Abstract
A complete kit, including components to assemble a U-tube apparatus, materials, and methods of using thereof, for the purpose of osmosis pedagogy, is described. The self-contained kit makes possible hands-on osmosis experiments that may be conducted safely at home, and is well-suited for STEM (science, technology, engineering and mathematics) education. The kit supplies unmodified glycerin and unmodified dextran as solutes, and components to assemble a watertight U-tube apparatus capable of accurate, repeatable quantitative measurements and bidirectional osmosis. One method describes osmotic rate measurements using glycerin as solute under varying parameters of solute concentration, temperature, and osmosis direction. Another method describes the comparison of experimental measurement of osmotic pressure at equilibrium to theoretical prediction using dextran as solute.
Claims
1. A kit with components to assemble a U-tube apparatus, necessary chemicals, and measurement tools to perform experiments for the pedagogy of osmosis, comprising: (a) two curved arms made of optically clear hollow tubes; (b) length measuring scales; (c) lids for the arms; wherein said lids include one or more closed lids that tightly caps a U-tube arm and one or more open lids consisting of a hollow cylinder with a removable narrow tube that can be inserted into the inner diameter of the hollow cylinder; (d) a center mount made of a tube encasing a semipermeable membrane sandwiched between two washers, with a removable, non-rigid, deformable sleeve on each end of the tube wherein one of the curved arms inserts inside each of the sleeves; (e) a stand on which the center mount rests; (f) unmodified, non-derivitized glycerin (hereinafter referred to as unmodified glycerin); (g) unmodified, non-derivitized, pre-weighed dextran of known molecular weight (hereinafter referred to as unmodified dextran); (h) food coloring dye; (i) at least one pipet and at least one graduated beaker or graduated cylinder for measuring and dispensing liquids; wherein long tip end of said pipet is able to fit inside the inner diameter of the removable narrow tube in open lid; (j) instruction manual that informs how to perform the osmosis experiments; wherein said instructions inform how to assemble a U-tube apparatus; wherein said instructions inform how to use glycerin-in-water solutions in U-tube apparatus to determine osmotic rates; wherein said instructions inform how to observe bidirectional osmosis with the same glycerin-in-water solution in one arm of the U-tube apparatus; wherein said instructions inform how to use a dextran-in-water solution to determine osmotic pressure at equilibrium.
2. A method for determining osmotic rate, or the rate of osmosis, using a U-tube apparatus, comprising steps of: (a) preparing solutions of unmodified glycerin-in-water with known glycerin concentration by adjusting volume ratio of glycerin to water; wherein a table is provided listing volume of unmodified glycerin and volume of water for varying concentrations of glycerin-in-water solutions; (b) filling one arm of the U-tube with water as a feed solution and filling the other arm of the U-tube with glycerin-in-water as the draw solution for osmosis to occur with water flowing from its arm into the glycerin-in-water arm; (c) with same glycerin-in-water solution in its arm of the U-tube, replacing water with pure or undiluted glycerin in the other arm of the U-tube for osmosis to occur in the opposite direction with water flowing from the glycerin-in-water arm into the pure or undiluted glycerin arm; (d) for slower osmosis experiments, filling both arms of the U-tube to same liquid level height and measuring the difference in liquid level heights between the two arms as a function of time; (e) for faster osmosis experiments, using an open lid with the narrow tube inserted, filling draw solution arm of the U-tube completely and allowing liquid to enter the narrow tube as osmosis occurs, and measuring the rise in liquid level inside the narrow tube as a function of time; (f) placing the filled U-tube at room temperature, inside a refrigerator, or inside an oven wherein osmosis may occur at different temperatures; (g) recording and plotting the difference in liquid level heights between the two arms of the U-tube as a function of time to determine the osmotic rate (slower experiments) or recording and plotting the rise in liquid level height inside the narrow tube as a function of time to determine the osmotic rate (faster experiments).
