Flexible orifice for wet wipes dispenser

A wet wipes dispenser having a flexible orifice for pop-up style dispensing comprising:

• a rigid port positioned adjacent an end portion of the dispenser;
• the rigid port surrounding a flexible, rubber-like sheet having a top surface and a bottom surface;
• a continuous slit extending across the top and bottom surfaces of the sheet and through which a wet wipe can pass from the bottom surface to the top surface or from the top surface to the bottom surface;
• and
• a first portion of the sheet having a first thickness and a second portion of the sheet located between the continuous slit and the first portion having a second thickness which is greater than or less than the first thickness such that a hinge is formed where the first portion joins the second portion and wherein the first and second Thicknesses are at least about 20 mils.