Shifting blocks to the right to remove empty spaces - C#

In the block matching game that I am creating I currently have the blocks falling upon elimination and because of this, there's a lot of leftover blocks and some empty spaces that could be filled with blocks and cause more matches to be available. How can I get the game to shift specific blocks over to the right in order to fill those spaces? I'll post the code I have currently that drops them down, now I just need them to shift to the right. I've also attached a screenshot of what's happening in the grid so that you can see the openings that the game is creating

 public void applyGravity() {
             // Go through every column
             for (int y = 0; y < 10; y++) {
                 // Track empty positions in the colum
                 int lastEmptyPos = 0; 
                     // Go through every row, starting from the bottom
                         for (int x = 0; x < 10; x++) {
                         // Check to see that the current block is not empty
                         if (grid[x, y].renderer.material.mainTexture != null) {
                                // Check for gaps
                             if (lastEmptyPos < x) {
                                 // Drop the blocks down
                                 grid[lastEmptyPos, y].renderer.material.mainTexture = grid[x, y].renderer.material.mainTexture;
                                 grid[x, y].renderer.material.mainTexture = null;
                                }
                     // Since we have a block (regardless if we moved it), the tower must be +1 higher
                     lastEmptyPos++;
             }
         }
     }
 }