Co- and counter-current spontaneous imbibition into groups of capillary tubes with lateral connections permitting cross-flow

Abstract

A model for co- and counter-current imbibition through independent capillaries has already been developed and experiments conducted to verify the theory [E. Unsal, G. Mason, N.R. Morrow, D.W. Ruth, J. Colloid Interface Sci. 306 (2007) 105]. In this paper, the work is extended to capillaries which are connected laterally and in which cross-flow can take place. The fundamental pore geometry is a rod in an angled round-bottomed slot with a gap between the rod and a capping glass plate. The surfaces of the slot, rod and plate form capillaries and interconnecting passages which have non-axisymmetric cross-sections. Depending on the gap size either (i) a large single meniscus, (ii) two menisci one on each side of the rod, or (iii) three menisci, one between the rod and the glass additional to the ones on each side can be formed. A viscous refined oil was applied to one end of the capillaries and co-current and counter-current spontaneous imbibition experiments were performed. The opposite end was left open to the atmosphere for co-current experiments. When the gap between the rod and the plate was large, the imbibing oil advanced into the tubes with the meniscus in the largest capillary always lagging behind the two menisci in the other two smaller capillaries. For counter-current imbibition experiments the open end was sealed and connected to a sensitive pressure transducer. In some experiments, the oil imbibed into the smaller capillaries and expelled air as a series of bubbles from the end of the largest capillary. In other experiments, the oil was allowed to imbibe part way into the tubes before counter-current imbibition was started. The meniscus curvatures of the capillaries have been calculated using the Mayer and Stowe–Princen method for different cell slot angles and gap sizes using a value of zero for the contact angle. These values have been compared with actual values by measuring the capillary rise in the tubes; agreement was very close. A model for co-current and counter-current imbibition has also been developed. The significance of this model is that some hydraulic/capillary properties are common for both co-current and counter-current imbibition. The experiments give an illustration of behavior expected in a real porous material and verify the importance of the ‘perfect cross-flow’ modification to the ‘bundle of parallel tubes’ model.