大连理工大学：《大学物理》课程教学资源（实验讲义）水的表面张力的测量 Measurement of the surface tension coefficient of water

Experiment 2.Measurement of the surface tension coefficient ofwaterSurface tension is an important property occurring at liquid surface. Similar withstress in solid matter,it also results fromthe attraction of liquid molecules to eachother and is viewed as a force tending to minimize the surface area. The coefficient ofsurface tension, represented by the symbol α, is measured in force per unit length,with unit of newton per meter (N/m). The value of surface tension is strongly dependon the type of liquid, but also affected by temperature, purity and atmosphere aboveliquid. It is a ubiquitous element in our lives, and can be observed in the capillaritytube, soap bubbles and spherical shape of small drops. It is also a underlyingmechanism to affect fluidity of the liquid and its ability to support pressure.There are several methods of surface tension measurements, like capillary rise method,plate or ring method, drop weight method and maximum bulk pressure method. In thisexperiment, we use ring method, also named Du Nouy Ring Tensiometer, proposed bya French physicist Pierre Lecomte du Nouy in 1925Experimental objectives(1) To gain a deeper understanding of surface tension(2) To measure the surface tension with the ring method (Du Nouy Ring Tensiometer)Experimental InstrumentsFD-NST-I ring tensiometer: as shown in figure 2-1, it iscomposed of a force meter (maximum of 10 g) and amoveable plate support for glass dish. The force meter canbe calibrated by weights (0.5 g each one) asV= Vo+kF(2.1)where Vis display voltage of the force meter, Vo is a initialvoltage of the force meter, k is the relationship betweenFigure 2-1 FD-NSF-I ring tensiometerforce and voltage, F is force generated by weights

Experiment 2. Measurement of the surface tension coefficient of water Surface tension is an important property occurring at liquid surface. Similar with stress in solid matter, it also results from the attraction of liquid molecules to each other and is viewed as a force tending to minimize the surface area. The coefficient of surface tension, represented by the symbol α, is measured in force per unit length, with unit of newton per meter (N/m). The value of surface tension is strongly depend on the type of liquid, but also affected by temperature, purity and atmosphere above liquid. It is a ubiquitous element in our lives, and can be observed in the capillarity tube, soap bubbles and spherical shape of small drops. It is also a underlying mechanism to affect fluidity of the liquid and its ability to support pressure. There are several methods of surface tension measurements, like capillary rise method, plate or ring method, drop weight method and maximum bulk pressure method. In this experiment, we use ring method, also named Du Noüy Ring Tensiometer, proposed by a French physicist Pierre Lecomte du Noüy in 1925. Experimental objectives (1) To gain a deeper understanding of surface tension (2) To measure the surface tension with the ring method (Du Noüy Ring Tensiometer) Experimental Instruments FD-NST-I ring tensiometer: as shown in figure 2-1, it is composed of a force meter (maximum of 10 g) and a moveable plate support for glass dish. The force meter can be calibrated by weights (0.5 g each one) as V = V0+kF (2.1) where V is display voltage of the force meter, V0 is a initial voltage of the force meter, k is the relationship between force and voltage, F is force generated by weights. Figure 2-1 FD-NSF-I ring tensiometer

Experimental principleAs shown in figure 2, intermolecular forces, includingforces of attraction and repulsion between molecules,changes with distance of molecules. At large distance,the significant force is attractive. At closer distance, arepulsive force becomes significant and increasesrapidly.At one distance, ro, the attractive andrepulsiveforcesexactlybalance.Commonly,duetothe intermolecularforces, a molecule is pulled equallyinevery directionbyneighboringliquidmolecules,Figure 2-2 Variation of intermolecularresultinginanetforceofzero.Themoleculesattheforcewithdistancesurface do not have the same molecules on all sides of them and therefore are pulledinward. This causes the surface tension and creates some internal pressure and forcesliquid surfacesto contracttotheminimal area.Theforce should linear increase withsurface length (L), and can be expressed as f-αLWhen a ring is submerged to water, the intermolecular force between solid and liquidis higher, and then the water molecules can attach to the surface of the ring. as the ringis pulled out, a water film will be formed between ring and water. In this case, thetotal force (Ftotal) needed to detach the ring equals the ring weight (W) and attractiveforce (Fwater)from surfacetension of water,Ftotl=Fwater + W,(2.2)In this experiment, the ring weight is constant and can be measured by force meter.The attractive force from water film increase with pulling out the ring. When theneeded Fwater is higher than the surface tension (Fst), the water film will detach fromthe ring. It means the force of Fwater measured at the moment of water detachmentequals toFst.Next, FsT can be calculated with the difference between thetotal forcesatthemoment of detachment and after detachment.Finally.the coefficient (N/m)ofsurface tension can beobtained with(2.3)α = FsT /((Din+Dout)where, Din and Dout are inner and outer diameters of the ring, respectively. Note thatsurface tension acts on the two circumferences of the ring, so we need calculate both.Usually the correction for buoyancy should be introduced, but to simplify thisexperiment, it is ignored here

