scholarly journals Wall slip of complex fluids: Interfacial friction versus slip length

2018 ◽  
Vol 3 (6) ◽  
Author(s):  
Benjamin Cross ◽  
Chloé Barraud ◽  
Cyril Picard ◽  
Liliane Léger ◽  
Frédéric Restagno ◽  
...  
Keyword(s):  
Slip Length ◽  
Complex Fluids ◽  
Wall Slip ◽  
Interfacial Friction

Slip due to Rarefaction, Surface Roughness, and Intermolecular Interactions for Gases and Liquids

2011 ◽  
Author(s):  
Phil Ligrani
Keyword(s):  
Surface Roughness ◽  
Intermolecular Interactions ◽  
Stokes Equations ◽  
Slip Length ◽  
Wall Slip ◽  
Mean Free Path ◽  
Working Fluid ◽  
Channel Height ◽  
Near Surface ◽  
Accommodation Coefficients

In the present study, slip phenomena are investigated in two different sets of experiments conducted in gases and one Newtonian liquid. Overall, differences in near-surface slip behavior are illustrated for these two different fluid mediums, where the slip is induced surface roughness and rarefaction in the gases, and by surface roughness and intermolecular interactions in the liquid. Within both sets of experiments, flows are induced within micro-fluidic passages by rotation within C-shaped fluid chambers formed between a rotating disk and a stationary surface. When gases are employed, accommodation coefficients are determined in a unique manner from experimental results and analysis based on the Navier-Stokes equations. In all cases, roughness size is large compared to molecular mean free path. When channel height is defined at the tops of the roughness elements, slip is believed to be a result of rarefaction as well as fluid shear. With this arrangement, tangential accommodation coefficients decrease and slip velocity magnitudes increase, at a particular value of Knudsen number, as the level of surface roughness increases. With Newtonian water as the working fluid, hydrophobic roughness is used to induce near-wall slip in the fluid chamber. The magnitudes of slip length and slip velocities increase as the average size of the surface roughness becomes larger. The resulting slip length data show a high degree of organization when normalized using the fluid chamber height, such that experimental data obtained using different chamber heights and different disk roughness magnitudes collapse along a single line, illustrating strong linear dependence of the slip length on the normalized radial-line-averaged shear stress.

scholarly journals The Graetz–Nusselt problem extended to continuum flows with finite slip

2015 ◽  
Vol 764 ◽  
Author(s):  
A. Sander Haase ◽  
S. Jonathan Chapman ◽  
Peichun Amy Tsai ◽  
Detlef Lohse ◽  
Rob G. H. Lammertink
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Shear Flow ◽  
Slip Length ◽  
Wall Slip ◽  
Partial Slip ◽  
Scaling Exponent ◽  
Constant Wall Temperature ◽  
Radial Heat ◽  
Transition Points

AbstractGraetz and Nusselt studied heat transfer between a developed laminar fluid flow and a tube at constant wall temperature. Here, we extend the Graetz–Nusselt problem to dense fluid flows with partial wall slip. Its limits correspond to the classical problems for no-slip and no-shear flow. The amount of heat transfer is expressed by the local Nusselt number $\mathit{Nu}_{x}$, which is defined as the ratio of convective to conductive radial heat transfer. In the thermally developing regime, $\mathit{Nu}_{x}$ scales with the ratio of position $\tilde{x}=x/L$ to Graetz number $\mathit{Gz}$, i.e. $\mathit{Nu}_{x}\propto (\tilde{x}/\mathit{Gz})^{-{\it\beta}}$. Here, $L$ is the length of the heated or cooled tube section. The Graetz number $\mathit{Gz}$ corresponds to the ratio of axial advective to radial diffusive heat transport. In the case of no slip, the scaling exponent ${\it\beta}$ equals $1/3$. For no-shear flow, ${\it\beta}=1/2$. The results show that for partial slip, where the ratio of slip length $b$ to tube radius $R$ ranges from zero to infinity, ${\it\beta}$ transitions from $1/3$ to $1/2$ when $10^{-4}<b/R<10^{0}$. For partial slip, ${\it\beta}$ is a function of both position and slip length. The developed Nusselt number $\mathit{Nu}_{\infty }$ for $\tilde{x}/\mathit{Gz}>0.1$ transitions from 3.66 to 5.78, the classical limits, when $10^{-2}<b/R<10^{2}$. A mathematical and physical explanation is provided for the distinct transition points for ${\it\beta}$ and $\mathit{Nu}_{\infty }$.

