While often the party will do this to themselves, most bits of Player advice will recommend against it, instead suggesting that players stick together. In general this is a good thing for them. By being together, the GM can more easily focus on them as a group, and thus everyone gets more "screen time" as it were by sticking together.
That being said though, sometimes you need to split the party up. Maybe one of them got kidnapped and the others have to save them. Maybe the only way for them to stop the current nefarious plan is to split up into smaller groups and cover the city faster. It doesn't really matter why it is happening, the point is that it is happening.
From a story perspective this is actually a common thing. Often in dramatic situations part of the drama comes solely from the fact that the group is split up. Johnny Storm needs to get past Dr. Doom on his own this time, or an evil wizard has scattered the heroes to their own various nightmare worlds that need to be handled before they can regroup together. Gameplay wise though, splitting a party up becomes a juggling act and is one of the fastest ways to find out just how good your time management skills actually are.
Time management, by the way, is exactly the way to handle this sort of a situation. You need to know what is going on with the players, and you need to keep it going from player to player. Don't focus on one character's situation for too long, or you will lose the other players. Keep an eye on the other players at the table, are they starting to look bored? Looking for something else to do? That means it is a time to switch. You don't even have to wait for a good moment, since you are cutting back and forth. In fact, using a Cliff hanger type cut can work wonders, hooking the one player in while simultaneously moving to the next player to get them involved with what is going on with them.
As you go along, you need to keep this up. Jumping from player to player. Don't stick to a set order, balance the tension in scenes. Leaving someone on a low note is almost as bad as leaving someone at an incredibly tense moment. So keep moving, if a player ever needs time to think, it is a good time to change. It both gives them more time to think, while also not making other people wait while they do just that. Ultimately though, it takes practice to get good at this. It really is a juggling act that you will get better at with experience. Quickly becoming a skill that while seldom employed will manage to keep people entertained even when they are simply an audience to another character's actions.
Remember the important thing is to have fun, and to make sure players waiting aren't bored. Don't be afraid to cut away during a tense moment and leave someone hanging for a few minutes while you handle the rest of the group. But don't leave anyone hanging on a tense moment for longer than you have to either.