Is the viscous white fluid that is discharged from a woman when her husband caresses her (without penetration), and which is not accompanied by a decrease in arousal, or may sometimes be discharged in large quantities, considered madhiy?

If the liquid that is discharged in the manner described is not considered semen and does not necessitate ghusl (definition) (full ritual bath), rather it is madhi (pre-seminal fluid). Madhi only necessitates wudu (ablution) along with washing the area from which it exited and any clothing it touched, because it is impure. This is not considered semen because semen is accompanied by desire and is followed by a feeling of languor, and such is not the case here.