Medical Physics - Surface tension.pdf

Medical Physics Surface tension Surface tension Contents : Introduction 3 Units of surface tension 5 liquid rise in capillary tube method. 6 Calculation method 8 Drop weight method 13 Experiment steps 14 Calculation method 15 Factors acting on surface tension 17 Surface tension Surface tension press...

Medical Physics Surface tension Surface tension Contents : Introduction 3 Units of surface tension 5 liquid rise in capillary tube method. 6 Calculation method 8 Drop weight method 13 Experiment steps 14 Calculation method 15 Factors acting on surface tension 17 Surface tension Surface tension pressure: It’s the pressure exerted by a liquid on its surface (Pa). Surface tension arises from cohesive forces between the liquid molecules. In the bulk, molecules are interacting equally with each other in all directions. However, at the surface, molecules don't have the same neighbours on all sides. Surface tension Thus, a net inward force pulls the molecules toward the bulk. This gives rise to a property called surface tension. How high the surface tension is, is dependent on the type of molecular interactions present. For example, the surface tension of water is high, as the water molecules interact with each other through hydrogen bonds which are relatively strong. Surface tension Units of surface tension: There are several different units for surface and interfacial tension; typically (N/m and dynes/cm) are used. Measurements of surface tension: There are several methods to measure surface tension: 1. Liquid rise in capillary tube method. 2. Drop weight method. 3. Pubble pressure method. 4. Using tensiometer device. Surface tension Liquid Rise In Capillary Tube Method: 1. We prepare the liquid whose surface tension is to be determined. We put it in a container (the density of that liquid is known, if not, it is measured using a density bottle of known volume). 2. We prepare a capillary tube open at both ends and with a known radius (r) and immerse one of its ends in the liquid. 3. We observe the rise of the liquid inside the capillary tube, and the liquid continues to rise inside the tube under the influence of surface tension forces (these forces act to reduce the surface area of the liquid). Surface tension 4. At a certain height inside the capillary tube, the liquid stops rising. At this point, the liquid is under the influence of two forces that are equal in magnitude and opposite in direction, namely the surface tension forces, which push the liquid upwards, and the gravitational forces, which pull the liquid downwards. 5. We measure the height of the liquid inside the capillary tube, let it be h in cm or meters. Surface tension Calculation method: When the liquid stops rising inside the capillary tube, the liquid is under the influence of two forces that are equal in magnitude and opposite in direction, namely: the downward pull due to gravity (the force of the liquid column) and the upward pull (surface tension forces). The equation of surface tension to be measured is: γ= Surface tension γ : Surface tension coefficient and its unit (dynes/cm) or (N/m). r: Radius of capillary tube in cm or m if the surface tension is measured in (N/m). h: Height of liquid in capillary tube (column height in cm) or can be in m if the surface tension is measured in (N/m). d: Density of liquid in (g/cm3) which is the same as (g/ml) or can be in (Kg/m3) if the surface tension is measured in (N/m). g: Acceleration due to gravity which is equal to (981 cm/s2) or can be (g = 9.81 m/s2). θ: Contact angle (for wetting liquids (such as water) it is nearly zero and (cos 0 = 1)). Surface tension Units: Unit SI CGS Surface tension N/M Dyne/cm Height of liquid M Cm Density of liquid Kg/m3 gm/cm3 or gm/ml Gravity m/s2 9.8 cm/s2 981 Radius M cm Surface tension Ex.1 If the radius of a capillary tube (r = 0.0335 cm) and when immersed in a liquid with a density (d = 0.866 g/cm3), the liquid rises in the capillary tube to a height of (h = 2.0 cm), and if you know that the acceleration due to gravity is (g = 981 cm/s2), calculate the surface tension of that liquid. The liquid makes convexity angle of 45 degree. Solution: Surface tension Ex.2 Calculate the height of the water inside a capillary tube with a radius of (r = 0.002 m) at a temperature of (300 C), knowing that the density of water is (996 kg/m3) and the surface tension of water is (71.18 × 10-3 N/m) and the acceleration due to gravity is (9.81 m/s2) Solution Surface tension Drop weight method: This method is used to determine the surface tension of a liquid by knowing the surface tension of another known liquid, which is known as the reference liquid. The device used for this purpose is called a stalagmometer, which is a capillary tube with a bubble, and a pipette can be used in the same way. In this method, the surface tension values of two different liquids (γA, γB) can be compared (A, B), where each of them passes individually through the same capillary tube, with the determination of the masses of the two drops (WA, WB). Accordingly: = -------------- (1) ‫‪Surface tension‬‬ ‫‪Experiment steps:‬‬ ‫‪.1‬نحضر جھاز األستاالجمومیتر(األنبوبة ذات الفقاعة) ‪ ،‬نغسل األنبوبة ونجففھا تماما‬ ‫‪.2‬نحضر السائل (‪ )A‬المراد تعیین التوتر السطحي له (‪ )γA‬ونمال االنبوبة بھذا السائل بواسطة السحب حتى العالمة‬ ‫(‪)A‬‬ ‫‪.3‬یسمح للسائل بالسقوط ببطء جدا على هیئة نقط تجمع في زجاجة معلومة الوزن‬ ‫‪.4‬یحصى عدد النقاط الساقطة (بمعدل نقطة في كل ثانیتین) ویعین وزنھا ‪ ,‬ویؤخذ متوسط وزن نقطة من السائل (‪)A‬‬ ‫وهو (‪)wA‬‬ ‫‪.5‬تعاد الخطوات السابقة باستخدام السائل (‪ )A‬وهو سائل معلوم التوتر السطحي له (‪ )γB‬حیت یمكن تیین متوسط وزن‬ ‫نقطة من السائل (‪ )B‬وهو (‪)wB‬‬ ‫‪Surface tension‬‬ ‫‪Calculations method‬‬ ‫نفرض ان (‪ )nB, nA‬هما اعداد النقاط التي تم الحصول علیھا من حجمین السائلین )‪ (A,B‬وكثاقفتھما (‪ )dB,dA‬على‬ ‫الترتیب ‪.‬‬ ‫یتحدد متوسط وزن النقطة من السائل (‪ )A‬وكذلك من السائل (‪ )B‬من العالقتین‪:‬‬ ‫= ‪WA‬‬ ‫وحیث ان‬ ‫‪------- 2‬‬ ‫ ‬ ‫= ‪ WB‬‬ ‫‪By substituting the values of WA , WB :‬‬ ‫‪we get:‬‬ ‫)‪----------------------- (3‬‬ Surface tension Ex.3: Find surface tension for a liquid A using drop weight method whish has 55 drops and density 0.8 g/cm3 with water (B) which has 25 drops, density 0.996 g/cm3 and surface tension (γ) of 72 dynes /cm. Surface tension Factors acting on surface tension: 1. Temperature: when temperature increases, surface tension decreases. 2. Impurities: when impurities increases, surface tension decreases. 3. Surfactants: Surfactants are compounds that can lower the surface tension of a liquid by adsorbing at the liquid-solid interface and reducing the cohesive forces between molecules.