Pushing fluid through microfluidics

yes. knowing the surface tension of the fluid and its contact angle with the channel walls, you can select a channel width that does not support two-phase flow, where bubbles and fluid can pass by one another and get mixed up in the channel.

For example, the tube diameter on a turkey baster's tip is made small enough so that air cannot flow up in the tube while juice flows down, which would cause the baster to spill out its contents.

The tradeoff between the effects of capillarity and inertial or gravitational effects is what sets the break point between the baster holding its contents and spilling them. The nondimensional similitude parameter that establishes this is called either the Froude number or the Weber number, I cannot remember which.

A cheap way to realize low pressure differences (and a method that is nearly unbeatable for smoothness) is gravity. Fill everything with liquid, run input and outlet tubes to two beakers/buckets/etc, with the one on the input side be higher than the output. Approximately 1 mbar per centimeter height difference for water at room temp.