Исследование гидродинамического сопротивления щелевого микроканала с текстурированной стенкой

The results of numerical investigation of the hydrodynamic drag of a slit microchannel with a textured wall surface, as well as the pressure drop in such a channel and the effective slip length on the wall for various Reynolds numbers, are presented. The channel height was 10 µm, and the length varied from 25 to 500 µm. It was found that the pressure drop in the textured microchannel was less than in a conventional channel for any of its lengths. The dependences of the relative pressure drop, the friction factor, and the effective slip length on the Reynolds number were obtained for various channel lengths. A correlation that describes the dependence of the relative pressure drop on the Reynolds number for small channel lengths was proposed. The friction factor is described by a correlation of form 20 / Re.

Analytical Modelling of Laminar Developing Flow Between Hydrophobic Surfaces with Different Slip-Velocities

Theoretical analysis of the entrance hydrodynamics of microchannels is an important design aspect in connection with the development of microfluidic devices. In this paper, pressure-driven fluid flow in the entrance region of two infinite hydrophobic parallel plates with dissimilar slip-velocities is analytically modelled. The linearized momentum equation is solved by applying the Navier-slip model at the boundaries to achieve the most generalized two-dimensional form. The velocity profile is obtained by combining the developed and developing velocities, which is estimated by invoking the separation of variable method. It is observed that the velocity profile is asymmetric and the shear-free region can be shifted from the geometrical central line by altering the wall hydrophobicity. Moreover, the zero shear zone is transferred more towards the surface having high hydrophobicity. The expression for wall shear stress is obtained analytically using Newton's law of viscosity. Moreover, the boundary layer growth from the upper and lower walls are found to be entirely different and they merge at the entrance length and is noticed to be off-setted from the geometric centre-line. The effect of slip-length on the entrance length is analysed and an empirical correlation is deduced.

Numerical study of the flow around a circular cylinder with the slip length boundary effect at a critical Reynolds number

The paper presents an investigation of the slip length effect on the flow around a circular cylinder at Reynolds number Re = 2.5·105. The study was performed by means of numerical simulation of the flow with the URANS approach based on the k-ω SST model. Calculations show a significant effect of the slip length on the flow patterns. With an increase in the slip length, the drag coefficient noticeably decreases and the pulsations of the lift force reduce. With an increase in the slip length, the separation of the flow from the cylinder is delayed, which significantly affects the flow patterns in the wake behind the cylinder.

The investigation of the height effect of a slit microchannel with a textured wall on its hydrodynamic drag

The numerical investigation of the fluid flow in a slit microchannel with a textured wall was carried out. The effect of the channel height on the hydrodynamic drag coefficient, as well as on the pressure drop in such channel and the effective slip length on the wall for various Reynolds numbers, are presented in the paper. The channel length was 100 µm, and its height was varied from 25 µm to 500 µm. The Reynolds number was varied from 0.1 to 100. The main studied characteristics were compared to the similar ones obtained for a channel with normal walls (no-slip conditions). It was found that the pressure drop in such textured microchannel was lower as compared to a conventional channel for any of its heights and for any Reynolds numbers. The dependences of the relative pressure drop, effective slip length, and drag coefficient on the Reynolds number were obtained for different channel heights. The drag coefficient was described as 20/Re for the average values of the channel height. A correlation that describes the dependence of the friction factor on the Reynolds number for small and large heights of the channel was proposed. The accuracy of the proposed correlation was about 90%.

Equilibrium tilt of slippery elliptical rods in creeping simple shear

It is shown that shape anisotropy and intrinsic surface slip lead to equilibrium tilt of slippery particles in a creeping simple shear flow, even for nearly shape-isotropic particles with a cross-section that is close to circular provided the Navier-slip length is sufficiently large. We study a rigid particle with an elliptical cross-section, and of infinite extent in the vorticity direction, in simple shear. A Navier-slip boundary condition is imposed on its surface. When a Navier-slip length parameter $\lambda$ is infinite, an analytical solution is derived for the Stokes flow around a particle tilting in equilibrium at an angle $(1/2)\cos ^{-1}((1-k)/(1+k))$ to the flow direction where $0 \le k \le 1$ is the ratio of the semi-minor to semi-major axes of its elliptical cross-section. A regular perturbation analysis about this analytical solution is then performed for small values of $1/\lambda$ and a numerical continuation method implemented for larger values. It is found that an equilibrium continues to exist for any anisotropic particle $k < 1$ provided $\lambda \ge \lambda _{crit}(k)$ where $\lambda _{crit}(k)$ is a critical Navier-slip length parameter determined here. As the case $k \to 1$ of a circular cross-section is approached, it is found that $\lambda _{crit}(k) \to \infty$ , so the range of Navier-slip lengths allowing equilibrium tilt shrinks as shape anistropy is lost. Novel theoretical connections with equilibria for constant-pressure gas bubbles with surface tension are also pointed out.

A review on slip boundary conditions at the nanoscale: recent development and applications

The slip boundary condition for nanoflows is a key component of nanohydrodynamics theory, and can play a significant role in the design and fabrication of nanofluidic devices. In this review, focused on the slip boundary conditions for nanoconfined liquid flows, we firstly summarize some basic concepts about slip length including its definition and categories. Then, the effects of different interfacial properties on slip length are analyzed. On strong hydrophilic surfaces, a negative slip length exists and varies with the external driving force. In addition, depending on whether there is a true slip length, the amplitude of surface roughness has different influences on the effective slip length. The composition of surface textures, including isotropic and anisotropic textures, can also affect the effective slip length. Finally, potential applications of nanofluidics with a tunable slip length are discussed and future directions related to slip boundary conditions for nanoscale flow systems are addressed.

