Open and Confined Systems

2 The Lucas-Washburn-Rideal (LWR) Law for Confined Cylindrical Channels 

The study of the dynamics of capillary flows started as early as the 1910s with the developments made by Bell, Cameron, Lucas, Washburn and Rideal 

Rectangular V-groove Trapezoidal Suspended Multi Multi 

The reasoning behind (1.23) is straightforward let us consider the two forces acting on the liquid, i.e. the capillary force f and the drag force 

Upon substitution of V = dzidt, and integration, one obtains (23). This expression, valid for a cylinder, has been frequently used for other shapes of channels by replacing the radius R by the hydraulic radius R The hydraulic radius is the half of the hydraulic diameter that is defined Djj = 4 Sf Jp where is the cross-sectional area, and p the perimeter. In our case, the hydraulic diameter is simply defined by 

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