3. A method for determining osmotic pressure at equilibrium and comparing it to theoretical prediction, using a U-tube apparatus, comprising steps of: (a) preparing a solution of unmodified dextran-in-water with known dextran molecular weight and known dextran concentration; (b) filling one arm of the U-tube with water as a feed solution and filling the other arm of the U-tube with unmodified dextran-in-water as the draw solution, with same initial liquid height level in both arms; (c) allowing osmosis to occur until liquid level heights in both arms no longer change, at which point equilibrium is reached; (d) comparing the actual difference in liquid level heights between the two arms at equilibrium to calculated theoretical values based on osmotic pressure and hydrostatic pressure; wherein an equation for osmotic pressure (Π) is provided, Π=iMRT, and i=van't Hoff factor with i=1 for unmodified, non-derivitized dextran, M=molar concentration of dextran solution, R=universal gas constant, T=absolute temperature; wherein an equation for hydrostatic pressure (P) is provided, P=ρgh, and ρ=density of unmodified dextran solution, g=acceleration due to gravity, and h=difference in liquid level heights; wherein a table listing densities for different concentrations of unmodified dextran solutions is provided; wherein a table listing calculated theoretical values of difference in liquid level heights for different concentrations of unmodified dextran solutions, based on said equations, is provided.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0020] FIG. 1A is a front view of an assembled U-tube apparatus, with an open lid with the narrow tube inserted on the left arm and a closed lid on the right arm.
[0021] FIG. 1B is a perspective view of an assembled U-tube apparatus without lids on the arms.
[0022] FIG. 2A is a perspective view of the center mount of the U-tube apparatus.
[0023] FIG. 2B is a cross-sectional view of a semipermeable membrane inside the center mount without a humectant coating.
[0024] FIG. 2C is a cross-sectional view of a semipermeable membrane inside the center mount with a humectant coating.
[0025] FIG. 2D is an exploded view of the center mount.
[0026] FIG. 3A illustrates an open lid for U-tube arm, which is a hollow cylinder with a narrow tube that can be reversibly inserted into the inner diameter of the hollow cylinder.
[0027] FIG. 3B illustrates a closed lid for U-tube arm.
[0028] FIG. 4 illustrates chemicals as well as tools for measuring and dispensing liquids: 1) unmodified, non-derivitized glycerin, 2) pre-weighed, unmodified, non-derivitized dextran of known molecular weight, 3) food coloring dye, 4) disposable beaker(s) or disposable graduated cylinder(s), and 5) disposable pipet(s).
[0029] FIG. 5 illustrates a flow diagram of a method to conduct osmosis experiments using unmodified, non-derivitized glycerin as solute to measure osmotic rates with variable parameters of solute concentration, temperature, and osmosis direction.
[0030] FIG. 6 illustrates a flow diagram of a method to conduct osmosis experiments using unmodified, non-derivitized, high molecular weight dextran as solute to measure hydrostatic pressure at equilibrium, determine osmotic pressure at equilibrium, and to compare with calculated values based on theory.
[0031] FIG. 7 is a graph showing difference in liquid height levels, h (mm), as a function of time, t (hours), when a 6 mole/liter (6M) glycerin solution with blue dye was in one arm of U-tube with either water or pure glycerin in the other arm. The ratio h/t is defined as the osmotic rate. In the experiments, open lids were used without the liquid rising into the narrow tube, the U-tube arms were not completely filled with liquid, so that h was the difference in liquid column heights between the two arms as osmosis occurred. Using the same U-tube and the same 6M glycerin with dye solution in one arm, when pure glycerin replaced water in the other arm, osmosis occurred in the opposite direction.
[0032] FIG. 8 is a graph showing how osmotic rate (h/t) varied depending on glycerin concentration (3M or 6M glycerin) and whether osmosis occurred versus water or versus pure glycerin, for two similar semipermeable membranes in two different U-tube apparatuses when temperature was maintained at ˜25° C. (room temperature). In the experiments, open lids were used without the liquid rising into the narrow tube, the U-tube arms were not completely filled with liquid, so that h was the difference in liquid column heights between the two arms as osmosis occurred.
