Abstract: A hair-penetrating shield 220 comprises a tooth array having top 280 and bottom 290 surfaces. In some embodiments, for a majority of the teeth, a cross section of each tooth (for example, triangular in shape) has an asymmetric width profile such that the tooth cross section, on average, is narrower near the top of the tooth and wider near the bottom of the tooth. In some embodiments, a ratio between: i) a first average tooth width describing the average tooth width below the top-bottom midpoint; and ii) a second average tooth width describing the average tooth width above the top-bottom midpoint is at least 1.2, or at least 1.6. In some embodiments, a non-viscous hair-coloring agent is dispensed as a mist over the top of the surface of the shield so as to color roots of hair passing through the spaces between the teeth of the user's hair. In some embodiments, closely-spaced teeth of the hair penetrating shield protect the user's scalp from the non-viscous hair-coloring agent.