When oil emerges from a water-wet constriction into a water-filled pore, the interfacial forces are such that a leading portion of the oil may separate into a droplet (snap off). Theory indicates that for a given shape of constriction, there is a minimum size to the protruding portion of the oil that permits snap-off. If the oil/solid contact angle is zero and if the constriction has the shape of the throat of a tore (a doughnut hole), the oil must protrude for a distance of at least seven times the throat radius before snap-off can occur. Experiments were performed in approximately toric constrictions constructed of glass. Liquids used were a dyed mineral oil and a water-ethanol mixture adjusted to the same density as the mineral oil to avoid gravitational effects. Within the limitations imposed by visual distortions through the glass and the liquids, the observations appear to be in accord with the theoretical predictions. Introduction: Production of oil from a reservoir involves flow of oil through a porous medium that also contains water. Because of the small size of the pores in the reservoir rock or sand capillary forces at the oil-water interface are of considerable importance in determining the nature of the flow through the pores. This report deals with one aspect of such pores. This report deals with one aspect of such How, determining the conditions that must be met in order that the oil emerging from a water-wet constriction will separate (snap off or pinch off) into a droplet in the larger parts of the channel. By applying the fundamental equation of capillarity to oil flowing through certain geometrically describable water-wet constrictions we can calculate the minimum size of the protruding body of oil that will permit snap-off of the oil to give a separate droplet. The theoretical treatment can be checked, at least semiquantitatively, by observations on dyed mineral oil flowing through glass pores previously filled with a water-alcohol mixture. This mixture should be adjusted to give be same density as that of the mineral oil in order to eliminate gravitational effects, which can be large relative to capillary effects in constrictions having an internal diameter of about 2 mm.