Delta Air Lines faces mounting litigation after one of its planes dumped jet fuel over schools last month in Los Angeles.

Lawyers on Wednesday filed a lawsuit on behalf of three students at local Pioneer High School that accused Delta of negligence. Teachers with the Los Angeles school district sued the airline last month, alleging that three elementary school teachers were doused with jet fuel on their clothes, arms and face during the incident.

The students are suing Delta in part to remind airlines that "safety is not just for people on the plane," Matthew McNicholas, a Los Angeles lawyer representing the students, told CBS MoneyWatch. "You don't want to be dumping jet fuel, but if you have to you want to do it in the safest way possible," he added.

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After a Delta flight heading from Los Angeles to Shanghai on January 14 experienced a compressor stall in its right engine, the pilot executed an emergency landing. During that maneuver, the pilots decided to release jet fuel in mid-air while returning to Los Angeles International Airport, the lawsuits allege. The FAA confirmed that the Delta crew did not inform air traffic control the plane needed to release fuel.

Local fire officials at the time said the fuel created a vapor that caused minor skin and lung irritation to 56 children and adults. The FAA is investigating still the incident.

"Itchy, sick, dizzy and nauseous"

McNicholas and other lawyers representing the students argue that Delta employees didn't control the plane in a way that avoided harm to people on the ground, failed to dump the jet fuel at a safe altitude and didn't tell air traffic control personnel they needed to dump fuel to lighten the weight of the plane.

Students were exposed to toxic jet fuel that penetrated their skin, mouths and noses, and the effects left students feeling "itchy, sick, dizzy, and nauseous," the lawsuit alleges. McNicholas said Delta, the FAA and the LA airport all have rules and procedures for emergency landings, which he believes were likely not followed that day. Air traffic controllers would have re-routed the Delta flight over water if pilots had alerted them about a possible need to dump fuel, he said.

The students' suit asks a judge to order Delta to pay for all damages students incurred, including for medical expenses as well as emotional distress, pain and suffering, but it does not specify a financial amount.

Delta officials said they have been working with LA community leaders on how to best help people who were affected by the fuel dump. After the incident, the company dispatched 13 cleaning crews to help open the schools the next morning.

Delta representatives have also attended town hall meetings to hear residents' concerns and paid for health screenings for people exposed to the fuel. The airline has also created a hotline for residents to report property damage and health effects.

"An open FAA investigation limits what we can say regarding some of the operational specifics of flight 89," Delta told CBS MoneyWatch, "but we will continue to work with the FAA and are focused on actions we can take to support the affected communities."