Most small plug-in refrigerators and freezers use a capillary tube as their metering device. It is a narrow copper tube, often a couple of metres long and coiled, whose bore and length are chosen at the factory so that the right amount of refrigerant flows at the design conditions. It has no moving parts and costs very little.
Its limitation is that it cannot adjust. A capillary is sized for a particular refrigerant charge, ambient and load. When conditions drift far from design, for example a very hot kitchen or a freezer packed with warm stock, the flow is no longer ideal. Capillary systems are also critically charged: a few grams too much or too little refrigerant noticeably changes performance.
Capillary tubes can block. Moisture can freeze at the outlet, and debris or sludge from a burnt-out compressor can choke the bore. A partial blockage often shows as a frost spot right where the capillary enters the evaporator and a cabinet that never quite reaches temperature. Replacing the filter drier and capillary together during a major repair is common practice.