Described are absorbent members useful in the containment of body liquids such as urine. These absorbent members comprise at least one osmotic absorbent (preferably a hydrogel-forming absorbent polymer) and a high surface area material, and have a high capillary suction capacity. For purposes of the present disclosure, capillary suction capacity is measured in terms of the member's ability to uptake liquid at high capillary heights, which are generally encountered when the member is positioned in an absorbent article. In particular, capillary suction capacity is measured in terms of a member's capillary sorption absorbent capacity, which is measured in accordance with the Capillary Sorption method described in the Test Methods section.