The usual cartridge has resistor elements under the jet holes.
  When the resistor is heated with electric current, the ink is
  heated and forced out the hole. These resistors are usually
   immersed in ink, but if the ink runs out, the resistor is in air
   and will overheat and can be destroyed.
   There is another means of forcing the ink out the jet hole
   which uses crystal elements which bend when a voltage is
   applied. The bending of the crystal can be used to push out
   the ink.         Link to Information About Piezoelectric Printers

   If the cartridge does not print properly, and normal cleaning
   does not correct the problem, it is now possible to buy kits
   which will clean the jets.
   The cartridges can be refilled, but can be messy if care is not
   taken.  Use disposable gloves, have lots of newspaper on the
   area, adhesive tape, scissors, paper tissues and any other items
   recommended.  Link to Refilling Instructions
   People have been refilling black ink cartridges with good grade
  ink bought from a stationary shop. 
   Link to Using Ordinary Black Ink - Find Ink Refilling
 Sometimes a vacuum is used to hold the ink in the container.
 The smallest air leak will cause ink leakage.
  Plain water has been used with satisfactory results if there is
  a foam pad in the cartridge.  It should not cause any harm.

  If the printer is not used for days at a time, it is worthwhile to
  remove the cartridge, put it in a small open container and place
  the container, along with a wad of paper saturated with water
  into a roomy plastic bag and sealing it securely.

       Photos of the business end of a HP inkjet cartridge
       The plate with the jet holes has been removed

More photos taken with a video camera
through a microscope
There was nothing which looked
like heating resistors.
Along the edge of the opening
into the interior of the cartridge there
was a strip of bright metal, whereas the
rest of the surface was coated with varnish.
The connecting strips ended with a small
semicircular raised section which could
have been the position of the jet.

 
 
 
 

                         An idea for an easy to refill ink cartridge