A container closure (14, 141, 142, 143, 144, 145, 146) is disclosed. The container closure (14, 141, 142, 143, 144, 145, 146) includes a fluid-drawing member (42, 421, 422, 423, 424, 425, 426) that extends axially away from and is integral with the inner surface (28I, 28I1, 28I2, 28I3, 28I4, 28I5, 28I6) of the end wall (28, 281, 282, 283, 284, 285, 286) of the container closure (14, 141, 142, 143, 144, 145, 146). A container assembly (10, 101, 102, 103, 104, 105, 106) is also disclosed. The container assembly (10, 101, 102, 103, 104, 105, 106) includes the container closure (14, 141, 142, 143, 144, 145, 146) and a container (12, 121, 122, 123, 124, 125, 126) connected to the container closure (14, 141, 142, 143, 144, 145, 146). A method for utilizing the container assembly (10, 101, 102, 103, 104, 105, 106) is also disclosed.