Activated charcoal has appeared in dark-colored café drinks and other consumer products. Its visual effect can make a drink distinctive, but appearance and popularity do not establish that it detoxifies the body. The source itself raises questions about transferring claims from clinical uses to an ordinary latte.
Medical applications depend on a defined situation and professional assessment. A beverage is not an equivalent treatment, and a description of an ingredient's ability to bind substances should not be turned into a broad promise about removing harmful material from a person's diet. No therapeutic benefit is claimed for a charcoal drink here.
There is also a relevant ingredient question for people taking medicines. The UK's Medicines and Healthcare products Regulatory Agency has described charcoal's potential to reduce absorption of other medicines and recommends seeking professional advice when medicines are involved. Read the actual product information and ask a pharmacist or clinician about that concern rather than using a café recipe to decide it. This is an ingredient assessment, not a medical or dosage guide.
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A good question can make a better brew.