A tubing interface assembly for a micro-fluidic valve apparatus having a disk surface defining at least one fluid communication port, said tubing interface assembly comprising: a tube apparatus including an elongated tube member having a tube port at a distal end thereof; an elastomeric ferrule device having a body member with a proximal end, a distal end, and a bore extending therethrough, said bore being formed and dimensioned for press-fit sliding receipt of the distal end of the tube member therethrough; a rigid support ring device disposed around a portion of the ferrule body member in a press-fit manner; and a cap member having an exterior surface, an opposed interior surface, and a tube receiving passage extending from said exterior surface to said interior surface thereof, said tube receiving passage being formed and dimensioned for axial sliding receipt of a transverse cross sectional dimension of said tube member therethrough, said cap member further defining a cup-shaped receiving recess extending from said interior surface toward said exterior surface, said cup-shaped receiving recess being formed and dimensioned for axial receipt of at least said proximal end of the ferrule body member such that at least a distal portion of the body member extends distally past the interior surface of the cap member, said cap member comprises a petal-shaped slot extending from said exterior surface to said interior surface, said petal-shaped slot having a ferrule passage on one side and tapering down to said tube receiving passage on an opposite end thereof, said ferrule passage being formed and dimensioned for sliding axial receipt of the ferrule device therethrough; wherein when said cap member is mounted to said valve apparatus in a manner aligning said tube port with said fluid communication port of the disk surface, said elastomeric ferrule device compressively cooperates with the cap member to form a fluid-tight seal between said tube port and said fluid communication port. a tube apparatus including an elongated tube member having a tube port at a distal end thereof; an elastomeric ferrule device having a body member with a proximal end, a distal end, and a bore extending therethrough, said bore being formed and dimensioned for press-fit sliding receipt of the distal end of the tube member therethrough; an elongated tube member having a tube port at a distal end thereof; an elastomeric ferrule device having a body member with a proximal end, a distal end, and a bore extending therethrough, said bore being formed and dimensioned for press-fit sliding receipt of the distal end of the tube member therethrough; a rigid support ring device disposed around a portion of the ferrule body member in a press-fit manner; and a cap member having an exterior surface, an opposed interior surface, and a tube receiving passage extending from said exterior surface to said interior surface thereof, said tube receiving passage being formed and dimensioned for axial sliding receipt of a transverse cross sectional dimension of said tube member therethrough, said cap member further defining a cup-shaped receiving recess extending from said interior surface toward said exterior surface, said cup-shaped receiving recess being formed and dimensioned for axial receipt of at least said proximal end of the ferrule body member such that at least a distal portion of the body member extends distally past the interior surface of the cap member, said cap member comprises a petal-shaped slot extending from said exterior surface to said interior surface, said petal-shaped slot having a ferrule passage on one side and tapering down to said tube receiving passage on an opposite end thereof, said ferrule passage being formed and dimensioned for sliding axial receipt of the ferrule device therethrough; wherein when said cap member is mounted to said valve apparatus in a manner aligning said tube port with said fluid communication port of the disk surface, said elastomeric ferrule device compressively cooperates with the cap member to form a fluid-tight seal between said tube port and said fluid communication port.