The Spartan and Chain of the Knife Drills are a skillset development series of ever increasing difficulties when facing an armed opponent.
Training partners must assume the Trainer/Trainee roles.
The Spartan Drill is usually practiced first and involves the attacker (trainer) delivering a strike, usually from one of the 12 angles of attack. The good guy (trainee) reponds with a hacking block. **It must be noted here that this must not be a slicing or slashing type block, but an agressive, offensive, bone striking, nerve deadening, hacking attack. (
Simulated to some extent during training of course 
) The attacker will drop his knife and the good guy will continue to a combat finish. Repeat this entire sequence multiple times from different angles and using different combative technics. Make sure you use a mixture of lethal and less-than-lethal combative finishes.
The Chain of the Knife Drill is used next to increase the degree of difficuty and to bring in certain realities of knife fighting.
They Don't Always Drop Their Knife! In the previous drill our opponent dropped their knife from our devastating impact and we could move in without having to be as concerned as we were when the attacker was armed. Now though, in the Chain of the Knife Drill the opponent does not drop the knife and we cannot just rush in for the finish as we had previously done in the Spartan Drill. The enemy is still in possession of a deadly weapon.
We now have to grab and control this weapon bearing limb, we must begin to diminish this enemies' capacity to continue the attack, etc...
To plan for this possibility (probability?) we practice in the following steps:
Step 1. The attacker (trainer) begins as before (Spartan Drill), but this time does not drop the knife, the good guy (trainee) grabs the weapon bearing limb and continues to diminish and disarm the attacker to a combat finish.
Step 2. The trainer attacks again, does not drop the knife, trainee grabs the weapon bearing limb and begins his attempt to dimish and disarm the attacker, but the trainer provides a first level of obstruction or resistance, i.e., - with free hand throws a punch. The good guy must deal with this while remembering and dealing with the fact that the opponent is still armed and then continues to a combat finish.
Step 3. Continue this pattern, adding one or two more levels of obstruction. These obstructions or more appropriately the manner in which one deals with them, form the links in the chain. Hence the name Chain of the Knife.
Hope this helps!