The tear film that protects the cornea is composed of three layers. These are an inner mucus layer, a middle watery layer and an outer oily layer. Tears flow from the various tear producing glands over the eye and exit through tear ducts located at the inner corner of the eye that drain into the nasal cavity.
Eye mucous is composed of tears that have lost some of the watery component resulting in a tick slippery substance. It can result from increased production of tears or decreased drainage.
Increased production is usually caused by irritation. Examples that can affect one eye only include eyelashes touching the cornea, facial hair that touches the cornea (common in wire and long haired breeds) and entropion (eyelids rolled inward).
Decreased drainage can be caused by blockage of a tear duct and irregular eyelid conformation.
Deep set eyes tend to accumulate mucus because it has time to dehydrate before draining. This combined with increased tear production produces increased mucous in one eye.
Unilateral damage to the innervation of the eye and eyelids can cause increased mucus accumulations on one side only.
If your dog has a problem with mucus accumulation in one eye only and he has not been looked at for this problem, a vet visit could help determine the cause and treatment. If he is squinting, or if the pupil is either constricted or dilated, he should be checked as soon as practical to diagnose and treat the problem.
Let me know if you have follow up questions.
Artificial tears are safe. they will sooth minor irritation, but will not treat more serious problems. They can be useful for minor irritation that clears within a day or two.
Antibiotic eye ointments help if the problem is an infection, but the discharge should be purulent (pus) and not mucus. Often they help sooth irritation because they are in an ointment base rather than that they contain antibiotics. Some contain steroids and help with allergic problems (affect both eyes), but can make some conditions worse (scratches, fungal infections).
You need to know why the eye is producing more mucous than normal in order to determine a specific treatment. If an eyelash is rubbing, it needs to be removed. Ointments might help temporarily, but will not fix. Viral, bacterial and fungal infections often affect both eyes and produce a pus type discharge usually with excessive tearing.