Pouches for dispensing products

1. A package comprising:

a first panel;

a second panel, wherein the first and second panels are sealed to each other to form a pouch, wherein the pouch includes a main section and a channel section; and

a product disposed within the pouch, wherein the product is capable of flowing from the main section through the channel section to a tip of the pouch;

wherein the pouch includes a valve that has a curve extending transversely across the channel section, wherein the curve is configured such that, when the product flows through the curve, the product flows by a convex side of the first panel in the curve and a concave side of the second panel in the curve;

wherein a portion of the first panel that includes the curve is less rigid than a portion of the second panel that includes the curve.

2. The package of claim 1 , wherein an initiation pressure of the valve is in a range from about 0.4 psi (2.8 kPa) to about 3.4 psi (23.4 kPa).

3. The package of claim 1 , wherein an initiation pressure of the valve is in a range from about 0.9 psi (6.2 kPa) to about 1.6 psi (11.0 kPa).

4. The package of claim 1 , wherein the portion of the second panel that includes the curve has a valve deflection constant defined as:

C

V

⁢

D

=

E

⁢

t

D

where CVD is the valve deflection constant, E is a modulus of elasticity of the portion of the second panel, t is a thickness of the portion of the second panel, and D is a diameter of the concave side of the second panel in the curve when the pouch is in a resting state.

5. The package of claim 4 , wherein the valve deflection constant is in a range from about 6.75 kpsi (46.5 MPa) to about 13.5 kpsi (92.4 MPa).

6. The package of claim 4 , wherein the valve deflection constant is in a range from about 8.5 kpsi (58.6 MPa) to about 12.9 kpsi (88.9 MPa).

7. The package of claim 4 , wherein the portion of the first panel that includes the curve has a valve deflection constant that is less than or equal to at least one of 40% of the valve deflection constant of the portion of the second panel, 20% of the valve deflection constant of the portion of the second panel, or 10% of the valve deflection constant of the portion of the second panel.

8. The package of claim 4 , wherein the diameter of the concave side of the second panel in the curve is a diameter of a most acute curvature of the concave side of the second panel in the curve.

9. The package of claim 1 , wherein the first panel includes a first film and the second panel includes a second film.

10. The package of claim 9 , wherein a rigidity of the second film is greater than a rigidity of the first film.

11. The package of claim 9 , wherein the second panel further includes a stiffening layer adhered to the second film, and wherein the portion of the second panel in the curve includes the stiffening layer.

12. The package of claim 11 , wherein a rigidity of the second film is substantially the same as a rigidity of the first film.

13. The package of claim 11 , wherein the first film and the second film are formed from a single sheet of film that is folded between the first and second films.

14. The package of claim 11 , wherein the portion of the second panel that includes the curve has a valve deflection constant defined as:

C

V

⁢

D

=

E

⁢

t

D

where CVD is the valve deflection constant, E is a modulus of elasticity of the stiffening layer, t is a thickness of the portion of the stiffening layer, and D is a diameter of the concave side of the stiffening layer in the curve when the pouch is in a resting state.

15. The package of claim 11 , wherein a ratio of a product of a thickness and a modulus of elasticity of the second film to a product of a thickness and a modulus of elasticity of the stiffening layer is less than or equal to about 1:4.

16. The package of claim 1 , further comprising:

a frangible seal between the first and second panels located such that the valve is between the tip of the package and the frangible seal, wherein, before the frangible seal is broken, the frangible seal is configured to deter flow of the product to the valve.

17. A method of dispensing a product from a package, wherein the package includes a first panel and a second panel, wherein the first and second panels are sealed to each other to form a pouch, wherein the pouch includes a main section and a channel section, and wherein a product disposed within the main section of the pouch, the method comprising:

applying an external force to the main section of the pouch, wherein applying the external force causes:

the product to flow from the main section to a valve in the channel section, wherein the valve has a curve extending transversely across the channel section,

the curve in the valve to straighten at least partially from a shape of the curve in a resting state of the pouch,

the product to flow through the curve by a convex side of the first panel in the curve and a concave side of the second panel in the curve, and

the product to be dispensed from a tip of the pouch

wherein a portion of the first panel that includes the curve is less rigid than a portion of the second panel that includes the curve; and

reducing the external force applied to the main section of the pouch, wherein reducing the external force causes the valve to return to the shape of the curve in a resting state of the pouch to deter flow of the product through the valve.

18. The method of claim 17 , wherein the applying the external force to the main section of the pouch comprises manually applying the external force to the main section of the pouch.

19. The method of claim 17 , wherein applying the external force further causes a break of a frangible seal in the pouch, and wherein, before the frangible seal is broken, the frangible seal is between the first and second panels and located such that the valve is between the tip of the pouch and the frangible seal.

20. The method of claim 17 , further comprising:

opening the tip of the pouch before applying the external force.