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Osmosis is net movement of water across a boundary whose permeability differs for water and relevant solutes. The direction depends on the chemical potential of water, including both dissolved material and pressure. A cell wall can let water reach the cell membrane, yet oppose expansion through turgor pressure. Zero net movement does not mean individual water molecules have stopped crossing.

Imagine pure water on side A and a chemical solution on side B of a semipermeable membrane. At equal temperature and pressure, dissolved particles lower the chemical potential of water in B, and net water transfer initially favors A to B. Retaining the solutes lets water redistribute without simply mixing everything. Increasing B's pressure opposes entry; enough pressure gives thermodynamic equilibrium with unequal solute concentrations. This is why “water moves toward more solute” requires a pressure condition.^[ref]

At thermodynamic equilibrium, the chemical potentials of exchangeable water are equal. Individual water molecules still move and cross in both directions, with equal mean opposing transfer rates and zero net flux. A stationary liquid level alone does not prove this: a blocked route can also give no visible transfer. Selective permeability provides a route; water potential supplies the direction, and neither alone determines the speed. The cell wall, turgor pressure and plasmolysis articles show why a living boundary's mechanical support and its selective permeability must be distinguished.

Take two reservoirs separated by a semipermeable membrane that passes water and retains one neutral solute. Stipulate $T=300\mathrm{K}$, $c_A=10\mathrm{mol}{\mathrm{m}}^{-3}$ and $c_B=30\mathrm{mol}{\mathrm{m}}^{-3}$, equivalent to $10$ and $30\mathrm{mmol}{\mathrm{L}}^{-1}$. Treat both chemical solutions as dilute and ideal. These are invented model conditions, not measurements or recommended biological conditions.

For pressures measured at the same height beside the membrane, define $\Delta P=P_B-P_A$. The model predictsAt $\Delta P=0$, net water transfer favors A to B. At $\Delta P\simeq 49.89\mathrm{kPa}$, the opposing pressure balances the osmotic pressure difference, giving zero net transfer with unequal concentrations. At $\Delta P=75\mathrm{kPa}$, the sign reverses and net water transfer favors B to A, toward the more dilute reservoir. Raising pressure changes the total water potential, rather than changing the membrane into a one-way gate.

Fixed concentrations require large maintained reservoirs or an instantaneous comparison. In a closed membrane osmometer, entering water causes dilution of the receiving chemical solution and changes its volume; the final balance must use final concentrations. A supported cell wall provides another way to develop the opposing pressure, as explained under turgor pressure.

Stomata are regulated pores of the plant epidermis; the primordial utricle is an older name for living peripheral cell contents; the vascular cambium is a tissue that produces secondary conducting tissues. These are respectively an opening apparatus, part of a cell's living contents, and a region of dividing cells.

A stoma is an aperture bounded by two guard cells, commonly with associated subsidiary cells. Changes of guard cell turgor pressure alter the aperture. Stomata permit entry of carbon dioxide for photosynthesis and loss of water vapour through transpiration, while also allowing other gas exchange. Most leaves have many on their lower surface, but distribution varies, so absence from the upper surface is not a definition. A pore is not itself a minute leaf blood vessel.

The primordial utricle was distinguished in nineteenth-century microscopy as the protoplasmic layer inside the cell wall, especially conspicuous around the large central vacuole of a mature plant cell. In modern vocabulary this includes peripheral cytoplasm bounded externally by the cell membrane; the vacuolar boundary is the tonoplast. The old term should not be reduced to a synonym of the rigid cell wall or assumed to designate an independently living bag. In plasmolysis, an appropriate external hypertonic solution draws water from the cell and the living contents withdraw from the wall, making the distinction visible.^[ref]

The vascular cambium is a lateral meristem, characteristically situated between the xylem and phloem of a woody stem. Its divisions produce secondary xylem towards the inside and secondary phloem towards the outside; radial derivatives also contribute to vascular rays. Activity connects the growth of the conducting system with thickening of the axis. It is not simply a film of nutritious liquid that spontaneously turns into wood. The cork cambium is a different lateral meristem, concerned with the protective outer covering.^[ref]

The course of sap can now be followed from soil to growing tissue. Root cells acquire mineral ions, and water enters along a water potential gradient. Water and dissolved minerals move into the xylem and upwards through the root and stem to the leaves. In a transpiring plant, evaporation from moist internal leaf surfaces and diffusion out through stomata maintain a pull on the continuous water columns. Cohesion between water molecules and the mechanical support of xylem walls allow tension to be transmitted. Root pressure can drive exudation or guttation under some conditions, but it is not a sufficient universal explanation for supply to the tops of tall trees.

