Answer: Sticky film and dripping residue usually indicates an insect infestation, typically either aphids or scale. Check your plant for small, soft bodied pests sucking on the new growth tips (aphids) or for scale insects which are often flat disks stuck to the leaves or stems (check top and bottom of foliage.)
Aphids can be treated with commercially formulated insecticidal soap, or can sometimes be rinsed off with a spray of tepid water or gently removed by hand. Take care that your plants are not overfertilized and that they are receiving enough sunlight, as weak growth tends to be more susceptible to aphids.
Scale can be carefully (and tediously) removed with the finger nail and/or sprayed with insecticidal soap or horticultural oil per the label directions. Scale can be difficult to control so it may be worthwhile to isolate that plant while you are trying to treat it.
Always read and follow all of the directions for application of soap or oil and reapply as indicated. Cover all portions of the plant from top to bottom when you spray, including the stems and undersides of all the leaves.
I hope this helps you trouble shoot.
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