[0033] FIG. 9 is a graph showing how osmotic rate (h/t) varied when osmosis occurred at room temperature (˜25° C.) compared to refrigerator temperature (˜4° C.) using the same glycerin concentration (6M) but for two different semipermeable membranes in two different U-tube apparatuses. Inset graph shows h/t for two experiments. In the experiments, open lids were used without the liquid rising into the narrow tube, the U-tube arms were not completely filled with liquid, so that h was the difference in liquid column heights between the two arms as osmosis occurred.
[0034] FIG. 10 is a graph showing difference in liquid height levels, h (mm), as a function of time, t (hours), during a long-term osmosis experiment to reach equilibrium with 0.16 mM native dextran (based on number-average molecular weight M.sub.n˜250,000 g/mole) as solute solution and water as solvent. Closed lids were used on both U-tube arms to prevent water evaporation.
[0035] FIG. 11 is a graph showing the rise in liquid height level in the narrow tube of the open lid as a function of time, t (minutes), under three different conditions 1) a 6M glycerin solution with blue dye (draw solution) in one arm of U-tube and water (feed solution) in the other arm, experiment conducted at room temperature, 2) a 6M glycerin solution with blue dye in one arm of U-tube (feed solution) and pure glycerin (draw solution) in the other arm, experiment conducted at room temperature, and 3) a 6M glycerin solution with blue dye in one arm of U-tube (draw solution) and water (feed solution) in the other arm, experiment conducted in refrigerator. In all three experiments, an open lid with the narrow tube inserted was used on the draw solution arm, which was completely filled with liquid so that liquid was rising into the narrow tube as osmosis occurred. In this configuration, the rise in liquid height level in the narrow tube was measured on the order of minutes, rather than hours.
DETAILED DESCRIPTION OF THE INVENTION
[0036] This invention describes an osmosis kit comprising components to assemble a U-tube apparatus, chemicals, supplies, and two methods of using the kit. The drawings are for illustrative purposes, and embodiments illustrate the characteristics and functionality of the apparatus, chemicals, and two methods in which specific steps and sequence are not to be limiting in scope. The sequence may occur in a different order, so long as it still performs the goals of the invention. The illustrative drawings are not intended to be to scale or to be exhaustive of all possible sizes and dimensions, which may be adjusted to fit user needs.
[0037] In the embodiment 10 shown in FIGS. 1A and 1B, there are two curved arms 12, one on the left and one on the right, connected to a center mount 20. Both curved arms are optically clear hollow tubes that may be filled with liquid. The curved arms 12 are interchangeable so that either curved arm 12 may be used on either side of the center mount 20 with no difference in functionality nor performance. The length of the arms determine the overall height of the U-tube, and may be designated by the user. Length measuring scales 14 enable measurement of liquid column heights. The entire U-tube apparatus is securely placed on a stand 16. Two different types of lids on the arms may be used, a closed lid 18 that tightly caps an arm, or an open lid 32 with a removable narrow tube that enables more rapid measurements of liquid level changes.
[0038] In the embodiment 20 shown in FIG. 2A, the center mount 20 contains a semipermeable membrane 22 affixed between two washers 24. Depending on the type of semipermeable membrane used, the membrane may be uncoated (FIG. 2B) or coated with a humectant coating 26 (FIG. 2C). Glycerin, provided in the osmosis kit, is itself a humectant and may be used as the coating. The washer-membrane-washer sandwich is affixed inside a protective tube 28. Each end (left and right) of the protective tube 28 accommodates a removable, non-rigid, deformable sleeve 30 that allows one curved arm 12 to be inserted in a watertight manner. The sleeves 30 are thin-walled and cylindrical in shape. The definition of removable is that a curved arm 12 can be inserted into or removed from a sleeve 30, and a sleeve 30 can be inserted into or removed from a center mount 20, without damaging any of the components, so that all components can be reused. The definition of non-rigid is that the shape of the sleeve 30 can be changed using manual pressure without the use of any external tools. The definition of deformable is that the shape, including the wall thickness, of the sleeve 30 can be reversibly changed when pressure is applied or removed. FIG. 2D illustrates an exploded view of the center mount 20.
