Litlle excerpt on the professional take on it..
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Cultivation of microalgae
Microalgae biomass production is based on the simple scheme:
CO2 + H2O + nutrients + light energy → biomass + O2
Challanges:
Algae cultivation has its own challenges as well:
Availability of the sources of nutrients (for large scale production). Often chemical or inorganic fertilizers are used to achieve appropriate growth
rate of microalgae. Distribution of CO2 even though CO2 may be available as flue gases from power or chemical plants on industrial scale, CO2 distribution is
problematic. Still, because of the benefits of algae cultivation, in many cases it is worth dealing with and overcoming these challenges!
The effect of light intensity
Microalgae use light as a source of energy for synthesizing the cell protoplasm, and their growth rate is maximum at the saturation intensity of light and decreases when its intensity increases or decreases
For many microalgae, increase in the light intensity causes photoinhibition because of disruption of the chloroplast lamellae growth and inactivation of the enzymes involved in the carbon dioxide fixation.
Optimum light intensity for microalgae varies depending on the strain. For example in literature can be found that for Desmodesmus sp. cultivation optimum light intensity was 98μmol/m2/s, but for Dunaliella viridis -700 μmol/m2/s.
Than there is also effect of temperature...
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http://bioreactors.net/wp-content/uploads/2015/10/Photobioreactor_applicationENG.pdf
It's not growing algae at home, but it might shed more light on techniques used to over come challanges.. Even nutrient composition does vary depending on Algae strain you like to grow.
https://www.google.com/search?q=growing+algae+in+lab