# Difference between revisions of "Slippery questions about complex fluids flowing past solids"

Slippery questions about complex fluids flowing past solids

Authors: Steve Granick, Yingxi Zhu and Hyungjung Lee

#### Soft matter keywords

Rough surfaces, slip control, hydrophobicity

By Alex Epstein

### Abstract from the original paper

Viscous flow is familiar and useful, yet the underlying physics is surprisingly subtle and complex. Recent experiments and simulations show that the textbook assumption of ‘no slip at the boundary’ can fail greatly when walls are sufficiently smooth. The reasons for this seem to involve materials chemistry interactions that can be controlled — especially wettability and the presence of trace impurities, even of dissolved gases. To discover what boundary condition is appropriate for solving continuum equations requires investigation of microscopic particulars. Here, we draw attention to unresolved topics of investigation and to the potential to capitalize on ‘slip at the wall’ for purposes of materials engineering.

## Soft matters

Aimed at a general audience like any other Nature paper, this "progress article" was an enlightening read about slip of fluids flowing on solid surfaces. This is a topic near and dear to wetting.

#### Lack of slip in everyday life

This article made me realize the simple reason it is impossible to blow a surface clean of dust particles. The no-slip boundary condition of fluid flow past a solid surface--that is, flow velocity vanishes at the interface--means that small dust particles do not extend far enough beyond the adsorbing surface to be blown off. Figure 1 shows this familiar situation. Other familiar instances in which the no-slip condition makes life a little more difficult include washing soap off in the shower or sink and washing dishes. In both cases, it is much more effective to scrub than to simply pour water.

Fig. 1

Perhaps less trivial issues are fluid flow through small pipes (the effect in large pipes is negligible), accumulation of fatty detritus in arteries, and the pumping required in these cases.

#### Exceptions to the "no-slip dogma"

The no-slip condition is so central to fluid mechanics and works so well in the majority of situations that the exceptions have not been appreciated much outside a small community of engineers and engineering literature. It must be emphasized that no-slip is valid provided that certain assumptions are met: a single component fluid, a wetted surface, and low levels of shear stress. Then careful experiments imply that the fluid comes to rest within 1-2 molecular diameters of the surface. However, the assumptions are more restrictive and the slip more controllable than most people appreciate.

Fig. 2

The exceptions fall into these categories:

• Flow of multicomponent fluids with different viscosity components
• Suspensions , foodstuffs, and emulsions
• Polymer melts (non-adsorbing polymers are dissolved in fluids of lower viscosity)
• Viscous polymers (where there is a range of molecular weights)
• Superhydrophobic lotus-leaf-type surfaces with Cassie-state trapped air
• "Weak-link" argument: given a sufficiently high flow rate, the shear rate will cause either failure of fluid cohesion or the no-slip condition
• Gas flowing past solids whose spacing is less that a few mean free paths (molecular scale pipes)
• Superfluid helium

As a result, many computer simulations predict and experiments confirm micron-scale slip lengths in newtonian fluids such as water and alkanes. While these can be ignored in macroscopic channels, the impact is great for micro/nanochannels. Experimental methods range from optical tracking of fluorescent dyes to laser particle velocimetry to NMR imaging.

There are in fact two possible types of slip: true and apparent. As shown in Figure 2, true slip occurs when the fluid velocity is literally nonzero at the surface, whereas in apparent slip the velocity is zero but the velocity gradient is higher. True slip may occur on superhydrophobic Cassie surfaces, since the fluid rides almost entirely on air, or on very smooth surfaces at very high shear (flow) rates. Apparent slip occurs, for example, in a multicomponent fluid in which the low viscosity component (or dissolved gas) segregates near the surface and facilitates flow. Because the viscosity near the boundary is low, the velocity gradient there is higher and the bulk velocity profile extrapolates to zero below the surface. In both the true and apparent cases, the slip length is defined by this zero-velocity extrapolated distance below the surface.

#### Deviation from no-slip, quantified

The flow rate is linked directly to the slip, and the main idea of the experiments that show this is the hydrodynamic force $F_H$ Two solid spheres of radius $R$, at spacing $D$, experience hydrodynamic force $F_H$ as they approach or retreat from one another in a liquid due to the flow of fluid out of or into the space between.

$F_H = f^{*} \frac{6\pi R^2 \eta}{D}\ \frac{dD}{dt}$


So $F_H \propto \frac{dD}{dt}, R^2, \eta, D^{-1}$. When the $f^{*}$ prefactor deviates from 1, this quantifies the deviation from classical no-slip condition.

Slip signifies that in the continuum model of low, the fluid velocity at the surface is finite, slip velocity = $v_s$, and increases linearly with distance from the surface.

$\eta v_s \equiv b \sigma_s$


where b is the slip length and $\sigma_s$ is the shear stress at the surface.

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