[0039] The assembled U-tube apparatus 10 is watertight over the long term so that water flows through only the semipermeable membrane 22 during osmosis but does not leak through any other opening. All components of the U-tube apparatus, curved arms 12, length measuring scales 14, center mount 20, closed lid 18, open lid 32, and stand 16 are washable and reusable. This design provides a watertight connection, in contrast to NeoSci 30-1125 Osmosis Simulation Activity Model. To be watertight, this design does not require threaded components, in contrast to U.S. patent 2018/0280881. This design does not require an external press tool to create the seal, in contrast to U.S. Pat. No. 8,888,145. The U-tube can be assembled, disassembled, and reassembled using only manual manipulation with minimal assembly and a minimum number of parts, in contrast to the PASCO Diffusion-Osmosis Apparatus ME-6940 and the osmosis device described by Rodriguez-Duenas, et. al, (2022). Finally, when the assembled U-tube apparatus 10 is filled with liquid in both curved arms 12, it is possible to disconnect only one curved arm 12 without disturbing the liquid in the other curved arm 12. A center mount 20 with only one liquid-filled curved arm 12 connected via a sleeve 30 remains watertight.
[0040] The embodiment in FIG. 3A illustrates an open lid 32, which consists of a thick-walled hollow cylinder 34 with a narrow tube 36 that can be reversibly inserted into the inner diameter of the hollow cylinder 34. The outer diameter of the thick-walled hollow cylinder 34 fits tightly into the opening of the U-tube arm 12. The outer diameter of the narrow tube 36 fits tightly into the inner diameter of the hollow cylinder 34. The inner diameter of the narrow tube 36 allows the long tip of a disposable pipet 50 to fit inside. When an open lid 32 with narrow tube 36 inserted is placed on top of a U-tube arm 12, and the arm 12 is completely filled with liquid, as liquid level rises during osmosis, liquid is forced to travel into the narrow tube 36. Forcing liquid into a smaller diameter narrow tube 36 compared to a larger diameter U-tube arm 12 allows faster measurement of osmotic rates. If slower measurements of osmotic rates are desired, the U-tube arms 12 are not completely filled with liquid during experiments, and the use of any lid is optional. The embodiment in FIG. 3B illustrates a closed lid 18, which tightly caps a U-tube arm 12. A closed lid 18 may be required for long term experiments because it prevents water evaporation.
[0041] The embodiment 40 in FIG. 4 illustrates some of the other components provided in the kit. These components include the following chemicals: unmodified, non-derivitized glycerin 44, unmodified, non-derivitized, pre-weighed dextran of known molecular weight 46, and a food coloring dye 42. Disposable (plastic) beaker(s) 48 and disposable (plastic) pipet(s) 50 are also provided to enable users to measure and dispense liquids. Although not illustrated, the kit contains an instruction manual which will describe the pertinent methods in embodiments 60 and 80.
[0042] Two methods (60 and 80) of using the U-tube apparatus are disclosed in this invention, and experiments may be performed with either method using the same assembled U-tube apparatus. The first method 60 is for the purpose of measuring osmotic rates as three experimental parameters are varied: solute concentration, temperature, and osmosis direction, as illustrated in FIG. 5.
