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1 SURFACE TENSION Definition Sufce tension is popety of liquid by which the fee sufce of liquid behves like stetched elstic membne, hving contctive tendency. The sufce tension is mesued by the foce cting pe unit length on eithe side of n imginy line dwn on the fee sufce of the liquid t est. The diection of the foce is t ight ngles to the line nd tngentil to the liquid sufce. Foce Sufce tension = Length F T = l Note: [ To denote sufce tension σ o T o γ (gmm) is used] S.I. unit Nm -1 C.G.S. unit dyne cm -1. Dimensionl fomul of sufce tension is MLT -2 L -1 = [MT -2 ] The sufce tension cts pependicul to the line AB nd tngentil to the liquid sufce. Illusttion of sufce Tension (i) Dip n odiny hi bush o shving bush into wte. When the bush is inside wte its hi will be seen septely. But when tken out, the his e seen to cling togethe, due to sufce tension. (ii) In the bsence of gvittionl foce dop will tke spheicl shpe. A mixtue of lcohol nd wte if density equl to olive oil ws tken in beke. A little oil ws poued into the beke, which sink into the mixtue nd emined s spheicl dop s shown. (iii) If some mecuy is poued on clen glss plte, smll dops e seen to be spheicl, whees lge ones e ellipitcl o cylindicl. This is due to sufce tension. (v) A metllic ing is dipped in sop solution. A closed loop of cotton thed is gently plced ove the film, s shown fig. () With hot needle, the sop film within the e-edge Eduction Clsses 1 of 7

2 loop is touched nd the film is boken. The thed expeiences foce dilly outwds nd pllel to the film. The loop ssumes cicul fom, s shown fig. (b) This is becuse, fo given peimete, cicle encloses the mximum e, nd hence the film suoundings the loop tends to ssume the lest e. (vi) Sufce tension of oil is less thn tht of wte so when it is spyed it speds nd foms thin film bove wte. This pevents mosquitos to beed on the sufce of oily wte. Cohesive nd Adhesive Foce Foce of ttction between molecules of the sme body is clled cohesive foce. The definite shpe nd igidity of solid body is due to cohesion. It is stongest in solids. Foce of ttction between diffeent kinds of molecules is clled dhesive foce. This popety is clled dhesion. A dop of wte sticks to due to dhesion. Molecul Rnge nd Sphee of Influence The mximum distnce upto which the cohesive foce between two molecules cn ct is clled thei molecul nge. A sphee dwn ound molecule s cente nd with dius equl to the molecul ge is clled the sphee of influence of the molecule. Sufce Tension bsed on Molecul Theoy Conside thee molecules A,B nd C of liquid. The sphee of influence of A is fully inside the liquid. So it is ttcted eqully in ll diection by othe molecules lying within sphee of influence. So esultnt cohesive on it is zeo. The sphee of influence of the molecule B lies ptly outside. This molecule expeiences less foce upwd nd moe downwd by the molecules in its sphee of influence. So thee is net downwd foce (R). Fo molecule C, hlf of the sphee of influence lies bove sufce, Thus the esultnt downwd foce T in this cse is mximum. Due to this net inwd foce on the molecules lying on the sufce, the sufce expeiences tension clled sufce tension. To bing molecule to the sufce of the liquid, wok hs to be done ginst the downwd foce. Hence, the molecules on the liquid sufce hve gete potentil enegy. Fo system to be stble, the potentil enegy must be minimum. A liquid will e-edge Eduction Clsses 2 of 7

