Clarification: My original description was not clear. The directions in the diagrams are NOT horizontal and vertical; they are all in a horizontal plane and gravity is in/out of the page.

I am attempting to model a situation where a block is sliding on a horizontal frictional surface and has an externally-applied force. Traditionally, since the block is moving the friction force vector would be opposite the direction of motion, as shown in the first diagram below. The net force acting on the block would have a component perpendicular to the direction of motion, which would cause perpendicular acceleration.

Experimentally, the mass does not accelerate perpendicular to the direction of motion if the applied force is small. This implies that the friction force also has a component that resists the applied force.

My question is how to model the friction force component that is perpendicular to the direction of motion. What is its limiting magnitude?