[0043] As shown in FIG. 5, after assembling the U-tube apparatus (step 62), the first variable parameter is the glycerin solute concentration (step 64). The user prepares a glycerin solution of desired concentration, i.e., glycerin-in-water solution, by selecting the proper volume ratio of glycerin to water, and a table is provided (step 66). The glycerin solution (draw solution) is placed in one arm of the U-tube while water (feed solution) is placed in the other arm. If color is desired, food coloring dye may be added to the glycerin solution, although osmosis occurs with glycerin only without any dye. For slower experiments (on the order of hours to overnight), the glycerin solution (draw solution) and water (feed solution) are placed to the same height in their respective arms with initial height difference being zero, and arms are not completely filled with liquid to leave enough room for liquid to rise during osmosis (step 68). For faster experiments (on the order of minutes to hours), the arm with glycerin solution (draw solution) has an open lid with narrow tube inserted, and is completely filled, so that during osmosis, liquid rises in the narrow tube (step 68). The rise in liquid level in a smaller diameter narrow tube 36 will be significantly faster than the rise in liquid level in a larger diameter U-tube arm 12.
[0044] The second variable parameter is temperature, and an experiment is conducted at room temperature (step 70), in a refrigerator above freezing point of water, or in an oven below boiling point of water (step 72). Whether at room temperature, in a refrigerator, or in an oven, osmosis occurs with water (feed solution) flowing from its arm into the glycerin solution (draw solution) arm, and over time, the liquid level height in the water arm decreases while the liquid level height in the glycerin solution arm increases. The osmotic rate may be determined by the difference in liquid level heights (h) between the arms as a function of time (t), or by the rise in liquid level in the narrow tube when it is used.
[0045] The third variable parameter is osmosis direction, and successive experiments can be conducted without disassembling the U-tube. If user desires osmosis to occur in the same direction in U-tube (step 74), then water (feed solution) remains in its arm, while a glycerin-in-water solution (draw solution) is replaced with a glycerin-in-water solution of different concentration, and process is repeated. It is possible to remove liquids from U-tube arms using a pipet 50 provided in the kit. It is also possible to disassemble and reassemble only one arm of U-tube without disturbing the liquid in the other arm, because each U-tube arm 12 remains watertight once inserted into the center mount 20 via a sleeve 30.
[0046] If user desires osmosis to occur in the opposite direction in U-tube (step 76), then the glycerin-in-water solution remains in its arm, and water is replaced with pure glycerin in the other arm. In this case, the glycerin-in-water solution becomes the feed solution and pure glycerin becomes the draw solution, and the direction of osmosis reverses with water (solvent) flowing from the glycerin-in-water arm into the pure glycerin arm.
[0047] FIG. 6 illustrates another method embodiment 80 of using the osmosis kit, for the purpose of experimentally determining the osmotic pressure at equilibrium and comparing it to theoretical prediction. After assembling a U-tube apparatus per instructions manual (step 82), an unmodified dextran solute solution of pre-determined concentration is prepared by dissolving pre-weighed dextran powder 46 in a known amount of water (step 84). The unmodified dextran solution (draw solution) is placed into one arm of the U-tube and water (feed solution) is filled to the same height in the other arm with initial height difference being zero (step 86). This method involves a long-term experiment to reach equilibrium, and closed caps 18 may be used to prevent water evaporation. As osmosis occurs, water flows from its arm into the dextran solution arm, resulting in a liquid level height difference that increases with time. The higher liquid level in the dextran solution arm exerts a hydrostatic pressure, due to the force of gravity, that interferes with osmosis. Eventually, when equilibrium is reached, the height difference in liquid levels ceases to change because osmotic pressure and hydrostatic pressure equalize. Water flow in is the same as water flow out.
[0048] At equilibrium, the height difference observed experimentally in the U-tube can be compared to theoretical prediction by setting the osmotic pressure equal to the hydrostatic pressure (step 88), and both pressures are described by well-established equations (step 88). A table of unmodified dextran solution density (step 90) is provided because determination of a solution's hydrostatic pressure requires its density. Another table is provided with calculated theoretical values of liquid level height differences expected at equilibrium for a range of unmodified dextran concentrations (step 92).
[0049] The kit and methods described herein may be better understood with reference to the accompanying examples, which are intended for illustrating but not limiting the invention.