In leaves, photosynthesis incorporates carbon dioxide into organic compounds. Soluble products, especially sucrose, enter the phloem and move from sources to sinks, such as growing roots, buds, fruits or storage organs. Thus elaborated sap is not invariably a single downward stream: the direction depends on where a source and a sink lie. The modern pressure-flow hypothesis explains bulk movement through differences of hydrostatic pressure associated with loading and unloading solutes. Neither the ascending nor the assimilate stream forms an exact analogue of an animal's closed blood circulation.^[ref]

A short experimental history makes these distinctions concrete. In Vegetable Staticks by Stephen Hales (1727), Stephen Hales measured water use and perspiration by plants and attached tubes and pressure gauges to cut vines. Exudation into a sealed vertical tube demonstrates a positive pushing pressure generated below the cut. The corresponding observation after the bleeding season differed, showing that root pushing and the supply to a leafy, transpiring shoot need not have the same explanation. Weighing a potted plant while limiting evaporation from the soil provides another balance: water lost from the system must be compared with its supply and changes of storage.^[ref] A cut shoot taking up water is informative, but its uptake alone does not establish all the forces acting in an intact rooted plant.

For the phloem, removal of a ring of bark can interrupt assimilate transport while leaving a substantial wood pathway intact; accumulation above the interruption distinguishes the two transport systems, although injury complicates any inference about a natural circulation. In an 1866 account, terms such as crude and elaborated sap could summarize these routes. The modern quantitative water potential and pressure-flow hypothesis accounts extend beyond that historical vocabulary.

Solute potential is the contribution to water potential from dissolved material, with pure water assigned zero. In the nearly incompressible description, ${\Psi }_s=(RT/{\bar{V}}_w)\ln a_w$. In a dilute ideal chemical solution, ${\Psi }_s\simeq -RT{c}_{\mathrm{osm}}$, where $c_{\mathrm{osm}}$ is the osmotic concentration of dissolved particles. Thus solute potential is negative while the corresponding osmotic pressure is positive: ${\Psi }_s\simeq -\Pi$. This sign difference distinguishes a contribution to water potential from the compensating mechanical pressure.^[ref]

Tonicity describes how a surrounding chemical solution changes cellular volume through osmosis. It depends on which solutes remain effectively excluded on the timescale of interest, not simply on the amount of dissolved material. The following comparisons take a functional cell membrane, an initially unpressurized biological cell, and effectively excluded solutes as the reference; rising turgor pressure can oppose entry in a walled biological cell.

Operationally, hypotonic solutions cause sustained swelling, hypertonic solutions sustained shrinking, and isotonic solutions no sustained volume change in the specified passive comparison. State the reference biological cell, membrane properties and observation interval. A permeating solute can transiently change water potential while crossing; after its chemical potential equilibrates, its initial unequal concentrations cannot be treated as a permanently retained osmotic load. Thus equal osmolarities need not imply isotonic solutions. Conversely, a stationary walled biological cell may have unequal osmolarities balanced by turgor pressure.^[ref]

Water potential expresses the chemical potential of water relative to a stated pure-water reference in units of pressure. For a nearly incompressible liquid at fixed temperature, use a constant reference molar volume ${\bar{V}}_w$ and writeThe reference is pure water at the same temperature and a chosen pressure $P_0$. Both sides must use the same reference. Neglecting height differences and interactions with solid surfaces, the approximation isHere $a_w$ is the dimensionless thermodynamic activity of water, $R$ the molar gas constant, and $T$ the absolute temperature. The natural logarithm is therefore applied to a dimensionless quantity. The pressure contribution ${\Psi }_p=P-P_0$ increases with pressure; the solute potential ${\Psi }_s$ is negative when $a_w<1$. Across an available passive water route, net water transfer favors higher to lower water potential. The familiar plant description adds effects of height and interactions with solid surfaces when they matter; they are omitted in the two liquid compartments here.^[ref]

Adding solute and raising pressure can thus cancel in water potential while each contribution remains nonzero. Equality of water potential does not imply equality of pressure or of every solute concentration. In a supported plant cell, the cell wall permits a positive turgor pressure to balance a negative solute potential; plasmolysis illustrates the opposite loss of support after water leaves.