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This ingredient gets a bad rep because it is irritating and drying due to its astringent property. Astringents draw out natural oils in tissue to constrict pores and dry out your skin.

However, alcohol denat. is not all that bad.

Due to its low molecular weight, alcohol denat. tends to evaporate quickly. One study on pig skin found half of applied alcohol evaporated in 10 seconds and less than 3% stayed on skin.

This also helps other ingredients become better absorbed upon application.

Studies are conflicted about whether this ingredient causes skin dehydration. One study from 2005 found adding emollients to propanol-based sanitizer decreased skin dryness and irritation. Another study found irritation only occurs if your skin is already damaged.

Small amounts of alcohol are generally tolerated by oily skin or people who live in humid environments.

The rule of thumb is this ingredient will probably not affect your skin much if it is near the end of an ingredients list.

One thing to note:
People with ALDH2 (aldehyde dehydrogenase 2) deficiency may experience skin irritation from continued alcohol use. About 8% of the world's population have this deficiency.

The Cosmetic Ingredient Review Expert Panel has determined denatured alcohols to be safe for use in concentrations between 0.05% and 12% (depending on which denaturant is used).

Also...

This ingredient has antimicrobial and solvent properties.

The antimicrobial property helps preserve products and increase their shelf life. As a solvent, it helps dissolve other ingredients.

Look for formulas that contain glycerin, hyaluronic acid, or panthenol if you want to offset any drying effect.

This ingredient will trip away your skin's natural oils/lipids that help it lock in moisture. This can worsen dryness, trigger eczema flare-ups, and aggravate rosacea.

Be sure to patch test any product with this ingredient if you have dry or sensitive skin, eczema, or rosacea.

The Cosmetic Ingredient Review (CIR) Expert Panel evaluated it (along with 22 other acryloyldimethyltaurate polymers) and concluded it's:

Due to its large molecular size, it sits on the surface of skin rather than penetrating it.

Your skin makes glycerin on its own (mostly from sebaceous oil breakdown) and shuttles it to your outermost layer of skin, or your epidermis, via aquaporin-3.

Aquaporin-3 is a transporter that is essential for normal skin hydration, elasticity, and repair. Interestingly, mice lacking in AQP3 have dry and less elastic skin that can be fully corrected with glycerin.

This ingredient is non-irritating, plays well with almost every ingredient, and works across all skin types. Typical use is anywhere between 3-10% but can go up to 79% in some leave-on products.

Just know very high concentrations (>40%) can feel tacky in low humidity.

Glycerin is the name for this ingredient in American English. British English uses Glycerol/Glycerine.