Interdisciplinary Applied Mathematics

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No-Slip Case


The slip velocity model discussed above can be employed when the Debye length is thin compared to the channel width. However, when the Debye


length is comparable to the channel width, the slip velocity model may not be accurate.    For    a capillary    slit,    the    velocity    profile    is given    by    the


expression (Patankar and Hu, 1998; Keh and Tseng, 2001)




(18.8)





and Ad    is    the    Debye    length;    see    equation    (7.1).    Integrating    the    velocity


profile (given in equation (18.8)) across the cross-section and using equation (18.9), we get the following expressions for the hydraulic conductance and the electrohydraulic conductance of the *th channel:









Fluidic Channels with Elastic Membranes


In the case of channels with integrated elastic parts in them (e.g., a flexible membrane) a capacitive element needs to be included in the circuit model of the fluidic domain as shown in Figure 18.4. The fluidic capacitor can be modeled as

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