Nanorheology of Polymers, Block Copolymers, and Complex Fluids

1994 ◽  
Vol 366 ◽  
Author(s):  
A. Levent Demirel ◽  
Lenore Cai ◽  
Ali Dhinojwala ◽  
Steve Granick ◽  
J. M. Drake
Keyword(s):  
Block Copolymers ◽  
Linear Response ◽  
Nonlinear Response ◽  
Fourier Transforms ◽  
Complex Fluids ◽  
Wall Slip ◽  
Sliding Velocity ◽  
Nonpolar Fluids ◽  
Induced Changes ◽  
Previous Identification

ABSTRACTThe shear rheology of molecularly-thin films of fluids has been studied experimentally as it depends on sinusoidal frequency (linear response) or on sliding velocity (nonlinear response). Building upon previous identification of a solidlike state that is induced by confinement, we find the shearinduced transition to a sliding state in which the viscous dissipation is essentially velocity-independent. The mechanism appears to involve wall slip but Fourier transforms of the response reveal fluctuations, intrinsic to the sliding state, over all accessible frequencies. Other ongoing studies involve shear-induced changes in the fluorescence of confined fluorescent probes, shear dilatancy, and the contrast between the shear of simple nonpolar fluids, and block copolymers.

Molecular mechanisms of liquid slip

2008 ◽  
Vol 600 ◽  
pp. 257-269 ◽  
Author(s):  
A. MARTINI ◽  
A. ROXIN ◽  
R. Q. SNURR ◽  
Q. WANG ◽  
S. LICHTER
Keyword(s):  
Md Simulation ◽  
Molecular Mechanisms ◽  
Dynamical Equation ◽  
Slip Length ◽  
Wall Slip ◽  
Md Simulations ◽  
Critical Value ◽  
Visual Evidence ◽  
Localized Defects ◽  
Low Levels

It is now well-established that the liquid adjacent to a solid need not be stationary – it can slip. How this slip occurs is unclear. We present molecular-dynamics (MD) simulation data and results from an analytical model which support two mechanisms of slip. At low levels of forcing, the potential field generated by the solid creates a ground state which the liquid atoms preferentially occupy. Liquid atoms hop through this energy landscape from one equilibrium site to another according to Arrhenius dynamics. Visual evidence of the trajectories of individual atoms on the solid surface supports the view of localized hopping, independent of the dynamics outside a local neighbourhood. We call this defect slip. At higher levels of forcing, the entire layer slips together, obviating the need for localized defects and resulting in the instantaneous motion of all atoms adjacent to the solid. The appearance of global slip leads to an increase in the number of slipping atoms and consequently an increase in the slip length. Both types of slip observed in the MD simulations are described by a dynamical model in which each liquid atom experiences a force from its neighbouring liquid atoms and the solid atoms of the boundary, is sheared by the overlying liquid, and damped by the solid. In agreement with the MD observations, this model predicts that above a critical value of forcing, localized slipping occurs in which atoms are driven from low-energy sites, but only if there is a downstream site which has been vacated. Also as observed, above a second critical value, all the liquid atoms adjacent to the wall slip. Finally, the dynamical equation predicts that at extremely large values of forcing, the slip length approaches a constant value, in agreement with the MD simulation results.

Breakdown of the Bretherton law due to wall slippage

2014 ◽  
Vol 741 ◽  
pp. 200-227 ◽  
Author(s):  
Yen-Ching Li ◽  
Ying-Chih Liao ◽  
Ten-Chin Wen ◽  
Hsien-Hung Wei
Keyword(s):  
Slip Length ◽  
Dynamic Contact Angle ◽  
Flow Characteristics ◽  
Wall Slip ◽  
Dynamic Contact ◽  
Precursor Film ◽  
Minor Role ◽  
Textured Surfaces ◽  
Slip Regime ◽  
A Minor

