What came to known as the Second US Civil War Battle of Bull Run opened on August 26, 1862. Union troop strength was being reinforced so most sources place the Union army at 75,000 men. The South had 50,000 troops.
The US Civil War Battle of Shiloh in April of 1862 was a Union victory. The two day battle saw each side with advantages. For the Union, the advantage was that reinforcements were close by and on the way. To aid US Grant at Pittsburg Landing. The reinforcements provided the Union with a troop advantage that carried the victory on the second day of the battle. The element of surprise was the significant advantage for the Confederates. Their attack on the Union army was not expected and the army was unprepared to properly defend their position.
The North - a big tactical advantage when it came to troop movement.
On the first day of the US Civil War Battle of Shiloh, the Confederates led by Albert S. Johnston took the Union forces by surprise and gained all the momentum. They pushed the Union forces to a point where the river was their rear guard. One the second day of the battle, however, fresh troops under the command of Union General Buell, gave the Union a tremendous troop advantage and their assault on the Rebels reversed the momentum, forcing the Southern army to retreat.
Th closest major battle could be Shiloh, however, the Confederate forces under P.T. Beauregard were clearly outnumbered by the reinforcements Grant received the night before the second day of battle. As an aside, if Robert E. Lee' s Army of Northern Virginia ever faced either Sherman or Grant with a two to one advantage, or even a three to two advantage in troop strength it's clear that Lee would be the victor.
The Battle of the Wilderness began in the first few days of May 1864. It was important in that it was the first time that General Grant would face General Lee. US Grant came will armed. His army numbered 100,000 troops and Lee had 60,000 troops. This battle became a Confederate victory.
Volunteers they had many American volunteers on each side which gave the south a troop number advantage
The Civil War
About 4 million men participated in the Civil War.
One of the reasons that the US Civil War Battle of Chancellorsville is so often written about was the imbalance between the armies of Lee and Hooker. Lee was victorious despite being outnumbered by a three to one ratio.
During the Civil War, the telegraph took on tremendous importance. The south made the first use of the telegraph to rush troops to battle. Later, General McClelland used a telegraph to send information from a balloon concerning troop positions during a battle. Of course such usage would continue.
battle of Princeton
This question requires a subjective answer. With that said, the Battle of Shiloh in April of 1862 is a good example of troop concentration. In this case, Confederate President Jefferson Davis helped coordinate with General Albert Sidney Johnston a focus of troops bent on attacking Union forces near Pittsburg Landing in Tennessee. Using rail transportation and marching, Johnston was able to amass a significant force to attack the army led by General US Grant.The first such concentration occurred at the First Battle of Bull Run.