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Revision as of 04:17, 28 October 2012

Simulation Models

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

1.1. Calculation for Speed

Bubbles detachment helps Biomolecular Rocket go straightforward.

The Biomolecular Rocket is accelerated by a single bubble detachment every Δt_d seconds .

Bubbles detachments occur when fixed time Δt_d passed.

We defined radius changes of bubbles with time as following formula.

Δt_d is defined as the time which is required bubbles to reach its detachment radius R_d.

We defined velocity v_i produced by single detachment and Δt_d as following formula.

1.2. Directional Calculation

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

>back to Results 2.2. Numerical estimation of the speed of the Biomolecular Rocket

>back to Results 3.3 Directional control of Biomolecular Rocket by the photo-switchable DNA system

References

• J. G. Gibbs and Y.-P. Zhao (2009) Autonomously motile catalytic nanomotors by bubble propulsion. University of Georgia, Athens, Georgia 30602, USA, American Institute of Physics.
• V. A. KiriUov and V. P. Patskov (1979) SOME REGULARITIES OF BUBBLE GROWTH UNDER CHEMICAL REACTION. Institute of Catalysis, Novosibirsk, USSR, React. Kinet. Catal. Lett., Vol. 11, No. 1, 15-19 (1979)