Osmotic-driven plant movements are widely recognized as impressive examples of energy efficiency and low power consumption. These aspects motivate the interest in developing an original biomimetic concept of new actuators based on the osmotic principle exploited by plants. This study takes a preliminary step in this direction, by modelling the dynamic behaviour of two exemplificative yet relevant implementations of an osmotic actuator concept. In more detail, the considered implementations differ from each other in the way actuation energy storage is achieved (through a piston displacement in the former case, through membrane bulging in the latter). The dynamic problem is analytically solved for both cases; scaling laws for the actuation figures of merit (namely characteristic time, maximum force, maximum power, power density, cumulated work and energy density) as a function of model parameters are obtained for the bulging implementation. Starting from such performance indicators, a preliminary dimensioning of the envisaged osmotic actuator is exemplified, based on design targets/constraints (such as characteristic time and/or maximum force). Moreover, model assumptions and limitations are discussed towards effective prototypical development and experimental testing. Nonetheless, this study takes the first step towards the design of new actuators based on the natural osmotic principle, which holds potential for disruptive innovation in many fields, including biorobotics and ICT solutions.