Figure 2-2 Variation of intermolecular force with distance Experimental principle As shown in figure 2, intermolecular forces, including forces of attraction and repulsion between molecules, changes with distance of molecules. At large distance, the significant force is attractive. At closer distance, a repulsive force becomes significant and increases rapidly. At one distance, r0, the attractive and repulsive forces exactly balance. Commonly, due to the intermolecular forces, a molecule is pulled equally in every direction by neighboring liquid molecules, resulting in a net force of zero. The molecules at the surface do not have the same molecules on all sides of them and therefore are pulled inward. This causes the surface tension and creates some internal pressure and forces liquid surfaces to contract to the minimal area. The force should linear increase with surface length (L), and can be expressed as f=αL. When a ring is submerged to water, the intermolecular force between solid and liquid is higher, and then the water molecules can attach to the surface of the ring. as the ring is pulled out, a water film will be formed between ring and water. In this case, the total force (Ftotal) needed to detach the ring equals the ring weight (Wr) and attractive force (Fwater) from surface tension of water, Ftotl = Fwater + Wr (2.2) In this experiment, the ring weight is constant and can be measured by force meter. The attractive force from water film increase with pulling out the ring. When the needed Fwater is higher than the surface tension (FST), the water film will detach from the ring. It means the force of Fwater measured at the moment of water detachment equals to FST. Next, FST can be calculated with the difference between the total forces at the moment of detachment and after detachment. Finally, the coefficient (N/m) of surface tension can be obtained with α = FST /(π(Din+Dout)) (2.3) where, Din and Dout are inner and outer diameters of the ring, respectively. Note that surface tension acts on the two circumferences of the ring, so we need calculate both. Usually the correction for buoyancy should be introduced, but to simplify this experiment, it is ignored here

Experimental content and procedure1.Experimental content(1)Calibration offorce meter(2) Measurement for the coefficient of surface tension2.Experimental procedure(1) Calibration of force meterFirst, switch on the force meter, and hang the small pan to it. In this step, theforce meter needs to warm up for at least 10 mins.Then, tune the voltage of the force meter to O mV.Next, put all the seven weights in the small pan one by one (0.5 g for eachone), and then take them out one by one. This step is to eliminate the errorfromforcemeter(2)MeasurementforthecoefficientofsurfacetensionFirst, clean the ring by NaOH solution, and then wash it with water.Next, put the glass dish with half water to the moveable plate and hang thering to the force meter. The ring should be hanged horizontallyFinally, rise the plate to let lower edge of the ring submerge in the water, andthen move the plate smoothly in the opposite direction to record the voltageof forcemeter at the moment of just detachment (Vo)and afterdetachment(V2). Note that the inner and outer diameter of the ring should be measuredfor calculating the coefficient of surface tension.Experimental data recording and processing() Measured diameters of the ring, expressed with uncertainty(2) Linear fit the calibration data, and then calculate the value of k and its uncertainty.It should be expressed as k = k ± Uk.(3) Repeat surface tension measurement 8 times and record the data.(4) Calculate the average value of V1 and V2, and express them as V= V ± Uv.(5) Calculate the coefficient of surface tension, and express as α = α ± Ua

Experimental content and procedure 1. Experimental content (1) Calibration of force meter (2) Measurement for the coefficient of surface tension 2. Experimental procedure (1) Calibration of force meter First, switch on the force meter, and hang the small pan to it. In this step, the force meter needs to warm up for at least 10 mins. Then, tune the voltage of the force meter to 0 mV. Next, put all the seven weights in the small pan one by one (0.5 g for each one), and then take them out one by one. This step is to eliminate the error from force meter. (2) Measurement for the coefficient of surface tension First, clean the ring by NaOH solution, and then wash it with water. Next, put the glass dish with half water to the moveable plate and hang the ring to the force meter. The ring should be hanged horizontally. Finally, rise the plate to let lower edge of the ring submerge in the water, and then move the plate smoothly in the opposite direction to record the voltage of force meter at the moment of just detachment (V1) and after detachment (V2). Note that the inner and outer diameter of the ring should be measured for calculating the coefficient of surface tension. Experimental data recording and processing (1) Measured diameters of the ring, expressed with uncertainty (2) Linear fit the calibration data, and then calculate the value of k and its uncertainty. It should be expressed as k = k _ ± Uk. (3) Repeat surface tension measurement 8 times and record the data. (4) Calculate the average value of V1 and V2, and express them as V = V _ ± UV. (5) Calculate the coefficient of surface tension, and express as α = α _ ± Uα

Questions(1) What is the variation of Fwater when the ring touches the water? Why?(2) What are the factors can cause errors in this experiment? what is the effect of thefactors onthemeasuredvalueof a?

Questions (1) What is the variation of Fwater when the ring touches the water? Why? (2) What are the factors can cause errors in this experiment? what is the effect of the factors on the measured value of α?