^{* \circ } }}{{\tau _w ^ \circ }}\left( {\frac{{dP}}{{dx^ \circ }}} \right)$$ profile of the velocity defect was calculated in [4] for such layers throughout the whole range ?0.5≤β≤∞, while a method was indicated in [5] for combining the defect velocity profiles with the universal profiles of the wall law, and a composite function defining the coefficient of turbulent viscosity was proposed. In this paper we construct the solution of the heat-transfer equation for equilibrium boundary layers under the assumption that the velocity distribution in the layer and the coefficient of turbulent viscosity are described by functions, obtained in [4, 5], of the dimensionless coordinateη=y/Δ, depending on two parametersβ and Re_*, while the turbulent Prandtl number Pr_t is either constant or is also a known function of η and the parametersβ and Re_*. The temperature of the surface T_w(x) is assumed to be an arbitrary function of the longitudinal coordinate and the solution is constructed in the form of series in the form parameters containing the derivatives of T_w(x). These form parameters are similar to those used in [6–9] to construct exact solutions of the equations of the laminar boundary layer.     

Electroviscous effect on non-Newtonian fluid flow in microchannels

Understanding non-Newtonian flow in microchannels is of both fundamental and practical significance for various microfluidic devices. A numerical study of non-Newtonian flow in microchannels combined with electroviscous effect has been conducted. The electric potential in the electroviscous force term is calculated by solving a lattice Boltzmann equation. And another lattice Boltzmann equation without derivations of the velocity when calculating the shear is employed to obtain flow field. The simulation of commonly used power-law non-Newtonian flow shows that the electroviscous effect on the flow depends significantly on the fluid rheological behavior. For the shear thinning fluid of the power-law exponent n < 1, the fluid viscosity near the wall is smaller and the electroviscous effect plays a more important role. And its effect on the flow increases as the ratio of the Debye length to the channel height increases and the exponent n decreases. While the shear thickening fluid of n > 1 is less affected by the electroviscous force, it can be neglected in practical applications.     

Electrorheological properties of PDMS/carbon black suspensions under shear flow

Suspensions of polydimethylsiloxane (PDMS) containing low amounts (1 wt.% or less) of a highly conducting carbon black (CB) filler are rendered conductive and exhibit electrorheological (ER) responses under shear flow when exposed to an externally applied AC electric field. The presence of columnar structures, consisting of CB particles aligned in the direction of the electric field is evidenced through optical microscopy experiments. The appearance of yielding behavior and positive ER response, manifested by an increase in the viscosity of the suspensions, depend strongly on the filler loading, strength of the electric field, magnitude of the shear field, and viscosity of the medium. The responses are stronger at low filler loadings, below the percolation threshold, and at very low shear rates, where the microstructure of the dispersed phase remains intact. At higher shear rates, corresponding to Mason numbers (Mn) above 1, the structure is disrupted and thus does not contribute to the observed shear stress. The rheological characterization is accompanied with admittance measurements, to demonstrate that the induced polarization forces between particles lead to the formation of electrically conductive structures within the polymer matrix. A critical comparison with the qualitative predictions based on the theory of induced dipole–dipole interactions shows that the theory is valid for these dilute systems.     

Influence of Property Variation on Natural Convection in a Gas Saturated Spherical Porous Annulus

The present study reports results of numerical investigation of natural convection in a spherical annulus filled with gas saturated porous medium. Boussinesq approximation has been relaxed considering variation of density, viscosity, and thermal conductivity of the gas with temperature. The momentum and energy equation along with boundary condition and property variation equations are solved by employing successive accelerated replacement scheme. There exists a reference parameter (q = 0.4) at which if thermo physical properties are evaluated, the average Nusselt number values for variable properties and constant properties are nearly same. Also, the effect of variable properties is negligible for temperature difference ratio, \(\theta ^{*}<0.1\) .     