EXAMPLE 1
[0050] Osmosis experiments were performed using a U-tube apparatus 10 (FIGS. 1A and 1B) with open lids 32 (FIG. 3A) on both arms, following method 60 (FIG. 5). A solution of 6M glycerin with blue dye (0.2 mM) was placed in right arm of U-tube while water was placed in left arm to the same height level (initial height difference in liquid level between the two arms was zero, i.e., h=0 at t=0). Arms were not completely filled with liquid and height difference in liquid columns between the two arms (h) was measured as a function of time (t). Osmosis occurred with water flowing from its arm across the semipermeable membrane into the 6M glycerin with blue dye arm, from left to right. Afterwards, water was pipetted out of its arm and replaced with pure (i.e., undiluted) glycerin, with the same 6M glycerin and dye solution remaining in its arm. Osmosis occurred with water flowing from the 6M glycerin and dye solution arm across the semipermeable membrane into the pure glycerin arm, in the opposite direction, from right to left. Shown in FIG. 7 are experimental data observed for 6M glycerin with dye vs. water and 6M glycerin with dye vs. pure glycerin. In both cases, linear regression of h/t showed excellent linear fit (goodness-of-fit measure R.sup.2>0.99). The ability to remove liquid (e.g., water) from its arm and replace with another liquid (e.g., glycerin) without disassembling the U-tube apparatus reduced time between experiments.
EXAMPLE 2
[0051] In this example, method embodiment 60 (FIG. 5) was used with solute concentration (steps 64 and 66) and osmosis direction (steps 74 and 76) as the variable parameters. Two U-tube apparatuses were utilized with semipermeable membranes made of similar, but not identical, materials used for dialysis. Open lids on both arms were used in all experiments, and both arms were filled to the same liquid level, but not completely full, and height difference in liquid columns between the two arms (h) was measured as a function of time (t) with h=0 at t=0 in each experiment. Four experiments were performed in each apparatus at room temperature back-to-back without disassembling apparatus between experiments: 1) 3M glycerin with blue dye vs. water, 2) 3M glycerin with blue dye vs. pure glycerin, 3) 6M glycerin with blue dye vs. water, and 4) 6M glycerin with blue dye vs. pure glycerin. FIG. 8 shows the results of osmotic rate h/t for both U-tube apparatuses with 3M glycerin and 6M glycerin, vs. water and vs. pure glycerin. In each case, whether 3M or 6M glycerin was in a U-tube arm, when water was replaced with pure glycerin in the other arm, osmosis occurred in the opposite direction. Osmotic rate h/t was linear in all experiments with goodness-of-fit measure R.sup.2>0.99. As observed in FIG. 8, results were similar between the two U-tubes since both had similar membrane material.
EXAMPLE 3
[0052] In this example, method embodiment 60 (FIG. 5) was used with temperature (steps 70 and 72) as the variable parameter. Two U-tube apparatuses were used with semipermeable membranes different from each other and different from those used in EXAMPLES 1 and 2. One apparatus contained a semipermeable membrane with smaller pores, while the other apparatus contained a semipermeable membrane with larger pores. Similar to EXAMPLES 1 and 2, open lids were used on both arms, arms were not completely filled with liquid, and height difference in liquid columns between the two arms (h) was measured as a function of time (t) with h=0 at t=0. As expected, osmotic rate (h/t) was faster when pores in the membrane were larger, and h/t was faster at higher temperature (FIG. 9). This example demonstrates that it is possible to obtain faster osmotic rates by changing the membrane. Also seen in FIG. 9 is that for both U-tubes, when apparatus was placed in refrigerator, h/t was slower at ˜4° C. than that at room temperature (˜25° C.), confirming that temperature does indeed affect osmosis. As observed in EXAMPLES 1 and 2, the osmotic rate h/t was linear in all experiments with goodness-of-fit R.sup.2>0.99 (FIG. 9).