3 hve minimum potentil enegy, if the numbe of molecules on the liquid sufce is the lest. This will hppen if the sufce e is minimum. Thus, liquid ties to hve minimum sufce e. Sufce Film If plne is dwn pllel to the fee sufce lye inside the liquid nd t distnce equl to the molecul nge fom it, the liquid lying in between the fee sufce nd this plne is clled the sufce film. Sufce Enegy The potentil enegy pe unit e of the sufce film is clled its sufce enegy. It is lso equl to the wok done to poduce fesh sufce of liquid film of unit e. Wok done 2 Sufce enegy = S. I unit is Jm e Sufce enegy is numeiclly equl to sufce tension (mens numbes e equl, but units e diffeent). Reltion between sufce tension nd sufce enegy Conside ectngul metl fme PQRS. The side PQ is movble. Dip the fme in sop solution. A sop film is fomed. Due to sufce tension PQ is pulled towds SR. To keep the wie in equilibium foce hs to be pplied in the opposite diection. The foce to be pplied on PQ = 2l x T. Hee 2 ppes becuse thee e two sufces. Suppose PQ is pulled though smll distnce x to the position P Q. Then wok done = foce x displcement = 2l x T x x Ae ceted = 2lx Sufce enegy = Wo k done 2l Tx = = T. e 2lx Sufce enegy is numeiclly equl to sufce tension. Angle of Contct The ngle between the tngent to the liquid sufce nd solid inside the liquid is clled the ngle of contct fo tht pi of solid nd liquid. Liquid which wet the glss, the ngle of contct is cute nd fo liquid which does not wet the glss it is obtuse. e-edge Eduction Clsses 3 of 7

4 Fo pue wte nd clen glss, the ngle of contct is 0 o. Fo odiny wte nd glss it is bout 8 o. Fo mecuy nd glss it is bout 140 o. The ngle of contct depends on (i) the ntue of the liquid (ii) the solid with which it is in contct (iii) the puity of solid nd liquid (iv) to cetin extent on the ntue of the vpou. Shpe of Liquid Meniscus in Tube The shpe of the liquids meniscus in glss tube depends upon dhesive foce F nd cohesive foce F c. Conside liquid molecule O ne the glss wll, s shown in fig. () This molecule is cted upon by net cohesive foce F c. Conside liquid molecule O ne the glss wll, s shown in fig. This molecule is cted upon by net cohesive foce F c cting inwds long OA within the liquid. This molecule is cted upon by net dhesive foce F cting pependicul to the glss sufce, diected long OB s shown. The cohesive foce epesented by OA mkes n ngle 45 o to the veticl wll of the tube. The two foce F nd F c e inclined to ech t n ngle of 135 o. The esultnt foce will depend on the eltive mgnitudes of the two foces F nd F c. The diection of the esultnt is given by α, whee α is the ngle between the esultnt foce nd F. o Fc sin135 tn α = o F + Fc cos135 Fc tn α = 2F Fc Now thee e thee cses (i) When 2 F > Fc, tn α is positive. So the ngle α is cute nd the esultnt OC is diected outside the liquid s shown in fig.(). The liquid is t est. So F must be pependicul to be liquid sufce. The foce F will become pependicul to the liquid sufce only if the sufce ssumes concve shpe upwd s shown in fig.() (ii) When 2 F < Fc, tn α is negtive. So the ngle α is obtuse. The esultnt OC lies inside the liquid. The foce F will become pependicul to the liquid sufce only if the sufce ssumes convex shpe upwd s shown in fig.(b) Conside mecy molecule t O, s shown in fig. In this cse the dhesive foce 2 F is less thn the cohesive foce F c. Hence the esultnt foce F lies within the mecuy column. To mke F pependicul to the liquid sufce, the ssumes (iii) When 2 F = Fc, tn α is infinity o α is 90 o. If 2 F = Fc, The esultnt foce cts veticlly downwds nd e-edge Eduction Clsses 4 of 7