An experimental study on turbulence modification in the near-wall boundary layer of a dilute gas-particle channel flow

Turbulence modifications of a dilute gas-particle flow are experimentally investigated in the lower boundary layer of a horizontal channel by means of a simultaneous two-phase PIV measurement technique. The measurements are conducted in the near-wall region with y ⁺?<?250 at Re _τ (based on the wall friction velocity u _τ and half channel height h)?=?430. High spatial resolution and small interrogation window are used to minimize the PIV measurement uncertainty due to the velocity gradient near the wall. Polythene beads with the diameter of 60?μm (d _p ⁺ ?=?1.71, normalized by the fluid kinematic viscosity ν and u _τ) are used as dispersed phase, and three low mass loading ratios (Φ _m ) ranging from 10^?4 to 10^?3 are tested. It is found that the addition of the particles noticeably modifies the mean velocity and turbulent intensities of the gas-phase, as well as the turbulence coherent structures, even at Φ _m ?=?0.025?%. Particle inertia changes the viscous sublayer of the gas turbulence with a smaller thickness and a larger streamwise velocity gradient, which increases the peak value of the streamwise fluctuation velocity ( $ u_{\text{rms}}^{ + } $ ) of the gas-phase with its location shifting to the wall. Particle sedimentation increases the roughness of the bottom wall, which significantly increases the wall-normal fluctuation velocity ( $ v_{\text{rms}}^{ + } $ ) and Reynolds shear stress ( $ - \langle u^{ \prime } v^{\prime } \rangle^{ + } $ ) of the gas-phase in the inner region of the boundary layer (y ⁺?<?10). Under effect of particle–wall collision, the Q2 events (ejections) of the gas-phase are slightly increased by particles, while the Q4 events (sweeps) are obviously decreased. The spatial scale of the coherent structures near the wall shrinks remarkably with the presence of the particles, which may be attributed to the intensified crossing-trajectory effects due to particle saltation near the bottom wall. Meanwhile, the $ v_{\text{rms}}^{ + } $ and $ - \langle u^{ \prime } v^{\prime } \rangle^{ + } $ of the gas-phase are significantly reduced in the outer region of the boundary layer (y ⁺?>?20).     

Turbulent boundary layer measurements over flat surfaces coated by nanostructured marine antifoulings

Whilst recent developments of nanotechnology are being exploited by chemists and marine biologists to understand how the completely environmentally friendly foul release coatings can control marine biofouling and how they can be developed further, the understanding of the hydrodynamic performances of these new generation coatings is being overlooked. This paper aims to investigate the relative boundary layer, roughness and drag characteristics of some novel nanostructured coatings, which were developed through a multi-European and multi-disciplined collaborative research project AMBIO (2010), within the framework of turbulent flows over rough surfaces. Zero-pressure-gradient, turbulent boundary layer flow measurements were conducted over flat surfaces coated with several newly developed nanostructured antifouling paints, along with some classic reference surfaces and a state-of-the-art commercial coating, in the Emerson Cavitation Tunnel (ECT) of Newcastle University. A large flat plane test bed that included interchangeable flat test sections was used for the experiments. The boundary layer data were collected with the aid of a two-dimensional DANTEC Laser Doppler Velocimetry (LDV) system. These measurements provided the main hydrodynamic properties of the newly developed nanostructured coatings including local skin friction coefficients, roughness functions and Reynolds stresses. The tests and subsequent analysis indicated the exceptionally good frictional properties of all coatings tested, in particular, the drag benefit of some new nanostructured coatings in the Reynolds number range investigated. The rapidly decreasing roughness function trends of AKZO19 and AKZO20 as the $ k_{s}^{ + } $ increases were remarkable along with the dissimilar roughness function character of all tested coatings to the well-known correlation curves warranting further research at higher Reynolds numbers. The wall similarity concept for the Reynolds stresses was only validated for the transitionally rough surfaces from $ (y + \varepsilon)^{ + } \approx 100 $ up to the end of the boundary layer.     

Numerical simulations of linear viscoelasticity of monodisperse emulsions of Newtonian drops in a Newtonian fluid from dilute to concentrated regime

The bulk viscoelastic properties of monodisperse emulsions of Newtonian drops in a Newtonian matrix subjected to small amplitude oscillatory shear (SAOS) flow are investigated by means of arbitrary Lagrangian Eulerian finite element method 3D numerical simulations. Volume fractions of the suspended phase from the dilute to the concentrated regime (up to 30 %), and a range of several orders of magnitude of the drops-to-matrix viscosity ratio and of the frequency of the oscillatory flow are examined; the eventual presence of slip between the two fluids is also considered. The computational results are compared with theory, yielding a quantitative agreement with Oldroyd (Proc R Soc Lond A 218:122–132, 1953) predictions in a wide range of values of the considered parameters, even well beyond the dilute regime, and also in the cases with slip.     