AbstractAgainst the common wisdom that wall slip plays only a minor role in global flow characteristics, here we demonstrate theoretically for the displacement of a long bubble in a slippery channel that the well-known Bretherton $2/3$ law can break down due to a fraction of wall slip with the slip length $\lambda $ much smaller than the channel depth $R$. This breakdown occurs when the film thickness $h_{\infty } $ is smaller than $\lambda $, corresponding to the capillary number $Ca$ below the critical value $Ca^{\ast } \sim (\lambda /R)^{3 / 2}$. In this strong slip regime, a new quadratic law $h_{\infty } /R \sim Ca^{2} (R/\lambda )^{2}$ is derived for a film much thinner than that predicted by the Bretherton law. Moreover, both the $2/3$ and the quadratic laws can be unified into the effective $2/3$ law, with the viscosity $\mu $ replaced by an apparent viscosity $\mu _{app}= \mu h_{\infty } /({\lambda } + h_{\infty })$. A similar extension can also be made for coating over textured surfaces where apparent slip lengths are large. Further insights can be gained by making a connection with drop spreading. We find that the new quadratic law can lead to $\theta _{d} \propto Ca^{1 / 2} $ for the apparent dynamic contact angle of a spreading droplet, subsequently making the spreading radius grow with time as $r \propto t^{1 / 8}$. In addition, the precursor film is found to possess $\ell _{f} \propto Ca^{ - 1 / 2}$ in length and therefore spreads as $\ell _{f} \propto t^{1 / 3}$ in an anomalous diffusion manner. All these features are accompanied by no-slip-to-slip transitions sensitive to the amount of slip, markedly different from those on no-slip surfaces. Our findings not only provide plausible accounts for some apparent departures from no-slip predictions seen in experiments, but also offer feasible alternatives for assessing wall slip effects experimentally.

scholarly journals Wall Slip Behaviour of Polymers Based on Molecular Dynamics at the Micro/Nanoscale and Its Effect on Interface Thermal Resistance

Polymers ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 2182
Author(s):  
Yan Lou ◽  
Gang Wu ◽  
Yanfeng Feng
Keyword(s):  
Molecular Dynamics ◽  
Thermal Resistance ◽  
Slip Length ◽  
Wall Slip ◽  
External Pressure ◽  
Liquid Interface ◽  
Dynamics Simulation ◽  
Interface Thermal Resistance ◽  
Solid Liquid Interface ◽  
Solid Liquid

Taking the Poiseuille flow of a molten polymer in parallel plates as the research object and polymethyl methacrylate (PMMA) as the research material, an all-atom analysis model of the molecular dynamic flow of polymer macromolecules is established according to the Navier slip law. The effects of wall wettability and external pressure on the wall slip behaviour of polymer macromolecules, as well as the spatial evolution process of the entanglement–unentanglement process of polymer chains near the wall under different shearing effects, were studied. The interface thermal resistance rule was explored, and an interface thermal resistance model considering the wall slip behaviour was established. Finally, a micro-injection experiment was used to verify the validity and accuracy of the model. The results show that when the wall is hydrophobic, the polymer melt exhibits significant wall slip. As the external pressure increases, the wall slip speed and the slip length increase. However, after a certain pressure is exceeded, the growth rate of the slip length is basically zero. As the external pressure increases, the PMMA molecular chains gradually start to separate, the single molecular chain becomes untangled from the entangled grid, and the chain detaches from the wall after exceeding a certain threshold. Wall slip reduces the interface thermal resistance between the solid–liquid interface and enhances the interface heat transfer performance. The interface thermal resistance value calculated by molecular dynamics can more accurately reflect the heat conduction rule of the solid–liquid interface at the micro/nanoscale than that measured by the thermal resistance experiment, indicating that the micro/nano interface thermal resistance obtained by molecular dynamics simulation is reliable.

Slip-induced suppression of Marangoni film thickening in surfactant-retarded Landau–Levich–Bretherton flows

2015 ◽  
Vol 781 ◽  
pp. 578-594 ◽  
Author(s):  
David Halpern ◽  
Yen-Ching Li ◽  
Hsien-Hung Wei
Keyword(s):  
Film Thickness ◽  
Surface Diffusion ◽  
Slip Length ◽  
Wall Slip ◽  
Coating Flow ◽  
Insoluble Surfactant ◽  
Slip Effects ◽  
Surfactant Effects ◽  
Deposited Film ◽  
As If

