2. As shown in Figure 1, in the rectangular prism, $A B$, $D B_{1}$, $A_{1} D_{1}$, and $C C_{1}$ are pairwise skew lines. Now, draw a pair of intersecting lines $l_{1}$ and $l_{2}$, such that $l_{1}$ intersects both $A B$ and $D B_{1}$, and $l_{2}$ intersects both $A_{1} D_{1}$ and $C C_{1}$. The number of such pairs of intersecting lines is ( ).
(A) 0 pairs
(B) 1 pair
(C) more than 1 but a finite number of pairs
(D) infinitely many pairs
2. (D).

Solution 1: As shown in Figure 12, draw a plane $\alpha$ through $AB$ intersecting $A_{1} D_{1}$ at $E$, $C C_{1}$ at $F$, and $D B_{1}$ at $P$ (think about how to accurately locate point $P$), and connect $E F$ as $l_{2}$. Then $E F$, point $P$, and $AB$ are all on plane $\alpha$. In $\alpha$, through $P$, infinitely many lines $P Q$ can be drawn intersecting $E F$ at $G$ and $AB$ at $Q$, denoted as $l_{1}$. Therefore, there are infinitely many pairs of such intersecting lines.

Solution 2: As shown in Figure 13, connect the diagonal $B D_{1}$, which must intersect $B_{1} D$. Denote the intersection point as $O$, then $B D_{1}$ intersects $AB$ at $B$ and $A_{1} D_{1}$ at $D_{1}$. Denote $B D_{1}$ as $l_{1}$. Then, take any point $M$ on $C C_{1}$ and connect $D_{1} M$ (or $BM$, $OM$), denoted as $l_{2}$. Thus, there are infinitely many such $l_{2}$. Therefore, there are infinitely many pairs of intersecting lines that satisfy the conditions.