Interdisciplinary Applied Mathematics

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FIGURE 10.19. Schematic of the surface force apparatus (SFA).

the treated cases compared to the untreated ones, but at higher pressure drop he observed the opposite. Interestingly, at velocities past the onset of turbulence there was no discerible difference in flowrate. Overall, Schnell’s experiments stood the test of time and are considered the first to prove convincingly that a boundary slip occurs for hydrophobic (i.e., water-repellent) surfaces. This result agrees with the physical intuition, i.e., that boundary slip is larger in hydrophobic surfaces, since the attractive forces between the liquid and the solid surface are less than for hydrophilic surfaces, and thus the solid-liquid interface friction is reduced. At about the same time, it was established by (Debye and Cleland, 1959) that boundary slip can also occur in liquid hydrocarbons for flow through porous Vycor glass.

In the last few decades there has been a renewed interest in determining the validity of the no-slip boundary condition for liquids due to the interest in polymers and other complex fluids but primarily due to microfluidic applications. In (Chuarev et al., 1984), both water and mercury were tested in flow through glass capillaries of diameter less than 10 p,m treated with trimethylchlorosilane. It was found that for water with contact angles less than    70°    the    no-slip    condition    was    valid,    but    for    higher    hydrophobicity

increased flowrates were obtained corresponding to a slip length between 30 and 200 nm according to Navier’s formula of equation (10.5). For mercury, a contact angle of more than 130° also led to boundary slip. These results suffer, however, from the limitation in determining the capillary diameter precisely as well as in controlling the homogeneity of the internal capillary surface.

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