Many viral infections, including the COVID-19 infection, are associated with the hindrance of blood oxygenation due to the accumulation of fluid, inflammatory cells, and cell debris in the lung alveoli. This condition is similar to Acute Respiratory Distress Syndrome (ARDS). Mechanical positive-pressure ventilation is often used to treat this condition, even though it might collapse pulmonary capillaries, trapping red blood cells and lowering the lung's functional capillary density. We posit that the hyperosmotic-hyperoncotic infusion should be explored as a supportive treatment for ARDS. As a first step in verifying the feasibility of this ARDS treatment, we model the dynamics of alveolar fluid extraction by osmotic effects. These are induced by increasing blood plasma osmotic pressure in response to the increase of blood NaCl concentration. Our analysis of fluid drainage from a plasma-filled pulmonary alveolus, in response to the intravenous infusion of 100 ml of 1.28 molar NaCl solution, shows that alveoli empty of fluid in approximately 15 minutes. These modeling results are in accordance with available experimental and clinical data; no new data were collected. They are used to calculate the temporal change of blood oxygenation, as oxygen diffusion hindrance decreases upon absorption of the alveolar fluid into the pulmonary circulation. Our study suggests the extraordinary speed with which beneficial effects of the proposed ARDS treatment are obtained and highlight its practicality, cost-efficiency, and avoidance of side effects of mechanical origin.