In one aspect, the present disclosure provides a brush for applying a formulation, the brush having a core having an outer surface and a longitudinal axis, a plurality of bristle rings protruding from the core and spaced apart along the longitudinal axis, each bristle ring having at least 6 bristles spaced radially apart around the outer surface of the core, and a high density zone that covers at least a portion of the outer surface of the core, the high density zone having an equivalent 360 degree linear bristle density of 13 to 31 whole bristles per 0.5 mm of length along the outer surface of the core measured along the longitudinal axis, and a surface bristle density of 3 to 5 bristles per square millimeter of area of the outer surface of the core.