  In this note, we revisit the problem of the pressure-driven transport of a
meniscus through a narrow cylindrical capillary or pore. This generic process
finds many applications in science and technology. As it is known that Direct
Numerical Simulations of moving contact line problems are highly demanding in
terms of computational costs, simplified models in the form of ordinary
differential equations offer an interesting alternative to perform a
mathematical optimization of the flow. Blake and De Coninck studied the
pressure-driven transport of a meniscus and identified two major competing
mechanisms. While a hydrophilic surface is favorable to enhance the spontaneous
imbibition into the pore, the friction is known to be significantly reduced on
a hydrophobic surface. Blake and De Coninck showed that, depending on the
applied pressure difference, there exists an optimal wettability that minimizes
the time required to move the meniscus over a certain distance. We revisit this
problem and derive analytical solutions in the limiting cases of negligible
inertia and negligible contact line friction.