Numerical study on supersonic mixing and combustion with hydrogen injection upstream of a cavity flameholder

Characteristics of supersonic mixing and combustion with hydrogen injection upstream of a cavity flameholder are investigated numerically using hybrid RANS/LES (Reynolds-Averaged Navier–Stokes/Large-Eddy Simulation) method. Two types of inflow boundary layer are considered. One is a laminar-like boundary layer with inflow thickness of $\delta_{\inf } = 0.0$ and the other is a turbulent boundary layer with inflow thickness of $\delta_{\inf } = 2.5\,{\text{mm}}$ . The hybrid RANS/LES method acts as a DES (Detached Eddy Simulation) model for the laminar-like inflow condition and a wall-modeled LES for the turbulent inflow condition where the recycling/rescaling method is adopted. Although the turbulent inflow seems to have just minor influences on the supersonic cavity flow without fuel injection, its effects on the mixing and combustion processes are great. It is found that the unsteady turbulent structures in upstream incoming boundary layer interact with the injection jet, resulting in fluctuations of the upstream recirculation region and bow shock, and induce quick dispersion of the hydrogen fuel jet, which enhances the mixing as well as subsequent combustion.     

On the Elastic Energy Density of Constrained Q-Tensor Models for Biaxial Nematics

Within the Landau–de Gennes theory, the order parameter describing a biaxial nematic liquid crystal assigns a symmetric traceless 3 × 3 matrix Q with three distinct eigenvalues to every point of the region Ω occupied by the system. In the constrained case of matrices Q with constant eigenvalues, the order parameter space is diffeomorphic to the eightfold quotient ${\mathbb{S}^3/\mathcal{H}}$ of the 3-sphere ${\mathbb{S}^3}$ , where ${\mathcal{H}}$ is the quaternion group, and a configuration of a biaxial nematic liquid crystal is described by a map from Ω to ${\mathbb{S}^3/\mathcal{H}}$ . We express the (simplest form of the) Landau–de Gennes elastic free-energy density as a density defined on maps ${q: \Omega \to \mathbb{S}^3}$ , whose functional dependence is restricted by the requirements that (1) it is well defined on the class of configuration maps from Ω to ${\mathbb{S}^3/\mathcal{H}}$ (residual symmetry) and (2) it is independent of arbitrary superposed rigid rotations (frame indifference). As an application of this representation, we then discuss some properties of the corresponding energy functional, including coercivity, lower semicontinuity and strong density of smooth maps. Other invariance properties are also considered. In the discussion, we take advantage of the identification of ${\mathbb{S}^3}$ with the Lie group of unit quaternions ${Sp(1) \cong SU(2)}$ and of the relations between quaternions and rotations in ${\mathbb{R}^3}$ and ${\mathbb{R}^4}$ .     

Determination of the magnitude of the separation criterion for a three-dimensional laminar boundary layer

A separation criterion, i.e., a definite relationship between the external flow and the boundary layer parameters [1], can be used to estimate the possibility of the origination of separation of a two-dimensional boundary layer. A functional form of the separation criterion has also been obtained for a three-dimensional boundary layer [2] on the basis of dimensional analysis. As in the case of the two-dimensional boundary layer, locally self-similar solutions can be used to determine the specific magnitude of the separation criterion as a function of the values of the governing parameters. Locally self-similar solutions of the two-dimensional laminar boundary-layer equations have been found at the separation point for a perfect gas with a linear dependence of the coefficient of viscosity on the temperature (Ω=1) and Prandtl number P=1 [3, 4]. The influence of blowing and suction has been studied for this case [5]. Self-similar solutions have been obtained for Ω=1, P=0.723 for the limit case of hypersonic perfect gas flow [6]. Locally self-similar solutions of the three-dimensional laminar boundary-layer equations at the separation point are presented in [7] for a perfect gas with Ω=1, P=1. There are no such computations for Ω≠1, P≠1; however, the results of computing several examples for a two-dimensional flow [8] show that the influence of the real properties of a gas can be significant and should be taken into account. Self-similar solutions of the two- and three-dimensional boundary-layer equations at the separation point are found in this paper for a perfect gas with a power-law dependence of the viscosity coefficient on the enthalpy (Ω=0.5, 0.75, 1.0) for different values of the Prandtl number (P=0.5, 0.7, 1.0) in a broad range of variation of the external stream velocity (v ₁ ² /2h₁* = 0–0.99) and the temperature of the streamlined surface. Magnitudes of the separation criterion for a laminar boundary layer have been obtained on the basis of these data.