Effective Slip Lengths for Stokes Flow over Rough, Mixed-Slip Surfaces

<p>In this thesis, homogenization and perturbation methods are used to derive analytic expressions for effective slip lengths for Stokes flow over rough, mixed-slip surfaces, where the roughness is periodic, and the variation in slip length has the same period. If the classical no-slip boundary condition of fluid mechanics is relaxed, the slip velocity of the fluid at the surface is non-zero. For simple shear flow, the slip velocity is proportional to the shear rate. The constant of proportionality has dimensions of length and is known as the slip length. Any variation in the slip length over the surface will cause a perturbation to the flow adjacent to the surface. Due to the diffusion of momentum, at sufficient height above the surface, the flow perturbations have diminished, and flow is smooth and uniform. The velocity and shear rate at this height imply an effective slip length of the surface. The purpose of this thesis is to predict that effective slip length. Homogenization is a technique for finding approximate solutions to partial differential equations. The essence of homogenization is to construct a mathematical model of a physical problem featuring some periodic heterogeneity, then generate a sequence of models such that the period in question reduces with each increment in the sequence. If the sequence is appropriately defined, it has a limit model in the limit of vanishing period, for which a solution can be found. The solution to the limit system is an approximation to the solutions of systems with a finite period. We use homogenization to find the effective slip length of a system of Stokes flow over a periodically rough surface, described by periodic function h(x; y), with a local slip length b(x; y) varying with the same period. For systems where the period L is smaller than both the domain height P and typical slip lengths, the effective slip length bₑff is well-approximated by the harmonic mean of local slip lengths, weighted by area of contact between liquid and surface: [See 'Thesis' document below for equation.] We further use a perturbation technique to verify the above expression in the special case of a flat surface, and to derive another effective slip length expression: For a flat surface with local slip lengths much smaller than the period and domain height, the effective slip length bₑff is well-approximated by the area-weighted average of local slip lengths: [See 'Thesis' document below for equation.]</p>

Effective Slip Lengths for Stokes Flow over Rough, Mixed-Slip Surfaces

<p>In this thesis, homogenization and perturbation methods are used to derive analytic expressions for effective slip lengths for Stokes flow over rough, mixed-slip surfaces, where the roughness is periodic, and the variation in slip length has the same period. If the classical no-slip boundary condition of fluid mechanics is relaxed, the slip velocity of the fluid at the surface is non-zero. For simple shear flow, the slip velocity is proportional to the shear rate. The constant of proportionality has dimensions of length and is known as the slip length. Any variation in the slip length over the surface will cause a perturbation to the flow adjacent to the surface. Due to the diffusion of momentum, at sufficient height above the surface, the flow perturbations have diminished, and flow is smooth and uniform. The velocity and shear rate at this height imply an effective slip length of the surface. The purpose of this thesis is to predict that effective slip length. Homogenization is a technique for finding approximate solutions to partial differential equations. The essence of homogenization is to construct a mathematical model of a physical problem featuring some periodic heterogeneity, then generate a sequence of models such that the period in question reduces with each increment in the sequence. If the sequence is appropriately defined, it has a limit model in the limit of vanishing period, for which a solution can be found. The solution to the limit system is an approximation to the solutions of systems with a finite period. We use homogenization to find the effective slip length of a system of Stokes flow over a periodically rough surface, described by periodic function h(x; y), with a local slip length b(x; y) varying with the same period. For systems where the period L is smaller than both the domain height P and typical slip lengths, the effective slip length bₑff is well-approximated by the harmonic mean of local slip lengths, weighted by area of contact between liquid and surface: [See 'Thesis' document below for equation.] We further use a perturbation technique to verify the above expression in the special case of a flat surface, and to derive another effective slip length expression: For a flat surface with local slip lengths much smaller than the period and domain height, the effective slip length bₑff is well-approximated by the area-weighted average of local slip lengths: [See 'Thesis' document below for equation.]</p>

Molecular Dynamics: A Study on Slip, Drops, and Graphene

<p>Molecular dynamics (MD) is a computational tool used to study physical systems by modeling the atomic-scale interactions between atoms. MD can accurately predict the properties of materials where models are well developed. For new materials, models may be in their early stages and may lack the ability to produce accurate results; however, MD can still provide insight into the physical properties of these new materials. This thesis will use MD to study two different systems. First, the Lennard-Jones (L-J) liquid is used to study how the intrinsic slip lengths of atomic sized surfaces add to produce an effective slip of a larger surface made up of these atomic constituents. The results show that the effective slip of a surface is dominated by its smallest slip, and these results show good agreement with a theory that predicts effective slip given the intrinsic slip and roughness of a surface. The L-J model is also used to investigate the rolling and sliding motion of viscous drops on super-hydrophobic surfaces. The effects of drop size, slip length, and gravity on drop velocities are investigated, and a model that predicts drop speed given the characteristics of a drop and a surface is proposed. The model shows good agreement with simulation results, especially for certain regimes. Second, graphene is studied with MD using various atomistic models. The energies of layers of graphene are reproduced using an Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential, and the energies required to exfoliate graphene from crystal graphite and nickel nano-particles are calculated. The calculations from MD show good agreement with literature and experiment, and these results demonstrate how simple models in MD can produce useful results to aid research and experiment. Finally, the formation of nano-bubbles in graphene grown on platinum is studied using the AIREBO and L-J potentials. The basic formation of graphene nano-bubbles is demonstrated by compressing the edges of graphene flakes. The simulations highlight the importance of proper boundary conditions, such as atom pinning, in order to produce tall, smooth nano-bubbles. The results also suggest that accurate models will be required to effectively demonstrate bubble formation.</p>