Final answer:
The sphincter closely associated with the larynx is the upper esophageal sphincter, which is continuous with the inferior pharyngeal constrictor muscle. It allows food to pass from the pharynx into the esophagus during swallowing and prevents it from moving back into the pharynx.
Step-by-step explanation:
The sphincter composed largely of a muscle that is closely associated with the larynx is the upper esophageal sphincter. This sphincter, which is continuous with the inferior pharyngeal constrictor, controls the movement of food from the pharynx into the esophagus. It is triggered to relax and open by the act of swallowing, which allows a bolus of food to enter the esophagus from the pharynx.
The upper esophageal sphincter then closes again to prevent food from moving back into the pharynx. During the swallowing process, the pharyngeal constrictor muscles contract to move the bolus through the oropharynx and laryngopharynx, and the relaxation of the upper esophageal sphincter allows food to enter the esophagus. Note that sphincters are anatomical sphincters, which can be composed of smooth or skeletal muscle, and serve to restrict flow when contracted, essentially acting as valves within the gastrointestinal tract.