Liquid rough surfaces

Fig. 5. Sessile drop on a rough surface true contact angle BTA and apparent contact angle BTH. Thick curve = surface of solid (s) thin curve = surface of liquid (1) v = vapour. T is the triple point HTR a horizontal AT a tangent to the solid surface BT a tangent to the liquid surface.

As long as the liquid actually wets the rough surface, a less contentious approach linking the roughness factor to the extent of contact would seem to be via the spreading coefficient as shown in Eq. 20 and summarised in Table 1. If air is trapped within pits by the liquid, a composite surface is produced. 

Cassie [39] extended Wenzel s treatment to composite surfaces. His treatment can be applied to a rough surface incompletely wetted by a liquid so that it consists of an area fraction f wetted and /2 unwetted surface. Then ... 

The major difference of the water structure between the liquid/solid and the liquid/liquid interface is due to the roughness of the liquid mercury surface. The features of the water density profiles at the liquid/liquid interface are washed out considerably relative to those at the liquid/solid interface [131,132]. The differences between the liquid/solid and the liquid/liquid interface can be accounted for almost quantitatively by convoluting the water density profile from the Uquid/solid simulation with the width of the surface layer of the mercury density distribution from the liquid/liquid simulation [66]. 

Flow of the liquid past the electrode is found in electrochemical cells where a liquid electrolyte is agitated with a stirrer or by pumping. The character of liquid flow near a solid wall depends on the flow velocity v, on the characteristic length L of the solid, and on the kinematic viscosity (which is the ratio of the usual rheological viscosity q and the liquid s density p). A convenient criterion is the dimensionless parameter Re = vLN, called the Reynolds number. The flow is laminar when this number is smaller than some critical value (which is about 10 for rough surfaces and about 10 for smooth surfaces) in this case the liquid moves in the form of layers parallel to the surface. At high Reynolds numbers (high flow velocities) the motion becomes turbulent and eddies develop at random in the flow. We shall only be concerned with laminar flow of the liquid. 

In many industrial applications, the concern is for both smooth and rough surfaces. The analyses of 9 on rough surfaces will be somewhat complicated than those on smooth surfaces. The liquid drop on a rough surface (Figure 5.4) may show the real 9 (solid line) or some lower value (apparent dotted line), dependent on the orientation of the drop. 

However, no matter how rough the surface, the forces will be the same as those that exist between a solid and a liquid. The surface roughness may show contact angle hysteresis if one makes the drop move, but this will arise from other parameters (e.g., wetting and dewetting). Further, in practice, the surface roughness is not easy to define. A fractal approach has been used to achieve a better understanding (Feder, 1988 Birdi, 1993). 

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