We report that the well-known Marangoni film thickening in surfactant-laden Landau–Levich–Bretherton coating flow can be completely suppressed by wall slip. The analysis is made by mainly looking at how the deposited film thickness varies with the capillary number $Ca$ ($\ll 1$) and the dimensionless slip length ${\it\Lambda}={\it\lambda}/R$ ($\ll 1$) in the presence of a trace amount of insoluble surfactant, where ${\it\lambda}$ is the slip length and $R$ is the radius of the meniscus. When slip effects are weak at sufficiently large $Ca$ (but still $\ll 1$) such that $Ca\gg {\it\Lambda}^{3/2}$, the film thickness can still vary as $Ca^{2/3}$ and be thickened by surfactant as if wall slip were absent. However, when slip effects become strong by lowering $Ca$ to $Ca\ll {\it\Lambda}^{3/2}$, the film, especially when surface diffusion of surfactant is negligible, does not get thinner according to the strong-slip quadratic law reported previously (Liao et al., Phys. Rev. Lett., vol. 111, 2013, 136001; Li et al., J. Fluid Mech., vol. 741, 2014, pp. 200–227). Instead, the film behaves as if both surfactant and wall slip were absent, precisely following the no-slip $2/3$ law without surfactant. Effects of surface diffusion are also examined, revealing three distinct regimes as $Ca$ is varied from small to large values: the strong-slip quadratic scaling without surfactant, the no-slip $2/3$ scaling without surfactant and the film thickening along the no-slip $2/3$ scaling with surfactant. An experiment is also suggested to test the above findings.

Speeding up thermocapillary migration of a confined bubble by wall slip

2014 ◽  
Vol 746 ◽  
pp. 31-52 ◽  
Author(s):  
Ying-Chih Liao ◽  
Yen-Ching Li ◽  
Yu-Chih Chang ◽  
Chih-Yung Huang ◽  
Hsien-Hung Wei
Keyword(s):  
Film Thickness ◽  
Slip Length ◽  
Flow Characteristics ◽  
Wall Slip ◽  
Fluid Viscosity ◽  
Tube Radius ◽  
Thermocapillary Migration ◽  
Slip Regime ◽  
Slip Effects ◽  
Slight Discrepancy

AbstractIt is usually believed that wall slip contributes small effects to macroscopic flow characteristics. Here we demonstrate that this is not the case for the thermocapillary migration of a long bubble in a slippery tube. We show that a fraction of the wall slip, with the slip length $\lambda $ much smaller than the tube radius $R$, can make the bubble migrate much faster than without wall slip. This speedup effect occurs in the strong-slip regime where the film thickness $b$ is smaller than $\lambda $ when the Marangoni number $S= \tau _{T} R/\sigma _{0}~ (\ll 1)$ is below the critical value $S^* \sim (\lambda /R)^{1/2}$, where $\tau _{T}$ is the driving thermal stress and $\sigma _{0}$ is the surface tension. The resulting bubble migration speed is found to be $U_{b} \sim (\sigma _{0}/\mu )S^{3}(\lambda /R)$, which can be more than a hundred times faster than the no-slip result $U_{b} \sim (\sigma _{0}/\mu )S^{5}$ (Wilson, J. Eng. Math., vol. 29, 1995, pp. 205–217; Mazouchi & Homsy, Phys. Fluids, vol. 12, 2000, pp. 542–549), with $\mu $ being the fluid viscosity. The change from the fifth power law to the cubic one also indicates a transition from the no-slip state to the strong-slip state, albeit the film thickness always scales as $b\sim RS^{2}$. The formal lubrication analysis and numerical results confirm the above findings. Our results in different slip regimes are shown to be equivalent to those for the Bretherton problem (Liao, Li & Wei, Phys. Rev. Lett., vol. 111, 2013, 136001). Extension to polygonal tubes and connection to experiments are also made. It is found that the slight discrepancy between experiment (Lajeunesse & Homsy, Phys. Fluids, vol. 15, 2003, pp. 308–314) and theory (Mazouchi & Homsy, Phys. Fluids, vol. 13, 2001, pp. 1594–1600) can be interpreted by including wall slip effects.

Scattering Methods in Complex Fluids

2015 ◽  
Author(s):  
Sow-Hsin Chen ◽  
Piero Tartaglia
Keyword(s):  
Complex Fluids
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