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Yeasts are fungi whose growth is predominantly unicellular, commonly through budding or division into two cells. The word describes a growth form across different fungal lineages, rather than one species or an exclusive clade; some fungi can switch between unicellular and filamentous growth. Thus Saccharomyces cerevisiae is a yeast, but yeast is not another name for that one species. See Kurtzman, Fell and Boekhout, The Yeasts, chapter 1 (2011): definition and classification.

A yeast cell has eukaryotic organization, including a cell nucleus, mitochondria and a cell wall. Small size and a unicellular lifestyle do not make it a member of bacteria. These compartments let an experimentally accessible biological cell retain much of the organization shared with other eukaryotes. See Clark, Douglas and Choi, Biology 2e, 24.1: fungal cells and yeast growth.

A motivating experiment: can fermentation continue without intact yeast cells? In 1897, Eduard Buchner ground brewers' yeast with quartz sand and diatomite, added water, and pressed out a liquid extract. Adding concentrated cane sugar produced carbon dioxide after 15–60 minutes. A cell-retaining filter still yielded an active filtrate: with sterilized cane sugar in an icebox, fermentation began after about a day. Saturated lactose gave no observed fermentation. These are reported observations, not invented control results. See Buchner, Alcoholic fermentation without yeast cells (1897), translated excerpt hosted by Carmen Giunta.

The filtration comparison addresses the objection that surviving intact yeast cells caused the activity. The lactose comparison tests substrate dependence; it is not a no-sugar blank, nor a comparison at matched sugar concentrations. A proposed modern follow-up would also compare the same extract with and without added sugar, accounting for material already in the extract. That is an experimental suggestion, not a result attributed to Buchner. His report specifies brewers' yeast; it does not identify the preparation here as a pure Saccharomyces cerevisiae strain.

Heat treatment asks a different question: does destroying activity in the extract stop fermentation? Buchner's preliminary report described weak or absent activity after heating and filtration, rather than one clean universal threshold. Harden's 1914 account of the subsequent work summarized loss of activity on heating the juice to $50{}^{\circ }\mathrm{C}$. Harden also described requirements for both enzymes and coenzymes. Cell-free therefore means neither chemical-free nor a preparation containing one purified enzyme. See Arthur Harden, Alcoholic Fermentation (1914), chapters II and VI: cell-free activity and the fermenting complex.

The inference is that extracted cellular machinery can sustain these chemical reactions without an intact living biological cell. This does not show that the extract reproduces, grows or maintains itself like a yeast. Moreover, gas evolution alone does not identify ethanol: cellular respiration can also release carbon dioxide. Product identification is a separate measurement; Harden's account describes both ethanol and carbon dioxide as products of cell-free alcoholic fermentation. The beautiful separation is between the organism that produces and maintains the machinery and the machinery that catalyzes a particular transformation.

Yeast extract is the water-soluble material obtained from broken-down yeast cells. In the preparation described by ATCC, Saccharomyces cerevisiae undergoes autolysis: its own enzymes break down cellular material, including proteins into peptides and amino acids. The resulting ingredient can supply nitrogen-containing nutrients, vitamins and other soluble constituents to a culture medium.^[ref]

The word extract matters. The ingredient is a mixture of recovered cellular substances, rather than a count of growing yeast cells or one chemically defined nutrient. Adding yeast extract therefore changes several inputs together. Its known total mass does not specify every individual constituent's concentration.^[ref]

An original accounting example illustrates the distinction. Suppose an analysis of a hypothetical dry extract finds 2 milligrams of nutrient X and 1 milligram of nutrient Y per 100 milligrams of extract. A 5-milligram addition then supplies 0.10 milligrams of X and 0.05 milligrams of Y. Equal additions of total extract would supply different amounts of X if another preparation had a different measured X fraction. These values are invented and do not describe a commercial product.

A defined medium can vary an explicitly specified component while holding the others fixed. With yeast extract, interpreting an observed growth change requires considering the accompanying mixture. Neither the total mass nor one measured constituent establishes that all remaining nutrient inputs were matched. The distinction helps separate a convenient composite ingredient from a chemically isolated experimental variable.

In the same gravity–Marangoni reduction, zero liquid flux gives $\Gamma =1+(H_0^2-H^2)/3$ and $6JX=(1+H_0^2/3)(H^3-H_0^3)/3-(H^5-H_0^5)/15$. The lower part of the liquid flows backwards while the surface and upper third flow forwards. For zero initial height and concentration drop $\delta$, $J={\delta }^{3/2}(1-3\delta /5)/(2\sqrt{3})$ is largest formally at complete depletion. Since surface velocity is $J/\Gamma$, that endpoint is singular and requires physical regularization by diffusion, capillarity or an edge model. The algebraic maximum is not by itself a regular zero-concentration outflow.

A zero-order reaction has a reaction rate independent of the relevant reactant concentration over the range where its rate law applies. For $\mathrm{A}⟶\mathrm{B}$, $[\mathrm{A}]=A_0-kt$ is valid only before depletion at $t=A_0/k$. The constant-consumption model must stop or change there.