5 pllel to the wll of the contine. The foce F will become pependicul to the liquid sufce. Hence liquid sufce will hoizontl. Pessue-diffeence coss Liquid Sufce Suppose the fee liquid sufce is concve, s shown in fig(). The sufce tension cts tngentil to the sufce. It cn be esolved into hoizontl nd veticl components dd togethe nd thee is esultnt foce noml to the sufce which is diected towds the cente of the cuvtue of the sufce fig () In the cse of convex sufce, s in fig(b), lso thee is esultnt foce due to sufce tension cting on molecule on the sufce of the liquid diected into the liquid towds the cente of cuvtue of the sufce. Thus, if the sufce of liquid is cuved, thee is pessue towds the cente of the sufce, due to tension. This pessue is gete on the concve side thn on the convex side. Due to this, the liquid sufce ties to contct. But liquid sufce is in equilibium. Hence, thee must be n excess pessue on the concve side of the liquid sufce so tht the sufce does not contct. This excess pessue depends on the sufce tension nd the dius of cuvtue of the meniscus. Excess Pessue Inside Dop Conside liquid dop of dius nd sufce tension T. Due to its spheicl shpe the inside pessue will be gete thn tht of the outside. Let the outside pessue be P o nd inside pessue be P i. Let the dius of the dop incese fom to +, whee is vey smll. Initil sufce e = 4π 2. Finl sufce = 4π( 2 + ) 2 = 4π( ) = 4π 2 + 8π. 2 is neglected s it is smll. Incese in sufce e = 4π 2 + 8π - 4π 2 = 8π Fom the definition of sufce tension, wok done to incese the sufce e by 8π is dw= 8π xt. This wok done is lso equl to excess foce times the distnce moved. Excess foce = excess pessue x e = (P i P o ) 4π 2 The distnce moved is. So wok done dw = (P i P o ) 4π 2 x (P i P o ) 4π 2 x = 8π T e-edge Eduction Clsses 5 of 7

6 8πT (P i P o ) = 2 4π = This is clled Lplce s Lw fo spheicl membnce. In the cse of bubble thee e two fee sufces in contct. Hence the totl incese in e is 2 x 8π x T Wok done, dw = 16π x T Wok done due to excess pessue = (P i P o ) 4π 2 x Fom bove two equtions. (P i P o ) 4π 2 = 16π x T 4T P i P o = 4 T The excess pessue inside spheicl bubble is. Cpillity A tube hving vey smll dimete is clled cpilly tube. If cpilly tube in liquid which wets the glss, the liquid ises up bove the level outside. This is clled cpilly ise. If the tube is dipped in liquid like mecuy which does not wet the glss the liquid is depessed below the level outside. This is clled cpilly depession. Fo 1. Keosene oil ise in lmp wick due to cpillity. 2. Blotting ppe soks ink by cpilly ction. Expession fo Cpilly Rise Conside cpilly tube of dius dipped veticlly in liquid of density ρ nd sufce tension T cts. The ngle of contct is θ which is cute ngle,so the liquid wets the glss tube. The sufce tension T cts long the tngent t the point of contct to the liquid meniscus whose dius is R. The pessue Pi t A is gete thn the pessue P o t B. So the liquid will ise in the tube nd ech height h, bove the hoizontl sufce outside the tube until the diffeence in pessue blnces the hydosttic pessue due to height h of the liquid column. At equilibium (P i P o ) = hρg () But (P i P o ) = R cosθ cos =, i. e., = 1 R R cosθ i. e.,( Pi Po ) = e-edge Eduction Clsses 6 of 7

7 cosθ = hρg hρ g T = 2 cos θ cosθ The cpilly ise h = ρg If the effect of liquid contined in the meniscus is tken into ccount then, Mss of liquid in meniscus is (π π π - )ρg = ρg 3 3 ( h + / 3) ρg So, T = This eltion is clled cpilly scent fomul 2cosθ Risk of Liquid in Tube of Insuffcient Length The height to which liquid ise in cpilly tube is cosθ h = ρg The dius of the cpilly tube nd the dius of the meniscus R e elted by = R cosθ cosθ h = = R cosθρg Rρg T,ρ nd g e constnt 1 hr = = cons tn t h. ρ g R Juin s Lw. The smlle the dius of the cpilly tube gete is the ise o fll of liquid in it. This mens if h is smll R should be lge so tht the poduct is constnt. If the length of the tube is less thn h, then the dius of cuvtue inceses to R, so tht hr = h R whee h is length of the tube less thn h. Now the meniscus will not hemispheicl. Thus in tube of insufficient length the liquid ises nd will sped out to new dius of cuvtue R = hr/h. The liquid will not oveflow. e-edge Eduction Clsses 7 of 7

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