[0053] Data collected in EXAMPLES 1 to 3 with goodness-of-fit R.sup.2>0.99 were possible because liquid glycerin was used as solute for osmosis. The center mount was reused in multiple experiments, saving time as well as cost. In the present disclosure, if the semipermeable membrane, e.g., dialysis membrane, needs to be maintained wet, glycerin itself is a humectant, and can be applied as a surface coating to the membrane. The present invention is not limited to dialysis membrane, which is soft and pliable, but permits any semipermeable membrane to be sandwiched between washers in the center mount.
EXAMPLE 4
[0054] Using method embodiment 80 (FIG. 6), experimental data for osmotic pressure was compared to calculated theoretical prediction. In this example, the experiment was long term (>45 days) and closed lids were placed on both arms of U-tube. High molecular weight unmodified dextran, not glycerin, was utilized as solute because the purpose of the experiment was to determine osmotic pressure, not osmotic rate. Dextran is a water soluble, biocompatible, and nontoxic polysaccharide. The molecular weight of dextran may vary from thousands to millions grams/mole (g/mol), and is an average value within a distribution of values because a precisely controlled molecular weight is nearly impossible. The reported average may be a number averaged molecular weight (M.sub.n) or a weight averaged molecular weight (M.sub.w), with M.sub.w greater than M.sub.n. The polydispersity index (M.sub.w/M.sub.n) is a measure of the broadness of the molecular weight distribution. For relatively high molecular weight dextran, a polydispersity index of 2 (M.sub.w/M.sub.n˜2) is typical.
[0055] In this example, unmodified dextran with M.sub.w˜500,000 g/mol was selected for osmotic pressure testing. In order to compare experimental results with theoretical prediction, the solute solution (draw solution) must be very dilute, and therefore the solute must have high molecular weight, e.g., in the range of 10.sup.5 to 10.sup.6 g/mol. Glycerin is not suitable for this purpose because its molecular weight is only 92 g/mol. A 0.08 mM unmodified dextran solution based on M.sub.w of 500,000 g/mol, same as a 0.16 mM unmodified dextran solution based on M.sub.n of 250,000 g/mol, was placed in one arm of U-tube while water was placed in the other arm, with h=0 at t=0. When equilibrium is reached, the liquid level heights no longer change. In this example, the observed h in the U-tube was compared to what is predicted by theory using tables 90 and 92 (FIG. 6). As seen in FIG. 10, h was approaching ˜40 mm after 1100 hours and beginning to plateau. A value of about 40 mm for h is what would be expected for a solute solution of 0.16 mM concentration (table 92, FIG. 6). This example demonstrates that with a properly configured U-tube and an appropriate method, it is possible to directly compare experimental results with theoretical predictions.
EXAMPLE 5
[0056] In this example, method embodiment 60 (FIG. 5) was used with temperature (steps 70 and 72) and osmosis direction (steps 74 and 76) as the variable parameters. The difference between this example (EXAMPLE 5) and the previous examples (EXAMPLES 1 to 3) is that liquid in the draw solution arm was forced into the narrow tube 36 inserted in an open lid 32. The draw solution arm was completely filled with liquid, and as osmosis occurred, liquid traveled up the narrow tube 36, and osmotic rate was determined by the rise in liquid level in the narrow tube (mm) as a function of time. In this case, a steady rise in liquid level in the narrow tube 36 could be measured within the order of minutes, instead of hours as in previous examples. Similar to EXAMPLES 1 and 2, with the same 6M with blue dye solution in one arm of the U-tube, when pure glycerin replaced water in the other arm, osmosis occurred in the opposite direction and h/t was slower. Similar to EXAMPLE 3, when osmosis occurred vs. water and the apparatus was placed in the refrigerator, h/t was slower at ˜4° (refrigerator) compared to ˜25° C. (room temperature). This example, however, shows that much more rapid measurements of osmotic rates are possible by measuring the rise in liquid level in a narrow tube 36 instead of measuring the difference in liquid height levels between two U-tube arms 12.
