< Biomod | 2012 | Titech/Nano-Jugglers
Physical principles for simulations
- We confirm the movement of rocket on 2D plots in simulation.
- We assumed that movement of biomolecular rocket is affected by following four forces and dynamics in simulation.
1. Driving forces from Bubble detachment
Calculation for Speed
- Bubbles detachment helps Biomolecular Rocket go straightforward.
- The Biomolecular Rocket is accelerated by a single bubble detachment every Δtd seconds .
- Bubbles detachments occur when fixed time Δtd passed.
- We defined radius changes of bubbles with time as following formula.
- Δtd is defined as the time which is required bubbles to reach its detachment radius Rd.
- We defined velocity vi produced by single detachment and Δtd as following formula.
- Where bubbles generation occured is determined randomly on the hemisphere surface with catalytic engine.
- We defined angle θ as bubbles detachment direction.
- θ is determined by uniformed numbers.
- Bubbles detachment supply the Biomolecular Rocket velocity of opposite direciton.
2. Fluid resistance
- Fluid resistance decreases speed of the Biomolecular Rocket.
- Fluid resistance depends on the velocity of the Biomolecular Rocket and viscosity of solution.
- Resistance is defined as
- Therefore, acceleration of the Biomolecular Rocket is
3. Translational Brownian displacement
- Translational Brownian movement prevents Biomolecular Rocket from going straight forward.
- This is because body of the Biomolecular Rocket is so small and smaller particles can't be controlled under Brownian Movement.
- Translational displacement by Brownian movement is described as
4. Rotatory Brownian changes
- Rotatory Brownian movement decreases the directional controllability of Biomolecular Rocket.
- Movement of Biomolecular Rocket is also much influenced by Rotatory Brownian Movement
- Rotatory changes by Brownian movement is described as