This is not exactly an answer to your question, but hopefully it explains how the process works. Since you didn't mention what hardware you are running for AD conversion, maybe this is the best that can be done:
With audio hardware, which faces the same problem, the solution comes from the hardware and the drivers working together: whenever the hardware has filled up enough of the buffer it signals the driver (via an interrupt or some similar mechanism). In some cases, it's also possible that the driver polls the hardware or something like that, but that's a less efficient solution, and I'm not sure anyone does it that way anymore (maybe on cheaper hardware?). From there, the driver process may call right into the end-user process, or it may simply mark the relevant end-user process as "runnable". Either way, control needs to be transferred to the end user process.
For that to happen, the end user process must be running at a higher priority than anything else occupying the CPUs at that moment. To guarantee that your process will always be first in the queue, you can run it at a high priority, with the appropriate permissions, you can even run in very high priorities.
The time it takes for the top priority process to go from runnable to running is sometimes called the "latency" of the OS, though I am sure there's a more specific technical term. The latency of Linux is on the order of 1 ms, but since it's not a "hard" real-time OS, this is not a guarantee. If this is too long to handle your chunks of data, you may have to buffer some of it in your driver.